Leptogenesis via the Relaxation of Higgs and other Scalar Fields

Transcript

1. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Leptogenesis via the Relaxation of Higgs and other Scalar Fields Louis Yang University of California, Los Angeles UC Riverside High Energy Physics Seminar November 18, 2016 Based on: A. Kusenko, L. Pearce, LY, Phys.Rev.Lett. 114 (2015) 6, 061302 L. Pearce, LY, A. Kusenko, M. Peloso, Phys.Rev. D92 (2015) 2, 023509 LY, L. Pearce, A. Kusenko, Phys.Rev. D92 (2015) 043506 H. Gertov, L. Pearce, F. Sannino, LY, Phys.Rev. D93 (2016) 115042 A. Kusenko, L. Pearce, LY, Phys.Rev. D93 (2016) 115005 Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 1) Louis Yang (UCLA)
2. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess The Higgs potential J. Elias-Miro et al., Phys. Lett. B709, 222 (2012) G. Degrassi et al., JHEP 1208, 098 (2012) D. Buttazzo et al., arXiv:1307.3536 [hep-ph] LHC has found the standard model Higgs boson V (Φ) = m2Φ†Φ+λ Φ†Φ 2 Φ = 1 √ 2 0 v + h Higgs boson mass: Mh = 125.09 ± 0.21 ± 0.11 GeV. A small λ (µ = Mt ) ≈ M2 h /2v2 ≈ 0.129 Due to the large top quark coupling, the λ (h) can be very small or negative at h 1010 GeV if no new physics comes in. Planckian vacuum appears but our universe is right on the meta-stable region. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 2) Louis Yang (UCLA)
3. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess The Higgs potential J. Elias-Miro et al., Phys. Lett. B709, 222 (2012) G. Degrassi et al., JHEP 1208, 098 (2012) D. Buttazzo et al., arXiv:1307.3536 [hep-ph] LHC has found the standard model Higgs boson V (Φ) = m2Φ†Φ+λ Φ†Φ 2 Φ = 1 √ 2 0 v + h Higgs boson mass: Mh = 125.09 ± 0.21 ± 0.11 GeV. A small λ (µ = Mt ) ≈ M2 h /2v2 ≈ 0.129 Due to the large top quark coupling, the λ (h) can be very small or negative at h 1010 GeV if no new physics comes in. Planckian vacuum appears but our universe is right on the meta-stable region. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 2) Louis Yang (UCLA)
4. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess The Higgs potential J. Elias-Miro et al., Phys. Lett. B709, 222 (2012) G. Degrassi et al., JHEP 1208, 098 (2012) D. Buttazzo et al., arXiv:1307.3536 [hep-ph] LHC has found the standard model Higgs boson V (Φ) = m2Φ†Φ+λ Φ†Φ 2 Φ = 1 √ 2 0 v + h Higgs boson mass: Mh = 125.09 ± 0.21 ± 0.11 GeV. A small λ (µ = Mt ) ≈ M2 h /2v2 ≈ 0.129 Due to the large top quark coupling, the λ (h) can be very small or negative at h 1010 GeV if no new physics comes in. Planckian vacuum appears but our universe is right on the meta-stable region. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 2) Louis Yang (UCLA)
5. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess The Higgs potential J. Elias-Miro et al., Phys. Lett. B709, 222 (2012) G. Degrassi et al., JHEP 1208, 098 (2012) D. Buttazzo et al., arXiv:1307.3536 [hep-ph] LHC has found the standard model Higgs boson V (Φ) = m2Φ†Φ+λ Φ†Φ 2 Φ = 1 √ 2 0 v + h Higgs boson mass: Mh = 125.09 ± 0.21 ± 0.11 GeV. A small λ (µ = Mt ) ≈ M2 h /2v2 ≈ 0.129 Due to the large top quark coupling, the λ (h) can be very small or negative at h 1010 GeV if no new physics comes in. Planckian vacuum appears but our universe is right on the meta-stable region. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 2) Louis Yang (UCLA)
6. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess The Higgs potential J. Elias-Miro et al., Phys. Lett. B709, 222 (2012) G. Degrassi et al., JHEP 1208, 098 (2012) D. Buttazzo et al., arXiv:1307.3536 [hep-ph] LHC has found the standard model Higgs boson V (Φ) = m2Φ†Φ+λ Φ†Φ 2 Φ = 1 √ 2 0 v + h Higgs boson mass: Mh = 125.09 ± 0.21 ± 0.11 GeV. A small λ (µ = Mt ) ≈ M2 h /2v2 ≈ 0.129 Due to the large top quark coupling, the λ (h) can be very small or negative at h 1010 GeV if no new physics comes in. Planckian vacuum appears but our universe is right on the meta-stable region. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 2) Louis Yang (UCLA)
7. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess The Higgs potential J. Elias-Miro et al., Phys. Lett. B709, 222 (2012) G. Degrassi et al., JHEP 1208, 098 (2012) D. Buttazzo et al., arXiv:1307.3536 [hep-ph] Higgs potential is very shallow at large scale. V(ϕ) ϕ Electroweak Vac. Planckian Vac. With such a shallow potential, Higgs field can develop a large vacuum expectation value (VEV) φ0 during inflation. This VEV in general relaxes after inflation. What can we do with this? Breaks T and is out of thermal equilibrium ⇒ Baryo- and Leptogenesis? Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 3) Louis Yang (UCLA)
8. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess The Higgs potential J. Elias-Miro et al., Phys. Lett. B709, 222 (2012) G. Degrassi et al., JHEP 1208, 098 (2012) D. Buttazzo et al., arXiv:1307.3536 [hep-ph] Higgs potential is very shallow at large scale. V(ϕ) ϕ Electroweak Vac. Planckian Vac. With such a shallow potential, Higgs field can develop a large vacuum expectation value (VEV) φ0 during inflation. This VEV in general relaxes after inflation. What can we do with this? Breaks T and is out of thermal equilibrium ⇒ Baryo- and Leptogenesis? Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 3) Louis Yang (UCLA)
9. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess The Higgs potential J. Elias-Miro et al., Phys. Lett. B709, 222 (2012) G. Degrassi et al., JHEP 1208, 098 (2012) D. Buttazzo et al., arXiv:1307.3536 [hep-ph] Higgs potential is very shallow at large scale. V(ϕ) ϕ Electroweak Vac. Planckian Vac. With such a shallow potential, Higgs field can develop a large vacuum expectation value (VEV) φ0 during inflation. This VEV in general relaxes after inflation. What can we do with this? Breaks T and is out of thermal equilibrium ⇒ Baryo- and Leptogenesis? Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 3) Louis Yang (UCLA)
10. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess The Higgs potential J. Elias-Miro et al., Phys. Lett. B709, 222 (2012) G. Degrassi et al., JHEP 1208, 098 (2012) D. Buttazzo et al., arXiv:1307.3536 [hep-ph] Higgs potential is very shallow at large scale. V(ϕ) ϕ Electroweak Vac. Planckian Vac. With such a shallow potential, Higgs field can develop a large vacuum expectation value (VEV) φ0 during inflation. This VEV in general relaxes after inflation. What can we do with this? Breaks T and is out of thermal equilibrium ⇒ Baryo- and Leptogenesis? Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 3) Louis Yang (UCLA)
11. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Outline 1 Scalar Field Relaxation 2 Leptogenesis via the Scalar Field Relaxation 3 Isocurvature perturbations 4 Excess in the Cosmic Infrared Background Fluctuation Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 4) Louis Yang (UCLA)
12. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Scalar Field Relaxation Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 5) Louis Yang (UCLA)
13. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Quantum Fluctuations during Inflation During inflation, a scalar field with a shallow potential can obtain a large VEV through quantum fluctuations. In a de Sitter space, scalar fields can do quantum jumps. The field might roll down classically ¨ φ + 3H ˙ φ = −V (φ) , which requires trlx ∼ d2V (φ) dφ2 −1/2 = 1 mφ If mφ HI, insufficient time to relax. ⇒ Develope a large VEV φ0 = φ2 V(ϕ) ϕ Quantum Jump ϕmin _ Bunch, Davies (1978); Linde (1982); Hawking, Moss (1982); Starobinsky (1982); Vilenkin, Ford (1982); Starobinsky, Yokoyama (1994). Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 6) Louis Yang (UCLA)
14. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Quantum Fluctuations during Inflation During inflation, a scalar field with a shallow potential can obtain a large VEV through quantum fluctuations. In a de Sitter space, scalar fields can do quantum jumps. The field might roll down classically ¨ φ + 3H ˙ φ = −V (φ) , which requires trlx ∼ d2V (φ) dφ2 −1/2 = 1 mφ If mφ HI, insufficient time to relax. ⇒ Develope a large VEV φ0 = φ2 V(ϕ) ϕ Quantum Jump ϕmin _ Bunch, Davies (1978); Linde (1982); Hawking, Moss (1982); Starobinsky (1982); Vilenkin, Ford (1982); Starobinsky, Yokoyama (1994). Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 6) Louis Yang (UCLA)
15. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Quantum Fluctuations during Inflation During inflation, a scalar field with a shallow potential can obtain a large VEV through quantum fluctuations. In a de Sitter space, scalar fields can do quantum jumps. The field might roll down classically ¨ φ + 3H ˙ φ = −V (φ) , which requires trlx ∼ d2V (φ) dφ2 −1/2 = 1 mφ If mφ HI, insufficient time to relax. ⇒ Develope a large VEV φ0 = φ2 V(ϕ) ϕ Quantum Jump ϕmin _ Bunch, Davies (1978); Linde (1982); Hawking, Moss (1982); Starobinsky (1982); Vilenkin, Ford (1982); Starobinsky, Yokoyama (1994). Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 6) Louis Yang (UCLA)
16. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Quantum Fluctuations during Inflation During inflation, a scalar field with a shallow potential can obtain a large VEV through quantum fluctuations. In a de Sitter space, scalar fields can do quantum jumps. The field might roll down classically ¨ φ + 3H ˙ φ = −V (φ) , which requires trlx ∼ d2V (φ) dφ2 −1/2 = 1 mφ If mφ HI, insufficient time to relax. ⇒ Develope a large VEV φ0 = φ2 V(ϕ) ϕ Quantum Jump ϕmin Roll Down Classically _ Bunch, Davies (1978); Linde (1982); Hawking, Moss (1982); Starobinsky (1982); Vilenkin, Ford (1982); Starobinsky, Yokoyama (1994). Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 6) Louis Yang (UCLA)
17. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Large Initial VEV of Scalar Fields A. A. Starobinsky (1982) A. Vilenkin (1982) The process is similar to Brownian motion and can be described by the Fokker-Planck equation. ∂Pc (φ, t) ∂t = − ∂jc ∂φ where − jc = ∂ ∂φ H3Pc 8π2 + Pc 3H dV dφ Pc (φ, t): probability distribution of φ For V (φ) ≈ 0, the field undergoes random walks φ0 = φ2 H3/2 I 2π √ t = HI 2π √ N, N: number of e-folds For V = 1 2 m2φ2, φ0 3 8π2 H2 I m For V = 1 4 λφ4, φ0 0.36 HI /λ1/4 Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 7) Louis Yang (UCLA)
18. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Large Initial VEV of Scalar Fields A. A. Starobinsky (1982) A. Vilenkin (1982) The process is similar to Brownian motion and can be described by the Fokker-Planck equation. ∂Pc (φ, t) ∂t = − ∂jc ∂φ where − jc = ∂ ∂φ H3Pc 8π2 + Pc 3H dV dφ Pc (φ, t): probability distribution of φ For V (φ) ≈ 0, the field undergoes random walks φ0 = φ2 H3/2 I 2π √ t = HI 2π √ N, N: number of e-folds For V = 1 2 m2φ2, φ0 3 8π2 H2 I m For V = 1 4 λφ4, φ0 0.36 HI /λ1/4 Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 7) Louis Yang (UCLA)
19. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Large Initial VEV of Scalar Fields A. A. Starobinsky (1982) A. Vilenkin (1982) The process is similar to Brownian motion and can be described by the Fokker-Planck equation. ∂Pc (φ, t) ∂t = − ∂jc ∂φ where − jc = ∂ ∂φ H3Pc 8π2 + Pc 3H dV dφ Pc (φ, t): probability distribution of φ For V (φ) ≈ 0, the field undergoes random walks φ0 = φ2 H3/2 I 2π √ t = HI 2π √ N, N: number of e-folds For V = 1 2 m2φ2, φ0 3 8π2 H2 I m For V = 1 4 λφ4, φ0 0.36 HI /λ1/4 Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 7) Louis Yang (UCLA)
20. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Large Initial VEV of Scalar Fields A. A. Starobinsky (1982) A. Vilenkin (1982) The process is similar to Brownian motion and can be described by the Fokker-Planck equation. ∂Pc (φ, t) ∂t = − ∂jc ∂φ where − jc = ∂ ∂φ H3Pc 8π2 + Pc 3H dV dφ Pc (φ, t): probability distribution of φ For V (φ) ≈ 0, the field undergoes random walks φ0 = φ2 H3/2 I 2π √ t = HI 2π √ N, N: number of e-folds For V = 1 2 m2φ2, φ0 3 8π2 H2 I m For V = 1 4 λφ4, φ0 0.36 HI /λ1/4 Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 7) Louis Yang (UCLA)
21. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Large Initial VEV for Scalar Fields In general, the average equilibrium VEV φ0 = φ2 is such that V (φ0 ) ∼ H4 I For inflation scale ΛI = 1016 GeV, HI = Λ2 I / √ 3Mpl ∼ 1013 GeV, with λ ∼ 0.01, the initial VEV is very large φ0 ∼ 1013 GeV. For such a large VEV, the scalar field can be sensitive to higher dimensional operators. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 8) Louis Yang (UCLA)
22. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Large Initial VEV for Scalar Fields In general, the average equilibrium VEV φ0 = φ2 is such that V (φ0 ) ∼ H4 I For inflation scale ΛI = 1016 GeV, HI = Λ2 I / √ 3Mpl ∼ 1013 GeV, with λ ∼ 0.01, the initial VEV is very large φ0 ∼ 1013 GeV. For such a large VEV, the scalar field can be sensitive to higher dimensional operators. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 8) Louis Yang (UCLA)
23. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Large Initial VEV for Scalar Fields In general, the average equilibrium VEV φ0 = φ2 is such that V (φ0 ) ∼ H4 I For inflation scale ΛI = 1016 GeV, HI = Λ2 I / √ 3Mpl ∼ 1013 GeV, with λ ∼ 0.01, the initial VEV is very large φ0 ∼ 1013 GeV. For such a large VEV, the scalar field can be sensitive to higher dimensional operators. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 8) Louis Yang (UCLA)
24. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Scalar Field Relaxation after Inflation As the inflation ends, H . When H < mφ , the scalar field can relax. ¨ φ + 3H ˙ φ = −V (φ, T(t)) φ rolls down and oscillates with decreasing amplitude due to the Hubble friction term H ˙ φ. V(ϕ) ϕ ϕmin Roll Down Classically Reheating 1 10 100 1000 104 Λ Φ0 t 0.2 0.4 0.6 0.8 1.0 Φ t Φ0 I 1016 GeV I 103 GeV Tmax 6.4 1012 GeV Λeff 0.003 Φ0 3.7 1013 GeV HI 2.4 1013 GeV End of Inflation at t 0 Φ T For λφ4 potential, the typical relaxation time is trlx ≈ 7/ √ λφ0 . This can happen during reheating or right after reheating. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 9) Louis Yang (UCLA)
25. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Scalar Field Relaxation after Inflation As the inflation ends, H . When H < mφ , the scalar field can relax. ¨ φ + 3H ˙ φ = −V (φ, T(t)) φ rolls down and oscillates with decreasing amplitude due to the Hubble friction term H ˙ φ. V(ϕ) ϕ ϕmin Roll Down Classically Reheating 1 10 100 1000 104 Λ Φ0 t 0.2 0.4 0.6 0.8 1.0 Φ t Φ0 I 1016 GeV I 103 GeV Tmax 6.4 1012 GeV Λeff 0.003 Φ0 3.7 1013 GeV HI 2.4 1013 GeV End of Inflation at t 0 Φ T For λφ4 potential, the typical relaxation time is trlx ≈ 7/ √ λφ0 . This can happen during reheating or right after reheating. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 9) Louis Yang (UCLA)
26. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Scalar Field Relaxation after Inflation As the inflation ends, H . When H < mφ , the scalar field can relax. ¨ φ + 3H ˙ φ = −V (φ, T(t)) φ rolls down and oscillates with decreasing amplitude due to the Hubble friction term H ˙ φ. V(ϕ) ϕ ϕmin Roll Down Classically Reheating 1 10 100 1000 104 Λ Φ0 t 0.2 0.4 0.6 0.8 1.0 Φ t Φ0 I 1016 GeV I 103 GeV Tmax 6.4 1012 GeV Λeff 0.003 Φ0 3.7 1013 GeV HI 2.4 1013 GeV End of Inflation at t 0 Φ T For λφ4 potential, the typical relaxation time is trlx ≈ 7/ √ λφ0 . This can happen during reheating or right after reheating. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 9) Louis Yang (UCLA)
27. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Scalar Field Relaxation after Inflation As the inflation ends, H . When H < mφ , the scalar field can relax. ¨ φ + 3H ˙ φ = −V (φ, T(t)) φ rolls down and oscillates with decreasing amplitude due to the Hubble friction term H ˙ φ. V(ϕ) ϕ ϕmin Roll Down Classically Reheating 1 10 100 1000 104 Λ Φ0 t 0.2 0.4 0.6 0.8 1.0 Φ t Φ0 I 1016 GeV I 103 GeV Tmax 6.4 1012 GeV Λeff 0.003 Φ0 3.7 1013 GeV HI 2.4 1013 GeV End of Inflation at t 0 Φ T For λφ4 potential, the typical relaxation time is trlx ≈ 7/ √ λφ0 . This can happen during reheating or right after reheating. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 9) Louis Yang (UCLA)
28. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Leptogenesis Sakharov’s conditions for Leptogenesis: 1 Deviation from thermal equilibrium ⇒ Relaxation of the Higgs field (or other scalar fields) 2 C and CP violations ⇒ CKM phase (not enough), SUSY, higher dimensional operators ... 3 Lepton number violation  L ⇒ Right-handed Majorana neutrinos NR , others ... Once the lepton asymmetry is generated, the Sphaleron process (violates B + L but conserves B − L) can turn −L into B. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 10) Louis Yang (UCLA)
29. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Leptogenesis Sakharov’s conditions for Leptogenesis: 1 Deviation from thermal equilibrium ⇒ Relaxation of the Higgs field (or other scalar fields) 2 C and CP violations ⇒ CKM phase (not enough), SUSY, higher dimensional operators ... 3 Lepton number violation  L ⇒ Right-handed Majorana neutrinos NR , others ... Once the lepton asymmetry is generated, the Sphaleron process (violates B + L but conserves B − L) can turn −L into B. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 10) Louis Yang (UCLA)
30. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Leptogenesis Sakharov’s conditions for Leptogenesis: 1 Deviation from thermal equilibrium ⇒ Relaxation of the Higgs field (or other scalar fields) 2 C and CP violations ⇒ CKM phase (not enough), SUSY, higher dimensional operators ... 3 Lepton number violation  L ⇒ Right-handed Majorana neutrinos NR , others ... Once the lepton asymmetry is generated, the Sphaleron process (violates B + L but conserves B − L) can turn −L into B. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 10) Louis Yang (UCLA)
31. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Leptogenesis Sakharov’s conditions for Leptogenesis: 1 Deviation from thermal equilibrium ⇒ Relaxation of the Higgs field (or other scalar fields) 2 C and CP violations ⇒ CKM phase (not enough), SUSY, higher dimensional operators ... 3 Lepton number violation  L ⇒ Right-handed Majorana neutrinos NR , others ... Once the lepton asymmetry is generated, the Sphaleron process (violates B + L but conserves B − L) can turn −L into B. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 10) Louis Yang (UCLA)
32. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Leptogenesis Sakharov’s conditions for Leptogenesis: 1 Deviation from thermal equilibrium ⇒ Relaxation of the Higgs field (or other scalar fields) 2 C and CP violations ⇒ CKM phase (not enough), SUSY, higher dimensional operators ... 3 Lepton number violation  L ⇒ Right-handed Majorana neutrinos NR , others ... Once the lepton asymmetry is generated, the Sphaleron process (violates B + L but conserves B − L) can turn −L into B. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 10) Louis Yang (UCLA)
33. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Leptogenesis Sakharov’s conditions for Leptogenesis: 1 Deviation from thermal equilibrium ⇒ Relaxation of the Higgs field (or other scalar fields) 2 C and CP violations ⇒ CKM phase (not enough), SUSY, higher dimensional operators ... 3 Lepton number violation  L ⇒ Right-handed Majorana neutrinos NR , others ... Once the lepton asymmetry is generated, the Sphaleron process (violates B + L but conserves B − L) can turn −L into B. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 10) Louis Yang (UCLA)
34. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Leptogenesis Sakharov’s conditions for Leptogenesis: 1 Deviation from thermal equilibrium ⇒ Relaxation of the Higgs field (or other scalar fields) 2 C and CP violations ⇒ CKM phase (not enough), SUSY, higher dimensional operators ... 3 Lepton number violation  L ⇒ Right-handed Majorana neutrinos NR , others ... Once the lepton asymmetry is generated, the Sphaleron process (violates B + L but conserves B − L) can turn −L into B. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 10) Louis Yang (UCLA)
35. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Leptogenesis Sakharov’s conditions for Leptogenesis: 1 Deviation from thermal equilibrium ⇒ Relaxation of the Higgs field (or other scalar fields) 2 C and CP violations ⇒ CKM phase (not enough), SUSY, higher dimensional operators ... 3 Lepton number violation  L ⇒ Right-handed Majorana neutrinos NR , others ... Once the lepton asymmetry is generated, the Sphaleron process (violates B + L but conserves B − L) can turn −L into B. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 10) Louis Yang (UCLA)
36. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess O6 and O5 operators Dine et. al. (1991) Cohen, Kaplan, Nelson (1991) During the relaxation, the scalar field can be sensitive to higher dimensional operators. Consider the derivative couplings like O6 = − 1 Λ2 n ∂µ |φ|2 jµ B+L or O5 = − 1 Λn (∂µ φ) jµ B+L jµ B+L : the B + L ferimion current Λn: new energy scale when the operator is relevant. Similar to those used in spontaneous baryogenesis scenarios. Break CPT spontaneously! So the second Sakharov’s condition doesn’t have to be satisfied explicitly. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 11) Louis Yang (UCLA)
37. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess O6 and O5 operators Dine et. al. (1991) Cohen, Kaplan, Nelson (1991) During the relaxation, the scalar field can be sensitive to higher dimensional operators. Consider the derivative couplings like O6 = − 1 Λ2 n ∂µ |φ|2 jµ B+L or O5 = − 1 Λn (∂µ φ) jµ B+L jµ B+L : the B + L ferimion current Λn: new energy scale when the operator is relevant. Similar to those used in spontaneous baryogenesis scenarios. Break CPT spontaneously! So the second Sakharov’s condition doesn’t have to be satisfied explicitly. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 11) Louis Yang (UCLA)
38. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess O6 and O5 operators Dine et. al. (1991) Cohen, Kaplan, Nelson (1991) During the relaxation, the scalar field can be sensitive to higher dimensional operators. Consider the derivative couplings like O6 = − 1 Λ2 n ∂µ |φ|2 jµ B+L or O5 = − 1 Λn (∂µ φ) jµ B+L jµ B+L : the B + L ferimion current Λn: new energy scale when the operator is relevant. Similar to those used in spontaneous baryogenesis scenarios. Break CPT spontaneously! So the second Sakharov’s condition doesn’t have to be satisfied explicitly. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 11) Louis Yang (UCLA)
39. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess O6 and O5 operators Dine et. al. (1991) Cohen, Kaplan, Nelson (1991) During the relaxation, the scalar field can be sensitive to higher dimensional operators. Consider the derivative couplings like O6 = − 1 Λ2 n ∂µ |φ|2 jµ B+L or O5 = − 1 Λn (∂µ φ) jµ B+L jµ B+L : the B + L ferimion current Λn: new energy scale when the operator is relevant. Similar to those used in spontaneous baryogenesis scenarios. Break CPT spontaneously! So the second Sakharov’s condition doesn’t have to be satisfied explicitly. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 11) Louis Yang (UCLA)
40. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess O6 and O5 operators Dine et. al. (1991) Cohen, Kaplan, Nelson (1991) During the relaxation, the scalar field can be sensitive to higher dimensional operators. Consider the derivative couplings like O6 = − 1 Λ2 n ∂µ |φ|2 jµ B+L or O5 = − 1 Λn (∂µ φ) jµ B+L jµ B+L : the B + L ferimion current Λn: new energy scale when the operator is relevant. Similar to those used in spontaneous baryogenesis scenarios. Break CPT spontaneously! So the second Sakharov’s condition doesn’t have to be satisfied explicitly. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 11) Louis Yang (UCLA)
41. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Effective Chemical Potential O6 = − 1 Λ2 n ∂µ |φ|2 jµ B+L or O5 = − 1 Λn (∂µ φ) jµ B+L Effective chemical potentials for baryon and lepton number µeff, 6 = 1 Λ2 n ∂t |φ|2 or µeff, 5 = 1 Λn ∂t φ While φ is rolling down, this shifts the energy levels between fermions and anti-fermions. , , V(ϕ) ϕ Scalar VEV Rolls Down Reheating Leads to Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 12) Louis Yang (UCLA)
42. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Effective Chemical Potential O6 = − 1 Λ2 n ∂µ |φ|2 jµ B+L or O5 = − 1 Λn (∂µ φ) jµ B+L Effective chemical potentials for baryon and lepton number µeff, 6 = 1 Λ2 n ∂t |φ|2 or µeff, 5 = 1 Λn ∂t φ While φ is rolling down, this shifts the energy levels between fermions and anti-fermions. , , V(ϕ) ϕ Scalar VEV Rolls Down Reheating Leads to Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 12) Louis Yang (UCLA)
43. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Effective Chemical Potential O6 = − 1 Λ2 n ∂µ |φ|2 jµ B+L or O5 = − 1 Λn (∂µ φ) jµ B+L Effective chemical potentials for baryon and lepton number µeff, 6 = 1 Λ2 n ∂t |φ|2 or µeff, 5 = 1 Λn ∂t φ While φ is rolling down, this shifts the energy levels between fermions and anti-fermions. , , V(ϕ) ϕ Scalar VEV Rolls Down Reheating Leads to Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 12) Louis Yang (UCLA)
44. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Derivative Couplings? M. E. Shaposhnikov (1987), M. E. Shaposhnikov (1988) Integration by part O6 = − 1 Λ2 n ∂µ |φ|2 jµ B+L → 1 Λ2 n |φ|2 ∂µ jµ B+L Through the electroweak anomaly equation: O6 ∝ 1 Λ2 n |φ|2 g2Wµν Wµν − 1 2 g 2Bµν Bµν , where W and B are SU(2)L and U(1)Y gauge field, and F are the dual tensors of F. For the case that φ = h is the Higgs field, this can be generated by 1 Heavy fermions in the loop: Λn = Mn 2 The thermal loop: Λn = T Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 13) Louis Yang (UCLA)
45. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Derivative Couplings? M. E. Shaposhnikov (1987), M. E. Shaposhnikov (1988) Integration by part O6 = − 1 Λ2 n ∂µ |φ|2 jµ B+L → 1 Λ2 n |φ|2 ∂µ jµ B+L Through the electroweak anomaly equation: O6 ∝ 1 Λ2 n |φ|2 g2Wµν Wµν − 1 2 g 2Bµν Bµν , where W and B are SU(2)L and U(1)Y gauge field, and F are the dual tensors of F. For the case that φ = h is the Higgs field, this can be generated by 1 Heavy fermions in the loop: Λn = Mn 2 The thermal loop: Λn = T Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 13) Louis Yang (UCLA)
46. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Derivative Couplings? M. E. Shaposhnikov (1987), M. E. Shaposhnikov (1988) Integration by part O6 = − 1 Λ2 n ∂µ |φ|2 jµ B+L → 1 Λ2 n |φ|2 ∂µ jµ B+L Through the electroweak anomaly equation: O6 ∝ 1 Λ2 n |φ|2 g2Wµν Wµν − 1 2 g 2Bµν Bµν , where W and B are SU(2)L and U(1)Y gauge field, and F are the dual tensors of F. For the case that φ = h is the Higgs field, this can be generated by 1 Heavy fermions in the loop: Λn = Mn 2 The thermal loop: Λn = T Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 13) Louis Yang (UCLA)
47. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Derivative Couplings? M. E. Shaposhnikov (1987), M. E. Shaposhnikov (1988) Integration by part O6 = − 1 Λ2 n ∂µ |φ|2 jµ B+L → 1 Λ2 n |φ|2 ∂µ jµ B+L Through the electroweak anomaly equation: O6 ∝ 1 Λ2 n |φ|2 g2Wµν Wµν − 1 2 g 2Bµν Bµν , where W and B are SU(2)L and U(1)Y gauge field, and F are the dual tensors of F. For the case that φ = h is the Higgs field, this can be generated by 1 Heavy fermions in the loop: Λn = Mn 2 The thermal loop: Λn = T Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 13) Louis Yang (UCLA)
48. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Derivative Couplings? M. E. Shaposhnikov (1987), M. E. Shaposhnikov (1988) Integration by part O6 = − 1 Λ2 n ∂µ |φ|2 jµ B+L → 1 Λ2 n |φ|2 ∂µ jµ B+L Through the electroweak anomaly equation: O6 ∝ 1 Λ2 n |φ|2 g2Wµν Wµν − 1 2 g 2Bµν Bµν , where W and B are SU(2)L and U(1)Y gauge field, and F are the dual tensors of F. For the case that φ = h is the Higgs field, this can be generated by 1 Heavy fermions in the loop: Λn = Mn 2 The thermal loop: Λn = T Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 13) Louis Yang (UCLA)
49. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess More Derivative Couplings O6 operators SM Higgs field h [A. Kusenko, L. Pearce, LY, PRL 114 (2015) 061302; PRD 92 (2015) 043506] Elementary Goldstone boson Higgs [H. Gertov, L. Pearce, F. Sannino, LY, Phys.Rev. D 93 (2016) 115042] O5 operators Axion a [A. Kusenko, K. Schmitz, T.T. Yanagida, arXiv:1412.2043] Leff ⊃ g2 2 32π2 a (t) fa F ˜ F = − a (t) Nf fa ∂µ ψγµψ Majoron χ [M. Ibe, and K. Kaneta, arXiv:1504.04125] Leff ⊃ − ∂µ χ √ 2MR jµ L Pseudoscalar S [A. Kusenko, L. Pearce, LY, Phys.Rev. D 93 (2016) 115005] L ⊃ ˜ λg αs 12πvEW SGa µν ˜ Gµν a + ˜ λγ α πvEW SFµν ˜ Fµν Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 14) Louis Yang (UCLA)
50. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Lepton-Number-Violating Processes While the energy levels for leptons and anti-leptons are different, we still need lepton-number-violating  L processes to produce net lepton asymmetry! Last ingredient: Right-handed neutrino NR with Majorana mass term MR. The processes for ∆L = 2 are νL h0 ↔ νL h0 νL νL ↔ h0h0 & νL νL ↔ h0h0 For mν ∼ 0.1 eV, σR ∼ i m2 ν,i 16πv4 EW ∼ 10−31 GeV−2. νL NR Nc R νc ℓ h0 h0 νL NR Nc R νc ℓ h0 h0 νL νℓ h0 h0 NR NR νc L νc ℓ h0 h0 Nc R Nc R Different from standard thermal leptogenesis: NR don’t have to be in the thermal plasma. Works for T MR Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 15) Louis Yang (UCLA)
51. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Lepton-Number-Violating Processes While the energy levels for leptons and anti-leptons are different, we still need lepton-number-violating  L processes to produce net lepton asymmetry! Last ingredient: Right-handed neutrino NR with Majorana mass term MR. The processes for ∆L = 2 are νL h0 ↔ νL h0 νL νL ↔ h0h0 & νL νL ↔ h0h0 For mν ∼ 0.1 eV, σR ∼ i m2 ν,i 16πv4 EW ∼ 10−31 GeV−2. νL NR Nc R νc ℓ h0 h0 νL NR Nc R νc ℓ h0 h0 νL νℓ h0 h0 NR NR νc L νc ℓ h0 h0 Nc R Nc R Different from standard thermal leptogenesis: NR don’t have to be in the thermal plasma. Works for T MR Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 15) Louis Yang (UCLA)
52. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Lepton-Number-Violating Processes While the energy levels for leptons and anti-leptons are different, we still need lepton-number-violating  L processes to produce net lepton asymmetry! Last ingredient: Right-handed neutrino NR with Majorana mass term MR. The processes for ∆L = 2 are νL h0 ↔ νL h0 νL νL ↔ h0h0 & νL νL ↔ h0h0 For mν ∼ 0.1 eV, σR ∼ i m2 ν,i 16πv4 EW ∼ 10−31 GeV−2. νL NR Nc R νc ℓ h0 h0 νL NR Nc R νc ℓ h0 h0 νL νℓ h0 h0 NR NR νc L νc ℓ h0 h0 Nc R Nc R Different from standard thermal leptogenesis: NR don’t have to be in the thermal plasma. Works for T MR Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 15) Louis Yang (UCLA)
53. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Lepton-Number-Violating Processes While the energy levels for leptons and anti-leptons are different, we still need lepton-number-violating  L processes to produce net lepton asymmetry! Last ingredient: Right-handed neutrino NR with Majorana mass term MR. The processes for ∆L = 2 are νL h0 ↔ νL h0 νL νL ↔ h0h0 & νL νL ↔ h0h0 For mν ∼ 0.1 eV, σR ∼ i m2 ν,i 16πv4 EW ∼ 10−31 GeV−2. νL NR Nc R νc ℓ h0 h0 νL NR Nc R νc ℓ h0 h0 νL νℓ h0 h0 NR NR νc L νc ℓ h0 h0 Nc R Nc R Different from standard thermal leptogenesis: NR don’t have to be in the thermal plasma. Works for T MR Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 15) Louis Yang (UCLA)
54. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Brief summary Basic Ingredients for the leptogenesis via scalar field relaxation: 1 Large initial VEV of a scalar field φ0 = φ2 during inflation 2 Relaxation of the scalar field after inflation 1 10 100 1000 104 Λ Φ0 t 0.2 0.4 0.6 0.8 1.0 Φ t Φ0 I 1016 GeV I 103 GeV Tmax 6.4 1012 GeV Λeff 0.003 Φ0 3.7 1013 GeV HI 2.4 1013 GeV End of Inflation at t 0 Φ T 3 Effective coupling between fermion currents and derivative of φ O6 = − 1 Λ2 n ∂µ |φ|2 jµ B+L or O5 = − 1 Λn (∂µ φ) jµ B+L 4 Lepton-number-violating processes: RH neutrino NR νL NR Nc R νc ℓ h0 h0 νL NR Nc R νc ℓ h0 h0 νL νℓ h0 h0 NR NR νc L νc ℓ h0 h0 Nc R Nc R Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 16) Louis Yang (UCLA)
55. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Brief summary Basic Ingredients for the leptogenesis via scalar field relaxation: 1 Large initial VEV of a scalar field φ0 = φ2 during inflation 2 Relaxation of the scalar field after inflation 1 10 100 1000 104 Λ Φ0 t 0.2 0.4 0.6 0.8 1.0 Φ t Φ0 I 1016 GeV I 103 GeV Tmax 6.4 1012 GeV Λeff 0.003 Φ0 3.7 1013 GeV HI 2.4 1013 GeV End of Inflation at t 0 Φ T 3 Effective coupling between fermion currents and derivative of φ O6 = − 1 Λ2 n ∂µ |φ|2 jµ B+L or O5 = − 1 Λn (∂µ φ) jµ B+L 4 Lepton-number-violating processes: RH neutrino NR νL NR Nc R νc ℓ h0 h0 νL NR Nc R νc ℓ h0 h0 νL νℓ h0 h0 NR NR νc L νc ℓ h0 h0 Nc R Nc R Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 16) Louis Yang (UCLA)
56. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Brief summary Basic Ingredients for the leptogenesis via scalar field relaxation: 1 Large initial VEV of a scalar field φ0 = φ2 during inflation 2 Relaxation of the scalar field after inflation 1 10 100 1000 104 Λ Φ0 t 0.2 0.4 0.6 0.8 1.0 Φ t Φ0 I 1016 GeV I 103 GeV Tmax 6.4 1012 GeV Λeff 0.003 Φ0 3.7 1013 GeV HI 2.4 1013 GeV End of Inflation at t 0 Φ T 3 Effective coupling between fermion currents and derivative of φ O6 = − 1 Λ2 n ∂µ |φ|2 jµ B+L or O5 = − 1 Λn (∂µ φ) jµ B+L 4 Lepton-number-violating processes: RH neutrino NR νL NR Nc R νc ℓ h0 h0 νL NR Nc R νc ℓ h0 h0 νL νℓ h0 h0 NR NR νc L νc ℓ h0 h0 Nc R Nc R Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 16) Louis Yang (UCLA)
57. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Brief summary Basic Ingredients for the leptogenesis via scalar field relaxation: 1 Large initial VEV of a scalar field φ0 = φ2 during inflation 2 Relaxation of the scalar field after inflation 1 10 100 1000 104 Λ Φ0 t 0.2 0.4 0.6 0.8 1.0 Φ t Φ0 I 1016 GeV I 103 GeV Tmax 6.4 1012 GeV Λeff 0.003 Φ0 3.7 1013 GeV HI 2.4 1013 GeV End of Inflation at t 0 Φ T 3 Effective coupling between fermion currents and derivative of φ O6 = − 1 Λ2 n ∂µ |φ|2 jµ B+L or O5 = − 1 Λn (∂µ φ) jµ B+L 4 Lepton-number-violating processes: RH neutrino NR νL NR Nc R νc ℓ h0 h0 νL NR Nc R νc ℓ h0 h0 νL νℓ h0 h0 NR NR νc L νc ℓ h0 h0 Nc R Nc R Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 16) Louis Yang (UCLA)
58. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess The Boltzmann transport equation The equilibrium lepton number density: nL,eq = 2 π2 µeff φ, ˙ φ T2. However, the interactions are not fast enough for the system to reach the equilibrium because T < MR. The system still make some L asymmetry. Describes by the Boltzmann transport equation d dt nL + 3HnL ≈ − 2 π2 T3σR nL − 2 π2 µeff T2 Washout: To suppressed the washout, turn off the  L interaction T3σR before the scalar field stop oscillating! Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 17) Louis Yang (UCLA)
59. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess The Boltzmann transport equation The equilibrium lepton number density: nL,eq = 2 π2 µeff φ, ˙ φ T2. However, the interactions are not fast enough for the system to reach the equilibrium because T < MR. The system still make some L asymmetry. Describes by the Boltzmann transport equation d dt nL + 3HnL ≈ − 2 π2 T3σR nL − 2 π2 µeff T2 Washout: To suppressed the washout, turn off the  L interaction T3σR before the scalar field stop oscillating! Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 17) Louis Yang (UCLA)
60. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess The Boltzmann transport equation The equilibrium lepton number density: nL,eq = 2 π2 µeff φ, ˙ φ T2. However, the interactions are not fast enough for the system to reach the equilibrium because T < MR. The system still make some L asymmetry. Describes by the Boltzmann transport equation d dt nL + 3HnL ≈ − 2 π2 T3σR nL − 2 π2 µeff T2 Washout: To suppressed the washout, turn off the  L interaction T3σR before the scalar field stop oscillating! Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 17) Louis Yang (UCLA)
61. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess The Boltzmann transport equation The equilibrium lepton number density: nL,eq = 2 π2 µeff φ, ˙ φ T2. However, the interactions are not fast enough for the system to reach the equilibrium because T < MR. The system still make some L asymmetry. Describes by the Boltzmann transport equation d dt nL + 3HnL ≈ − 2 π2 T3σR nL − 2 π2 µeff T2 Washout: To suppressed the washout, turn off the  L interaction T3σR before the scalar field stop oscillating! Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 17) Louis Yang (UCLA)
62. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess The Boltzmann transport equation The equilibrium lepton number density: nL,eq = 2 π2 µeff φ, ˙ φ T2. However, the interactions are not fast enough for the system to reach the equilibrium because T < MR. The system still make some L asymmetry. Describes by the Boltzmann transport equation d dt nL + 3HnL ≈ − 2 π2 T3σR nL − 2 π2 µeff T2 Washout: To suppressed the washout, turn off the  L interaction T3σR before the scalar field stop oscillating! Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 17) Louis Yang (UCLA)
63. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess The evolution of the lepton asymmetry LY, Pearce, Kusenko Phys.Rev. D92 (2015) -16 -14 -12 -10 -8 -6 -14 -12 -10 -8 -6 -4 log(t [GeV-1 ]) log(Y = n / s) End of inflation T = Tmax First ϕ crossing 0 Radiation Domination μeff ∝ Mn -2 μeff ∝ T-2 φ = h is the Higgs field. ΛI = 1.5 × 1016 GeV, ΓI = 108 GeV, TRH = 5 × 1012 GeV, and φ0 = 6 × 1013 GeV. For µeff ∝ M−2 n case, choose Mn = 5 × 1012 GeV. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 18) Louis Yang (UCLA)
64. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Resulting asymmetry Analytical formula for the approximate final lepton asymmetry Y ≡ nL /s (lepton to entropy density ratio) Y ≈ 90σR π6g∗S φ0 Λn n T2 rlx    T 3 rlx t2 rlx T 3 RH t2 RH exp −8+ √ 15 π2 σRT 3 RH ΓI for trlx < tRH exp − √ 15 π2 σRT 2 RH Trlx ΓI for trlx > tRH where n = 2 for µeff ∝ ∂t |φ|2 /Λ2 n , and n = 1 for µeff ∝ ∂t φ/Λn. Accurate to within an order of magnitude. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 19) Louis Yang (UCLA)
65. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Isocurvature perturbations Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 20) Louis Yang (UCLA)
66. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Fluctuations in the initial VEV φ0 φ0 = φ2 is the average over several Hubble volumes. Due to quantum fluctuations, different patches of the universe start with different initial φ0. Since the final asymmetry depends on YB ∝ φn 0 with n ∼ 1, 2 Different baryon asymmetry YB in each Hubble volume. Leads to large primordial baryonic isocurvature perturbation, which is constrained by CMB observations. ⇒ Need to suppress somehow... [Figure from Lauren Pearce] Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 21) Louis Yang (UCLA)
67. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Fluctuations in the initial VEV φ0 φ0 = φ2 is the average over several Hubble volumes. Due to quantum fluctuations, different patches of the universe start with different initial φ0. Since the final asymmetry depends on YB ∝ φn 0 with n ∼ 1, 2 Different baryon asymmetry YB in each Hubble volume. Leads to large primordial baryonic isocurvature perturbation, which is constrained by CMB observations. ⇒ Need to suppress somehow... [Figure from Lauren Pearce] Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 21) Louis Yang (UCLA)
68. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Fluctuations in the initial VEV φ0 φ0 = φ2 is the average over several Hubble volumes. Due to quantum fluctuations, different patches of the universe start with different initial φ0. Since the final asymmetry depends on YB ∝ φn 0 with n ∼ 1, 2 Different baryon asymmetry YB in each Hubble volume. Leads to large primordial baryonic isocurvature perturbation, which is constrained by CMB observations. ⇒ Need to suppress somehow... φ′ 0 φ0 φ′′ 0 [Figure from Lauren Pearce] Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 21) Louis Yang (UCLA)
69. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Fluctuations in the initial VEV φ0 φ0 = φ2 is the average over several Hubble volumes. Due to quantum fluctuations, different patches of the universe start with different initial φ0. Since the final asymmetry depends on YB ∝ φn 0 with n ∼ 1, 2 Different baryon asymmetry YB in each Hubble volume. Leads to large primordial baryonic isocurvature perturbation, which is constrained by CMB observations. ⇒ Need to suppress somehow... [Figure from Lauren Pearce] Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 21) Louis Yang (UCLA)
70. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Fluctuations in the initial VEV φ0 φ0 = φ2 is the average over several Hubble volumes. Due to quantum fluctuations, different patches of the universe start with different initial φ0. Since the final asymmetry depends on YB ∝ φn 0 with n ∼ 1, 2 Different baryon asymmetry YB in each Hubble volume. Leads to large primordial baryonic isocurvature perturbation, which is constrained by CMB observations. ⇒ Need to suppress somehow... [Figure from Lauren Pearce] Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 21) Louis Yang (UCLA)
71. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Fluctuations in the initial VEV φ0 φ0 = φ2 is the average over several Hubble volumes. Due to quantum fluctuations, different patches of the universe start with different initial φ0. Since the final asymmetry depends on YB ∝ φn 0 with n ∼ 1, 2 Different baryon asymmetry YB in each Hubble volume. Leads to large primordial baryonic isocurvature perturbation, which is constrained by CMB observations. ⇒ Need to suppress somehow... [Figure from Lauren Pearce] Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 21) Louis Yang (UCLA)
72. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Fluctuations in the initial VEV φ0 φ0 = φ2 is the average over several Hubble volumes. Due to quantum fluctuations, different patches of the universe start with different initial φ0. Since the final asymmetry depends on YB ∝ φn 0 with n ∼ 1, 2 Different baryon asymmetry YB in each Hubble volume. Leads to large primordial baryonic isocurvature perturbation, which is constrained by CMB observations. ⇒ Need to suppress somehow... [Figure from Lauren Pearce] Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 21) Louis Yang (UCLA)
73. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Solutions to the isocurvature perturbation issue Possible solutions by modifying the initial conditions (IC): 1 IC-1: Metastable vacuum (second min- imum) at large VEVs E.g. Llift = φ10 Λ6 lift + ... To stablize the electroweak vacuum in the standard model Higgs potential. V(ϕ) ϕ Second Min. 2 IC-2: Inflaton couplings induced mass term E.g. LφI = c Im Mn+m−4 pl φn Isocurvature perturbation only in small spatial scales. Unobservable by CMB. Not limited to the Higgs field. V(ϕ) ϕ Very Steep Potential due to Inflaton Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 22) Louis Yang (UCLA)
74. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Solutions to the isocurvature perturbation issue Possible solutions by modifying the initial conditions (IC): 1 IC-1: Metastable vacuum (second min- imum) at large VEVs E.g. Llift = φ10 Λ6 lift + ... To stablize the electroweak vacuum in the standard model Higgs potential. V(ϕ) ϕ Second Min. 2 IC-2: Inflaton couplings induced mass term E.g. LφI = c Im Mn+m−4 pl φn Isocurvature perturbation only in small spatial scales. Unobservable by CMB. Not limited to the Higgs field. V(ϕ) ϕ Very Steep Potential due to Inflaton Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 22) Louis Yang (UCLA)
75. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Solutions to the isocurvature perturbation issue Possible solutions by modifying the initial conditions (IC): 1 IC-1: Metastable vacuum (second min- imum) at large VEVs E.g. Llift = φ10 Λ6 lift + ... To stablize the electroweak vacuum in the standard model Higgs potential. V(ϕ) ϕ Second Min. 2 IC-2: Inflaton couplings induced mass term E.g. LφI = c Im Mn+m−4 pl φn Isocurvature perturbation only in small spatial scales. Unobservable by CMB. Not limited to the Higgs field. V(ϕ) ϕ Very Steep Potential due to Inflaton Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 22) Louis Yang (UCLA)
76. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Solutions to the isocurvature perturbation issue Possible solutions by modifying the initial conditions (IC): 1 IC-1: Metastable vacuum (second min- imum) at large VEVs E.g. Llift = φ10 Λ6 lift + ... To stablize the electroweak vacuum in the standard model Higgs potential. V(ϕ) ϕ Second Min. 2 IC-2: Inflaton couplings induced mass term E.g. LφI = c Im Mn+m−4 pl φn Isocurvature perturbation only in small spatial scales. Unobservable by CMB. Not limited to the Higgs field. V(ϕ) ϕ Very Steep Potential due to Inflaton Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 22) Louis Yang (UCLA)
77. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Solutions to the isocurvature perturbation issue Possible solutions by modifying the initial conditions (IC): 1 IC-1: Metastable vacuum (second min- imum) at large VEVs E.g. Llift = φ10 Λ6 lift + ... To stablize the electroweak vacuum in the standard model Higgs potential. V(ϕ) ϕ Second Min. 2 IC-2: Inflaton couplings induced mass term E.g. LφI = c Im Mn+m−4 pl φn Isocurvature perturbation only in small spatial scales. Unobservable by CMB. Not limited to the Higgs field. V(ϕ) ϕ Very Steep Potential due to Inflaton Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 22) Louis Yang (UCLA)
78. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess IC-1: Metastable vacuum at large VEVs V(ϕ) ϕ Second Min. The scenario: 1 Large VEV at early stage of inflation due to the shallow potential 2 The Higgs VEV is trapped at the metastable vacuum at the end of inflation (but does’t dominate the energy density of the universe.) 3 Reheating destablizes the metastable vacuum. ∆V ∼ T2φ2 4 Higgs field rolls down from the second minimum. V(ϕ) ϕ Second Min. 4 Early stage of inflation Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 23) Louis Yang (UCLA)
79. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess IC-1: Metastable vacuum at large VEVs V(ϕ) ϕ Second Min. The scenario: 1 Large VEV at early stage of inflation due to the shallow potential 2 The Higgs VEV is trapped at the metastable vacuum at the end of inflation (but does’t dominate the energy density of the universe.) 3 Reheating destablizes the metastable vacuum. ∆V ∼ T2φ2 4 Higgs field rolls down from the second minimum. V(ϕ) ϕ Second Min. Trapped 4 Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 23) Louis Yang (UCLA)
80. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess IC-1: Metastable vacuum at large VEVs V(ϕ) ϕ Second Min. The scenario: 1 Large VEV at early stage of inflation due to the shallow potential 2 The Higgs VEV is trapped at the metastable vacuum at the end of inflation (but does’t dominate the energy density of the universe.) 3 Reheating destablizes the metastable vacuum. ∆V ∼ T2φ2 4 Higgs field rolls down from the second minimum. V(ϕ) ϕ Thermal correction Reheating Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 23) Louis Yang (UCLA)
81. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess IC-1: Metastable vacuum at large VEVs V(ϕ) ϕ Second Min. The scenario: 1 Large VEV at early stage of inflation due to the shallow potential 2 The Higgs VEV is trapped at the metastable vacuum at the end of inflation (but does’t dominate the energy density of the universe.) 3 Reheating destablizes the metastable vacuum. ∆V ∼ T2φ2 4 Higgs field rolls down from the second minimum. V(ϕ) ϕ Higgs VEV Rolls Down Reheating Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 23) Louis Yang (UCLA)
82. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess IC-2: Inflaton induced mass term V(ϕ) ϕ Very Steep Potential due to Inflaton LφI = c Im Mn+m−4 pl φn where I: inflaton, φ: the scalar field 1 At the beginning of the inflation, I is large. mφ ( I ) HI . φ ∼ 0. 2 At the last Nlast e-folds of inflation, I , meff,φ ( I ) < HI , the scalar VEV starts to develop. 3 By the end of inflation, the scalar field has obtained a VEV φ0 HI 2π Nlast . 4 The Higgs VEV then rolls down from φ0 . The isocurvature perturbation only on the small scales. ϕ Quantum jumps 2 ~0 Early stage of inflation 4 Rolls down classically V(ϕ) Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 24) Louis Yang (UCLA)
83. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess IC-2: Inflaton induced mass term V(ϕ) ϕ Very Steep Potential due to Inflaton LφI = c Im Mn+m−4 pl φn where I: inflaton, φ: the scalar field 1 At the beginning of the inflation, I is large. mφ ( I ) HI . φ ∼ 0. 2 At the last Nlast e-folds of inflation, I , meff,φ ( I ) < HI , the scalar VEV starts to develop. 3 By the end of inflation, the scalar field has obtained a VEV φ0 HI 2π Nlast . 4 The Higgs VEV then rolls down from φ0 . The isocurvature perturbation only on the small scales. ϕ Last N e-folds of inflation V(ϕ) 2 starts to grow 4 Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 24) Louis Yang (UCLA)
84. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess IC-2: Inflaton induced mass term V(ϕ) ϕ Very Steep Potential due to Inflaton LφI = c Im Mn+m−4 pl φn where I: inflaton, φ: the scalar field 1 At the beginning of the inflation, I is large. mφ ( I ) HI . φ ∼ 0. 2 At the last Nlast e-folds of inflation, I , meff,φ ( I ) < HI , the scalar VEV starts to develop. 3 By the end of inflation, the scalar field has obtained a VEV φ0 HI 2π Nlast . 4 The Higgs VEV then rolls down from φ0 . The isocurvature perturbation only on the small scales. ϕ 2 = 2/42 End of inflation V(ϕ) Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 24) Louis Yang (UCLA)
85. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess IC-2: Inflaton induced mass term V(ϕ) ϕ Very Steep Potential due to Inflaton LφI = c Im Mn+m−4 pl φn where I: inflaton, φ: the scalar field 1 At the beginning of the inflation, I is large. mφ ( I ) HI . φ ∼ 0. 2 At the last Nlast e-folds of inflation, I , meff,φ ( I ) < HI , the scalar VEV starts to develop. 3 By the end of inflation, the scalar field has obtained a VEV φ0 HI 2π Nlast . 4 The Higgs VEV then rolls down from φ0 . The isocurvature perturbation only on the small scales. ϕ After inflation V(ϕ) Rolls down classically Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 24) Louis Yang (UCLA)
86. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Evolution of the Higgs field with IC-1 & 2 IC-1: Metastable vacuum < IC1 > ΛI = 1015 GeV ΓI = 109 GeV ϕ0 = 1015 GeV T(t) 0 1000 2000 3000 4000 -0.5 0.0 0.5 1.0 ϕ0 t ϕ/ϕ0 φ0 = 1015 GeV, Λlift = 6.5 × 1015 GeV, Tmax = 6.4 × 1013 GeV. Dashed line: maximum reheating. IC-2: Large inflaton induced mass < IC2 > ΛI = 1017 GeV ΓI = 108 GeV Nlast = 8 ϕ0 = 1015 GeV 0 200 400 600 800 1000 1200 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 ϕ0 t ϕ/ϕ0 φ0 = 1015 GeV, Nlast = 8. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 25) Louis Yang (UCLA)
87. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Plots of Asymmetry Evolution V(ϕ) ϕ Second Min. 16 14 12 10 8 6 14 12 10 8 6 4 2 log t GeV 1 log Η Blue: IC-1 Metastable vacuum ΛI = 1015 GeV, ΓI = 109 GeV, and Tmax = 6 × 1013 GeV. With Λn = T in µeff . Vertical lines: 1) First Higgs VEV crossing, 2) T = Tmax , 3) Start of radation domination. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 26) Louis Yang (UCLA)
88. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Plots of Asymmetry Evolution V(ϕ) ϕ Very Steep Potential due to Inflaton 16 14 12 10 8 6 14 12 10 8 6 4 2 log t GeV 1 log Η Red: IC-2 Inflaton induced mass term ΛI = 1017 GeV, ΓI = 108 GeV, and Tmax = 3 × 1014 GeV. With Λn = 5 × 1012 GeV in µeff . Vertical lines: 1) T = Tmax , 2) First Higgs VEV crossing, 3) Start of radation domination. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 27) Louis Yang (UCLA)
89. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Parameter space plots LY, Pearce, Kusenko Phys.Rev. D92 (2015) IC-1: Metastable vacuum 6 7 8 9 10 11 14.0 14.5 15.0 15.5 16.0 16.5 log I GeV log I GeV MR Φ0 y2 4Π 1 No Inflation No Higgs Relaxation Quantum Fluctuations Destabilize the 2nd Vacuum V HI 4 7 8 9 10 11 12 φ0 = 1015 GeV, Λlift = 6.5 × 1015 GeV with Λn = T. IC-2: Large inflaton induced mass 20 20 18 18 16 14 12 10 8 6 4 2 5 6 7 8 9 10 8 10 12 14 16 log I GeV log Mn GeV y2 4Π 1 φ0 = 1015 GeV, Nlast = 8, with Λn = Mn . Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 28) Louis Yang (UCLA)
90. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Parameter Space Plots LY, Pearce, Kusenko Phys.Rev. D92 (2015) IC-1: Metastable vacuum 6 7 8 9 10 11 14.0 14.5 15.0 15.5 16.0 16.5 log I GeV log I GeV MR Φ0 y2 4Π 1 No Inflation No Higgs Relaxation Quantum Fluctuations Destabilize the 2nd Vacuum V HI 4 7 8 9 10 11 12 φ0 = 1015 GeV, Λlift = 6.5 × 1015 GeV with Λn = T. In general, IC-1 produces more lep- ton asymmetry. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 29) Louis Yang (UCLA)
91. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Parameter Space Plots LY, Pearce, Kusenko Phys.Rev. D92 (2015) But IC2 leaves an interesting ob- servable consequence in the matter power spectrum. IC-2: Large inflaton induced mass 20 20 18 18 16 14 12 10 8 6 4 2 5 6 7 8 9 10 8 10 12 14 16 log I GeV log Mn GeV y2 4Π 1 φ0 = 1015 GeV, Nlast = 8, with Λn = Mn . Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 30) Louis Yang (UCLA)
92. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Isocurvature Perturbations in More Detail During inflation, quantum fluctuation makes perturbation for all modes inside the horizon p = k/a > HI. For massless fields experienced N e-folds of inflation, δφ0 φ0 k HI 2π 2π HI √ N = 1 √ N For N ∼ 50, this produces large perturbations in YB and ρB δρB ρB = δYB YB ≈ n δφ0 φ0 ≈ n √ N ∼ 0.1 − 0.3 with n ∼ 1 − 2 Since φ is not inflaton I, the perturbation is independent from the curvature perturbation. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 31) Louis Yang (UCLA)
93. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Isocurvature Perturbations in More Detail During inflation, quantum fluctuation makes perturbation for all modes inside the horizon p = k/a > HI. For massless fields experienced N e-folds of inflation, δφ0 φ0 k HI 2π 2π HI √ N = 1 √ N For N ∼ 50, this produces large perturbations in YB and ρB δρB ρB = δYB YB ≈ n δφ0 φ0 ≈ n √ N ∼ 0.1 − 0.3 with n ∼ 1 − 2 Since φ is not inflaton I, the perturbation is independent from the curvature perturbation. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 31) Louis Yang (UCLA)
94. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Isocurvature Perturbations in More Detail During inflation, quantum fluctuation makes perturbation for all modes inside the horizon p = k/a > HI. For massless fields experienced N e-folds of inflation, δφ0 φ0 k HI 2π 2π HI √ N = 1 √ N For N ∼ 50, this produces large perturbations in YB and ρB δρB ρB = δYB YB ≈ n δφ0 φ0 ≈ n √ N ∼ 0.1 − 0.3 with n ∼ 1 − 2 Since φ is not inflaton I, the perturbation is independent from the curvature perturbation. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 31) Louis Yang (UCLA)
95. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Isocurvature Perturbations in More Detail During inflation, quantum fluctuation makes perturbation for all modes inside the horizon p = k/a > HI. For massless fields experienced N e-folds of inflation, δφ0 φ0 k HI 2π 2π HI √ N = 1 √ N For N ∼ 50, this produces large perturbations in YB and ρB δρB ρB = δYB YB ≈ n δφ0 φ0 ≈ n √ N ∼ 0.1 − 0.3 with n ∼ 1 − 2 Since φ is not inflaton I, the perturbation is independent from the curvature perturbation. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 31) Louis Yang (UCLA)
96. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess IC-2: Isocurvature Perturbations only at Small Scales In IC-2, quantum fluctuation only grows in the late time of inflation And, the produced perturbation only appear at small spatial scales k ks ≡ e−Nlast HI TRH ΛI 4/3 g1/3 ∗S (TCMB ) g1/3 ∗S (TRH ) TCMB TRH where Nlast is the number of e-folds of inflation that the fluctuation of φ has grow. For small scales (k 0.1 Mpc−1), CMB observations are limited by Silk damping (photon diffusion damping). There are also Lyman-α forest constraints but now only covers 0.4 Mpc−1 k 9 Mpc−1. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 32) Louis Yang (UCLA)
97. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess IC-2: Isocurvature Perturbations only at Small Scales In IC-2, quantum fluctuation only grows in the late time of inflation And, the produced perturbation only appear at small spatial scales k ks ≡ e−Nlast HI TRH ΛI 4/3 g1/3 ∗S (TCMB ) g1/3 ∗S (TRH ) TCMB TRH where Nlast is the number of e-folds of inflation that the fluctuation of φ has grow. For small scales (k 0.1 Mpc−1), CMB observations are limited by Silk damping (photon diffusion damping). There are also Lyman-α forest constraints but now only covers 0.4 Mpc−1 k 9 Mpc−1. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 32) Louis Yang (UCLA)
98. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess IC-2: Isocurvature Perturbations only at Small Scales In IC-2, quantum fluctuation only grows in the late time of inflation And, the produced perturbation only appear at small spatial scales k ks ≡ e−Nlast HI TRH ΛI 4/3 g1/3 ∗S (TCMB ) g1/3 ∗S (TRH ) TCMB TRH where Nlast is the number of e-folds of inflation that the fluctuation of φ has grow. For small scales (k 0.1 Mpc−1), CMB observations are limited by Silk damping (photon diffusion damping). There are also Lyman-α forest constraints but now only covers 0.4 Mpc−1 k 9 Mpc−1. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 32) Louis Yang (UCLA)
99. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess IC-2: Isocurvature Perturbations only at Small Scales In IC-2, quantum fluctuation only grows in the late time of inflation And, the produced perturbation only appear at small spatial scales k ks ≡ e−Nlast HI TRH ΛI 4/3 g1/3 ∗S (TCMB ) g1/3 ∗S (TRH ) TCMB TRH where Nlast is the number of e-folds of inflation that the fluctuation of φ has grow. For small scales (k 0.1 Mpc−1), CMB observations are limited by Silk damping (photon diffusion damping). There are also Lyman-α forest constraints but now only covers 0.4 Mpc−1 k 9 Mpc−1. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 32) Louis Yang (UCLA)
100. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess IC-2: Isocurvature Perturbations only at Small Scales 35 40 45 50 55 10-4 0.01 1 100 104 106 Nlast of e-folds ks [Mpc-1 ] CMB constraint Lyman-α Forest constraint Λ I = 10 16 GeV Λ I = 10 14 GeV Λ I = 10 12 GeV TRH = 1010 GeV 35 40 45 50 55 10-4 0.01 1 100 104 106 Nlast of e-folds ks [Mpc-1 ] CMB constraint Lyman-α Forest constraint Λ I = 10 16 GeV Λ I = 10 14 GeV Λ I = 10 12 GeV TRH = 6⨯1011 GeV For ΛI = 1016 GeV, TRH = 6 × 1011 GeV, the fluctuations for Nlast 45 only appear at small scales (k 100 Mpc−1). This can leave interesting imprint in the structure formation and help on resolving the excess found in CIB fluctuation. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 33) Louis Yang (UCLA)
101. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Excess in the Cosmic Infrared Background Fluctuation Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 34) Louis Yang (UCLA)
102. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Cosmic Infrared Background (CIB) Anisotropies CIB is the IR part of extragalactic backgound, which contains radiation from galaxies at all redshifts through out the entire cosmic history. The absolute intensity of CIB is difficult to be determined due to the large uncertainty associated with the foreground signal, Galactic components, and zodiacal light. Therefore, recent measurements focus on the anisotropies (spatial fluctuation) of CIB, which can provide information on the early structure formation in the distant universe. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 35) Louis Yang (UCLA)
103. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Cosmic Infrared Background (CIB) Anisotropies CIB is the IR part of extragalactic backgound, which contains radiation from galaxies at all redshifts through out the entire cosmic history. The absolute intensity of CIB is difficult to be determined due to the large uncertainty associated with the foreground signal, Galactic components, and zodiacal light. Therefore, recent measurements focus on the anisotropies (spatial fluctuation) of CIB, which can provide information on the early structure formation in the distant universe. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 35) Louis Yang (UCLA)
104. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Cosmic Infrared Background (CIB) Anisotropies CIB is the IR part of extragalactic backgound, which contains radiation from galaxies at all redshifts through out the entire cosmic history. The absolute intensity of CIB is difficult to be determined due to the large uncertainty associated with the foreground signal, Galactic components, and zodiacal light. Therefore, recent measurements focus on the anisotropies (spatial fluctuation) of CIB, which can provide information on the early structure formation in the distant universe. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 35) Louis Yang (UCLA)
105. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Excess in CIB Fluctuation A. Kashlinsky, astro-ph/0412235 A. Cooray et. al., 1205.2316 K. Helgason et. al., 1505.07226 Akari and Spitzer have observed (source-subtracted) anisotropies at few arcmin scale in the near-IR spectrum (2 - 5 µm, δF 0.09 nWm−2sr−1) Not from known galaxy populations at z < 6. Might come from first stars forming at z 10. But the produced flux is not enough since the matter perturbation from inflation at very small scales at z 10 is insufficient. [Figure from K. Helgason et. al., 1505.07226] Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 36) Louis Yang (UCLA)
106. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Excess in CIB Fluctuation A. Kashlinsky, astro-ph/0412235 A. Cooray et. al., 1205.2316 K. Helgason et. al., 1505.07226 Akari and Spitzer have observed (source-subtracted) anisotropies at few arcmin scale in the near-IR spectrum (2 - 5 µm, δF 0.09 nWm−2sr−1) Not from known galaxy populations at z < 6. Might come from first stars forming at z 10. But the produced flux is not enough since the matter perturbation from inflation at very small scales at z 10 is insufficient. [Figure from K. Helgason et. al., 1505.07226] Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 36) Louis Yang (UCLA)
107. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Excess in CIB Fluctuation A. Kashlinsky, astro-ph/0412235 A. Cooray et. al., 1205.2316 K. Helgason et. al., 1505.07226 Akari and Spitzer have observed (source-subtracted) anisotropies at few arcmin scale in the near-IR spectrum (2 - 5 µm, δF 0.09 nWm−2sr−1) Not from known galaxy populations at z < 6. Might come from first stars forming at z 10. But the produced flux is not enough since the matter perturbation from inflation at very small scales at z 10 is insufficient. [Figure from K. Helgason et. al., 1505.07226] Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 36) Louis Yang (UCLA)
108. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Excess in CIB Fluctuation A. Kashlinsky, astro-ph/0412235 A. Cooray et. al., 1205.2316 K. Helgason et. al., 1505.07226 Akari and Spitzer have observed (source-subtracted) anisotropies at few arcmin scale in the near-IR spectrum (2 - 5 µm, δF 0.09 nWm−2sr−1) Not from known galaxy populations at z < 6. Might come from first stars forming at z 10. But the produced flux is not enough since the matter perturbation from inflation at very small scales at z 10 is insufficient. [Figure from K. Helgason et. al., 1505.07226] Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 36) Louis Yang (UCLA)
109. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Extra Perturbations at Small Scales Work in progress A possible solution from the scalar field relaxation leptogenesis: 1 In IC-2, fluctuations in the scalar VEV produce more baryon perturbations (δB = δρB /ρB ∼ 0.1) at small compared to inflation. 2 Total matter perturbations δM at small scales reaches non-linear regime slightly earlier. 3 Small structures (Mhalo ∼ 106M ) form earlier at z > 10 without affecting larger structure (M 107M ). 4 More stars forming and produce more CIB at z > 10. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 37) Louis Yang (UCLA)
110. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Extra Perturbations at Small Scales Work in progress A possible solution from the scalar field relaxation leptogenesis: 1 In IC-2, fluctuations in the scalar VEV produce more baryon perturbations (δB = δρB /ρB ∼ 0.1) at small compared to inflation. 2 Total matter perturbations δM at small scales reaches non-linear regime slightly earlier. 3 Small structures (Mhalo ∼ 106M ) form earlier at z > 10 without affecting larger structure (M 107M ). 4 More stars forming and produce more CIB at z > 10. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 37) Louis Yang (UCLA)
111. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Extra Perturbations at Small Scales Work in progress A possible solution from the scalar field relaxation leptogenesis: 1 In IC-2, fluctuations in the scalar VEV produce more baryon perturbations (δB = δρB /ρB ∼ 0.1) at small compared to inflation. 2 Total matter perturbations δM at small scales reaches non-linear regime slightly earlier. 3 Small structures (Mhalo ∼ 106M ) form earlier at z > 10 without affecting larger structure (M 107M ). 4 More stars forming and produce more CIB at z > 10. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 37) Louis Yang (UCLA)
112. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Extra Perturbations at Small Scales Work in progress A possible solution from the scalar field relaxation leptogenesis: 1 In IC-2, fluctuations in the scalar VEV produce more baryon perturbations (δB = δρB /ρB ∼ 0.1) at small compared to inflation. 2 Total matter perturbations δM at small scales reaches non-linear regime slightly earlier. 3 Small structures (Mhalo ∼ 106M ) form earlier at z > 10 without affecting larger structure (M 107M ). 4 More stars forming and produce more CIB at z > 10. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 37) Louis Yang (UCLA)
113. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Growth of the Matter Perturbation -2 -1 0 1 2 -8 -6 -4 -2 0 2 log(τ/τeq) log|δλ| ρr = ρm Decoupling z = 10 now Without isocurvature pert. k = 100 Mpc-1 Only adiabatic perturbation from inflation with R = 5 × 10−5 -2 -1 0 1 2 -8 -6 -4 -2 0 2 log(τ/τeq) log|δλ| ρr = ρm Decoupling z = 10 now With isocurvature pert. k = 100 Mpc-1 δB δCDM δM With isocurvature perturbation from leptogenesis with δB, i = 0.14 For Nlast = 45.7, ΛI = 1016 GeV, TRH = 6 × 1011 GeV, the isocurvature starts at ks = 100 Mpc−1. The matter density perturbation enter nonlinear regime before z = 10 for the isocurvature perturbation ⇒Structures form earlier. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 38) Louis Yang (UCLA)
114. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Growth of the Matter Perturbation -2 -1 0 1 2 -8 -6 -4 -2 0 2 log(τ/τeq) log|δλ| ρr = ρm Decoupling z = 10 now Without isocurvature pert. k = 100 Mpc-1 Only adiabatic perturbation from inflation with R = 5 × 10−5 -2 -1 0 1 2 -8 -6 -4 -2 0 2 log(τ/τeq) log|δλ| ρr = ρm Decoupling z = 10 now With isocurvature pert. k = 100 Mpc-1 δB δCDM δM With isocurvature perturbation from leptogenesis with δB, i = 0.14 For Nlast = 45.7, ΛI = 1016 GeV, TRH = 6 × 1011 GeV, the isocurvature starts at ks = 100 Mpc−1. The matter density perturbation enter nonlinear regime before z = 10 for the isocurvature perturbation ⇒Structures form earlier. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 38) Louis Yang (UCLA)
115. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Matter Power Spectrum -2 -1 0 1 2 -4 -2 0 2 4 k [h/Mpc] P(k) [h-3 Mpc3 ] The present matter power spectrum with isocurvature perturbations from the scalar field relaxation leptogenesis with δB = 0.14 and ks = 100 Mpc−1. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 39) Louis Yang (UCLA)
116. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Minihalos with M ∼ 106M Collapse Before z = 10 5 6 7 8 9 10 11 0.05 0.10 0.50 1 5 log(M/M⊙ ) σM δc/ 2 z = 10 z = 20 z = 40 z = 80 The RMS density constrast σM . Dashed line: No isocurvature perturbation. Solid line: With isocurvature perturbation with δB = 0.14 and ks = 100 Mpc−1. Minihalos Mhalo ∼ 106M collapse by z ≈ 10 without producing larger structure (M 107M ). Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 40) Louis Yang (UCLA)
117. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Summary During inflation, scalar fields can obtain large VEVs through quantum fluctuation. Relaxations of the Higgs and other scalar fields generally happen after inflation. Leptogenesis driven by the relaxation of the Higgs fields is possible and this provides an alternative to the standard thermal leptogenesis. This also generates additional baryonic isocurvature perturbations, which is not constrained by CMB observation at small angular scales. Isocurvature perturbation at small scale can then lead to first star forming earlier than what is expected from ΛCDM. This might be the origin of the excess in CIB fluctuations. Last but not least, post-inflationary Higgs relaxation can be a very important epoch in the early universe. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 41) Louis Yang (UCLA)
118. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Summary During inflation, scalar fields can obtain large VEVs through quantum fluctuation. Relaxations of the Higgs and other scalar fields generally happen after inflation. Leptogenesis driven by the relaxation of the Higgs fields is possible and this provides an alternative to the standard thermal leptogenesis. This also generates additional baryonic isocurvature perturbations, which is not constrained by CMB observation at small angular scales. Isocurvature perturbation at small scale can then lead to first star forming earlier than what is expected from ΛCDM. This might be the origin of the excess in CIB fluctuations. Last but not least, post-inflationary Higgs relaxation can be a very important epoch in the early universe. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 41) Louis Yang (UCLA)
119. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Summary During inflation, scalar fields can obtain large VEVs through quantum fluctuation. Relaxations of the Higgs and other scalar fields generally happen after inflation. Leptogenesis driven by the relaxation of the Higgs fields is possible and this provides an alternative to the standard thermal leptogenesis. This also generates additional baryonic isocurvature perturbations, which is not constrained by CMB observation at small angular scales. Isocurvature perturbation at small scale can then lead to first star forming earlier than what is expected from ΛCDM. This might be the origin of the excess in CIB fluctuations. Last but not least, post-inflationary Higgs relaxation can be a very important epoch in the early universe. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 41) Louis Yang (UCLA)
120. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Summary During inflation, scalar fields can obtain large VEVs through quantum fluctuation. Relaxations of the Higgs and other scalar fields generally happen after inflation. Leptogenesis driven by the relaxation of the Higgs fields is possible and this provides an alternative to the standard thermal leptogenesis. This also generates additional baryonic isocurvature perturbations, which is not constrained by CMB observation at small angular scales. Isocurvature perturbation at small scale can then lead to first star forming earlier than what is expected from ΛCDM. This might be the origin of the excess in CIB fluctuations. Last but not least, post-inflationary Higgs relaxation can be a very important epoch in the early universe. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 41) Louis Yang (UCLA)
121. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Summary During inflation, scalar fields can obtain large VEVs through quantum fluctuation. Relaxations of the Higgs and other scalar fields generally happen after inflation. Leptogenesis driven by the relaxation of the Higgs fields is possible and this provides an alternative to the standard thermal leptogenesis. This also generates additional baryonic isocurvature perturbations, which is not constrained by CMB observation at small angular scales. Isocurvature perturbation at small scale can then lead to first star forming earlier than what is expected from ΛCDM. This might be the origin of the excess in CIB fluctuations. Last but not least, post-inflationary Higgs relaxation can be a very important epoch in the early universe. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 41) Louis Yang (UCLA)
122. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Summary During inflation, scalar fields can obtain large VEVs through quantum fluctuation. Relaxations of the Higgs and other scalar fields generally happen after inflation. Leptogenesis driven by the relaxation of the Higgs fields is possible and this provides an alternative to the standard thermal leptogenesis. This also generates additional baryonic isocurvature perturbations, which is not constrained by CMB observation at small angular scales. Isocurvature perturbation at small scale can then lead to first star forming earlier than what is expected from ΛCDM. This might be the origin of the excess in CIB fluctuations. Last but not least, post-inflationary Higgs relaxation can be a very important epoch in the early universe. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 41) Louis Yang (UCLA)
123. Scalar Field Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Summary During inflation, scalar fields can obtain large VEVs through quantum fluctuation. Relaxations of the Higgs and other scalar fields generally happen after inflation. Leptogenesis driven by the relaxation of the Higgs fields is possible and this provides an alternative to the standard thermal leptogenesis. This also generates additional baryonic isocurvature perturbations, which is not constrained by CMB observation at small angular scales. Isocurvature perturbation at small scale can then lead to first star forming earlier than what is expected from ΛCDM. This might be the origin of the excess in CIB fluctuations. Last but not least, post-inflationary Higgs relaxation can be a very important epoch in the early universe. Thank you for your attention! Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 41) Louis Yang (UCLA)
124. Matter-Antimatter Asymmetry CMB observations and BBN ηB = nB − n B nγ ∼ = 6 × 10−10 ΩB = 0.0484(10) Sakharov’s conditions for Baryogenesis 1 B violation 2 C and CP violations 3 Deviation from thermal equilibrium Standard Model do satisfy all the conditions but the CP phase is too small to generate enough asymmetry. (And, the Higgs mass is too heavy) Leptogenesis: Generate L first. Then, Sphaleron process (violates B + L but conserves B − L) can turn −L into B. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 42) Louis Yang (UCLA)
125. Matter-Antimatter Asymmetry CMB observations and BBN ηB = nB − n B nγ ∼ = 6 × 10−10 ΩB = 0.0484(10) Sakharov’s conditions for Baryogenesis 1 B violation 2 C and CP violations 3 Deviation from thermal equilibrium Standard Model do satisfy all the conditions but the CP phase is too small to generate enough asymmetry. (And, the Higgs mass is too heavy) Leptogenesis: Generate L first. Then, Sphaleron process (violates B + L but conserves B − L) can turn −L into B. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 42) Louis Yang (UCLA)
126. Matter-Antimatter Asymmetry CMB observations and BBN ηB = nB − n B nγ ∼ = 6 × 10−10 ΩB = 0.0484(10) Sakharov’s conditions for Baryogenesis 1 B violation 2 C and CP violations 3 Deviation from thermal equilibrium Standard Model do satisfy all the conditions but the CP phase is too small to generate enough asymmetry. (And, the Higgs mass is too heavy) Leptogenesis: Generate L first. Then, Sphaleron process (violates B + L but conserves B − L) can turn −L into B. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 42) Louis Yang (UCLA)
127. Matter-Antimatter Asymmetry CMB observations and BBN ηB = nB − n B nγ ∼ = 6 × 10−10 ΩB = 0.0484(10) Sakharov’s conditions for Baryogenesis 1 B violation 2 C and CP violations 3 Deviation from thermal equilibrium Standard Model do satisfy all the conditions but the CP phase is too small to generate enough asymmetry. (And, the Higgs mass is too heavy) Leptogenesis: Generate L first. Then, Sphaleron process (violates B + L but conserves B − L) can turn −L into B. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 42) Louis Yang (UCLA)
128. Matter-Antimatter Asymmetry CMB observations and BBN ηB = nB − n B nγ ∼ = 6 × 10−10 ΩB = 0.0484(10) Sakharov’s conditions for Baryogenesis 1 B violation 2 C and CP violations 3 Deviation from thermal equilibrium Standard Model do satisfy all the conditions but the CP phase is too small to generate enough asymmetry. (And, the Higgs mass is too heavy) Leptogenesis: Generate L first. Then, Sphaleron process (violates B + L but conserves B − L) can turn −L into B. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 42) Louis Yang (UCLA)
129. Matter-Antimatter Asymmetry CMB observations and BBN ηB = nB − n B nγ ∼ = 6 × 10−10 ΩB = 0.0484(10) Sakharov’s conditions for Baryogenesis 1 B violation 2 C and CP violations ← Is this necessary? 3 Deviation from thermal equilibrium Standard Model do satisfy all the conditions but the CP phase is too small to generate enough asymmetry. (And, the Higgs mass is too heavy) Leptogenesis: Generate L first. Then, Sphaleron process (violates B + L but conserves B − L) can turn −L into B. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 42) Louis Yang (UCLA)
130. Matter-Antimatter Asymmetry CMB observations and BBN ηB = nB − n B nγ ∼ = 6 × 10−10 ΩB = 0.0484(10) Sakharov’s conditions for Baryogenesis 1 B violation 2 C and CP violations ← Is this necessary? 3 Deviation from thermal equilibrium Standard Model do satisfy all the conditions but the CP phase is too small to generate enough asymmetry. (And, the Higgs mass is too heavy) Leptogenesis: Generate L first. Then, Sphaleron process (violates B + L but conserves B − L) can turn −L into B. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 42) Louis Yang (UCLA)
