Can a pseudo-Nambu-Goldstone-Boson Higgs lead to symmetry non-restoration?

Talk given in the "Many-Body Theory" class.

Transcript

1. Can a pNGB Higgs lead to symmetry Can a pNGB Higgs lead to symmetry non-restoration? non-restoration? (w/ Can Kilic) (w/ Can Kilic) Sivaramakrishnan Swaminathan Sivaramakrishnan Swaminathan arXiv:1508.05121 arXiv:1508.05121 20 October 2015 (Many-body theory) 20 October 2015 (Many-body theory)
2. The big picture The big picture
3. Motivations Motivations What happens to electroweak symmetry at high temperatures? Baryogenesis (How was matter created?) Heuristic thermodynamic argument hints at symmetry restoration Counter examples (Rochelle salts, �nite chemical potential, etc.) F = E − TS
4. The effective potential The effective potential
5. The idea (a la Landau-Ginzburg) The idea (a la Landau-Ginzburg) Let the order parameter be a �eld Free-energy cost of homogeneous �eld con�gurations Include quantum effects ("integrate out" all �uctuations) Think "bubbles" ( ) Position of minimum corresponds to particle density in the condensate F = −β log Z
6. Integrating out the �uctuations Integrating out the �uctuations Cost of zero-point energies of �eld �uctuations around a putative background �eld value: harmonic oscillator for each mode VCW (H) VCW = STr ∫ [ ] d3k⃗ 1 2 + k2 m2 − − − − − − − √ = STr [ (H) + (log ( ) − )] m2 Λ2 16π2 (H) m4 64π2 (H) m2 Λ2 3 2 At one-loop, the cost of one-�uctuation depends only on the background, and is independent of other �uctuations "Integrate out �uctuations" : up to what scale?
7. At �nite temperature At �nite temperature For each �uctuation: Modify spectral function by adding thermal occupations (ϕ, T) = (ϕ) + Δ (ϕ, T) Veff, 1-loop VCW V T 1 Δ = ( ) V T 1 ∑ i T 4 2π2 ni Jb/f m2 i T 2 ( ) Jb xi ( ) Jf xi = dt log [1 − ] ∫ ∞ 0 t2 e− + xi t2 √ = dt log [1 + ] ∫ ∞ 0 t2 e− + xi t2 √
8. High temperature expansion High temperature expansion (x) Jb − (x) Jf = = − π4 45 − 7π4 360 + x π2 12 + x π2 24 − πx 3 2 6 − log ( ) x2 32 x ab + log ( ) x2 32 x af + … + … Note the correspondence with the zero temperature contribution bosons: fermions: − Λ2 16π2 Λ2 16π2 ⟶ T 2 12 ⟶ . T 2 24 Both fermions and bosons contribute to with the same sign! T 2
9. Particle physics today Particle physics today
10. We We �nally �nally found the Higgs! found the Higgs! v ≈ 173GeV , ≈ 125GeV mh
11. The Standard Model The Standard Model
12. The hierarchy problem The hierarchy problem Mass term: Self energy of background �eld, at zero-external momentum Mass term, and hence VEV depends sensitively on the UV-cutoff! Supersymmetry models try to exploit the opposite sign between fermion (quark) and scalar ("squark") corrections above.
13. The Twin Higgs The Twin Higgs
14. SU(4)/SU(3) SU(4)/SU(3) NLSM NLSM H = [ ] = − [− + λ ] HA HB Lscalar |∂H|2 m2|H|2 |H|4 This leads to SSB: Integrate out the radial mode; work with NLSM symmetry prevents contributions to ! H = exp i f ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ h∗ 1 0 h