131. Matter-Antimatter Asymmetry CMB observations and BBN ηB = nB − n B nγ ∼ = 6 × 10−10 ΩB = 0.0484(10) Sakharov’s conditions for Baryogenesis 1 B violation 2 C and CP violations ← Is this necessary? 3 Deviation from thermal equilibrium Standard Model do satisfy all the conditions but the CP phase is too small to generate enough asymmetry. (And, the Higgs mass is too heavy) Leptogenesis: Generate L first. Then, Sphaleron process (violates B + L but conserves B − L) can turn −L into B. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 42) Louis Yang (UCLA)
132. Standard Thermal Leptogenesis Fukugita and Yanagida (1986) SM + Right Handed Majorana neutrinos NR Majorana mass term of NR → Violates L Neutrino Yukawa couplings → CP-violating phase Out of equilibrium decay of NR Requirements: Need to produce RH neutrinos (T ∼ MR ) Light neutrino mass mν < 0.2 eV Alternative which works without producing RH neutrinos (T < MR)? Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 43) Louis Yang (UCLA)
133. Standard Thermal Leptogenesis Fukugita and Yanagida (1986) SM + Right Handed Majorana neutrinos NR Majorana mass term of NR → Violates L Neutrino Yukawa couplings → CP-violating phase Out of equilibrium decay of NR Requirements: Need to produce RH neutrinos (T ∼ MR ) Light neutrino mass mν < 0.2 eV Alternative which works without producing RH neutrinos (T < MR)? Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 43) Louis Yang (UCLA)
134. Standard Thermal Leptogenesis Fukugita and Yanagida (1986) SM + Right Handed Majorana neutrinos NR Majorana mass term of NR → Violates L Neutrino Yukawa couplings → CP-violating phase Out of equilibrium decay of NR Requirements: Need to produce RH neutrinos (T ∼ MR ) Light neutrino mass mν < 0.2 eV Alternative which works without producing RH neutrinos (T < MR)? Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 43) Louis Yang (UCLA)
135. Standard Thermal Leptogenesis Fukugita and Yanagida (1986) SM + Right Handed Majorana neutrinos NR Majorana mass term of NR → Violates L Neutrino Yukawa couplings → CP-violating phase Out of equilibrium decay of NR Requirements: Need to produce RH neutrinos (T ∼ MR ) Light neutrino mass mν < 0.2 eV Alternative which works without producing RH neutrinos (T < MR)? Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 43) Louis Yang (UCLA)
136. Standard Thermal Leptogenesis Fukugita and Yanagida (1986) SM + Right Handed Majorana neutrinos NR Majorana mass term of NR → Violates L Neutrino Yukawa couplings → CP-violating phase Out of equilibrium decay of NR Requirements: Need to produce RH neutrinos (T ∼ MR ) Light neutrino mass mν < 0.2 eV Alternative which works without producing RH neutrinos (T < MR)? Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 43) Louis Yang (UCLA)
137. Standard Thermal Leptogenesis Fukugita and Yanagida (1986) SM + Right Handed Majorana neutrinos NR Majorana mass term of NR → Violates L Neutrino Yukawa couplings → CP-violating phase Out of equilibrium decay of NR Requirements: Need to produce RH neutrinos (T ∼ MR ) Light neutrino mass mν < 0.2 eV Alternative which works without producing RH neutrinos (T < MR)? Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 43) Louis Yang (UCLA)
138. Standard Thermal Leptogenesis Fukugita and Yanagida (1986) SM + Right Handed Majorana neutrinos NR Majorana mass term of NR → Violates L Neutrino Yukawa couplings → CP-violating phase Out of equilibrium decay of NR Requirements: Need to produce RH neutrinos (T ∼ MR ) Light neutrino mass mν < 0.2 eV Alternative which works without producing RH neutrinos (T < MR)? Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 43) Louis Yang (UCLA)
139. Standard Thermal Leptogenesis Fukugita and Yanagida (1986) SM + Right Handed Majorana neutrinos NR Majorana mass term of NR → Violates L Neutrino Yukawa couplings → CP-violating phase Out of equilibrium decay of NR Requirements: Need to produce RH neutrinos (T ∼ MR ) Light neutrino mass mν < 0.2 eV Alternative which works without producing RH neutrinos (T < MR)? Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 43) Louis Yang (UCLA)
140. Backup Slides: Generating the O6 Operator Requirements To generate the O6 operator, need the following: 1 Heavy states which do NOT get masses via the Higgs mechanism 2 Which couple to SUL (2), U(1) gauge bosons Options: 1 Scalars: SU(2) triplet which also couples to Higgs If neutral member, no or small VEV (electroweak precision) 2 Fermions: Requires two doublets, L and R, each of which couples to SU(2) (see below) Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 44) Louis Yang (UCLA)
141. Backup Slides: Generating the O6 Operator Requirements To generate the O6 operator, need the following: 1 Heavy states which do NOT get masses via the Higgs mechanism 2 Which couple to SUL (2), U(1) gauge bosons Options: 1 Scalars: SU(2) triplet which also couples to Higgs If neutral member, no or small VEV (electroweak precision) 2 Fermions: Requires two doublets, L and R, each of which couples to SU(2) (see below) Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 44) Louis Yang (UCLA)
142. Backup Slides: Generating the O6 Operator Requirements To generate the O6 operator, need the following: 1 Heavy states which do NOT get masses via the Higgs mechanism 2 Which couple to SUL (2), U(1) gauge bosons Options: 1 Scalars: SU(2) triplet which also couples to Higgs If neutral member, no or small VEV (electroweak precision) 2 Fermions: Requires two doublets, L and R, each of which couples to SU(2) (see below) Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 44) Louis Yang (UCLA)
143. Backup Slides: Generating the O6 Operator Requirements To generate the O6 operator, need the following: 1 Heavy states which do NOT get masses via the Higgs mechanism 2 Which couple to SUL (2), U(1) gauge bosons Options: 1 Scalars: SU(2) triplet which also couples to Higgs If neutral member, no or small VEV (electroweak precision) 2 Fermions: Requires two doublets, L and R, each of which couples to SU(2) (see below) Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 44) Louis Yang (UCLA)
144. Backup Slides: Generating the O6 Operator Requirements To generate the O6 operator, need the following: 1 Heavy states which do NOT get masses via the Higgs mechanism 2 Which couple to SUL (2), U(1) gauge bosons Options: 1 Scalars: SU(2) triplet which also couples to Higgs If neutral member, no or small VEV (electroweak precision) 2 Fermions: Requires two doublets, L and R, each of which couples to SU(2) (see below) Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 44) Louis Yang (UCLA)
145. Backup Slides: Generating the O6 Operator Requirements To generate the O6 operator, need the following: 1 Heavy states which do NOT get masses via the Higgs mechanism 2 Which couple to SUL (2), U(1) gauge bosons Options: 1 Scalars: SU(2) triplet which also couples to Higgs If neutral member, no or small VEV (electroweak precision) 2 Fermions: Requires two doublets, L and R, each of which couples to SU(2) (see below) Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 44) Louis Yang (UCLA)
146. Backup Slides: Generating the O6 Operator Explicit Fermionic Model: Set of Dirac spinors ψDi (both left and right): SU(2) doublet, hypercharge −1/2 Dirac spinor ψS (both left and right): SU(2) singlet, hypercharge −1 Higgs field Φ: SU(2) doublet, hypercharge 1/2 where YW = Q − T3. With these fields, we can write the Lagrangian: L = kinetic terms + yi eiδi Φ( ¯ ψDLi ψSR + ¯ ψDRi ψSL ) + m ¯ ψS ψS + Mij ( ¯ ψDLi ψDRj + ¯ ψDRj ψDLi ) + h.c.. Last line is allowed because both ¯ ψDL and ¯ ψDR are SU(2) doublets Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 45) Louis Yang (UCLA)
147. Backup Slides: Generating the O6 Operator Explicit Fermionic Model: Set of Dirac spinors ψDi (both left and right): SU(2) doublet, hypercharge −1/2 Dirac spinor ψS (both left and right): SU(2) singlet, hypercharge −1 Higgs field Φ: SU(2) doublet, hypercharge 1/2 where YW = Q − T3. With these fields, we can write the Lagrangian: L = kinetic terms + yi eiδi Φ( ¯ ψDLi ψSR + ¯ ψDRi ψSL ) + m ¯ ψS ψS + Mij ( ¯ ψDLi ψDRj + ¯ ψDRj ψDLi ) + h.c.. Last line is allowed because both ¯ ψDL and ¯ ψDR are SU(2) doublets Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 45) Louis Yang (UCLA)
148. Backup Slides: Generating the O6 Operator Explicit Fermionic Model: Set of Dirac spinors ψDi (both left and right): SU(2) doublet, hypercharge −1/2 Dirac spinor ψS (both left and right): SU(2) singlet, hypercharge −1 Higgs field Φ: SU(2) doublet, hypercharge 1/2 where YW = Q − T3. With these fields, we can write the Lagrangian: L = kinetic terms + yi eiδi Φ( ¯ ψDLi ψSR + ¯ ψDRi ψSL ) + m ¯ ψS ψS + Mij ( ¯ ψDLi ψDRj + ¯ ψDRj ψDLi ) + h.c.. Last line is allowed because both ¯ ψDL and ¯ ψDR are SU(2) doublets Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 45) Louis Yang (UCLA)
149. Backup Slides: Generating the O6 Operator Explicit Fermionic Model: Set of Dirac spinors ψDi (both left and right): SU(2) doublet, hypercharge −1/2 Dirac spinor ψS (both left and right): SU(2) singlet, hypercharge −1 Higgs field Φ: SU(2) doublet, hypercharge 1/2 where YW = Q − T3. With these fields, we can write the Lagrangian: L = kinetic terms + yi eiδi Φ( ¯ ψDLi ψSR + ¯ ψDRi ψSL ) + m ¯ ψS ψS + Mij ( ¯ ψDLi ψDRj + ¯ ψDRj ψDLi ) + h.c.. Last line is allowed because both ¯ ψDL and ¯ ψDR are SU(2) doublets Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 45) Louis Yang (UCLA)
150. Backup Slides: Generating the O6 Operator Explicit Fermionic Model: Set of Dirac spinors ψDi (both left and right): SU(2) doublet, hypercharge −1/2 Dirac spinor ψS (both left and right): SU(2) singlet, hypercharge −1 Higgs field Φ: SU(2) doublet, hypercharge 1/2 where YW = Q − T3. With these fields, we can write the Lagrangian: L = kinetic terms + yi eiδi Φ( ¯ ψDLi ψSR + ¯ ψDRi ψSL ) + m ¯ ψS ψS + Mij ( ¯ ψDLi ψDRj + ¯ ψDRj ψDLi ) + h.c.. Last line is allowed because both ¯ ψDL and ¯ ψDR are SU(2) doublets Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 45) Louis Yang (UCLA)
151. Backup Slides: Solutions to the isocurvature perturbation issue For the O5 and O6: For λφ4 potential, the equilibrium fluctuation is δφ0 φ0 HI 2π λ1/4 HI = λ1/4 2π . One can suppressed the fluctuation by tuning λ 1.7 × 10−16. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 46) Louis Yang (UCLA)
152. Backup slide: Isocurvature perturbations: Limits from CMB CMB observation by Planck satellite (2015) constrains the isocurvature perturbation by βiso (k∗ ) = PII (k∗ ) PRR (k∗ ) + PII (k∗ ) < 0.033 and 0.038, at comoving wavenumbers k∗ = 0.002 Mpc−1 and 0.1 Mpc−1. These can be translated into a limit on baryonic isocurvature perturbations δYB YB k∗ 5 × 10−5. The constraint is only for large scales l 60 Mpc (k 0.1 Mpc−1). Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 47) Louis Yang (UCLA)
153. Backup slide: Parameter Space for the Pseudoscalar S 2 4 6 8 10 6 8 10 12 14 log(mS [GeV]) log(TR [GeV]) No inflation Isocurvature constraint Tensor mode constraint ΛI < 1.88⨯1016 GeV Λ I = 10 16 GeV Λ I = 10 15 GeV Λ I = 10 14 GeV ΛI = 1013.5 GeV Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 48) Louis Yang (UCLA)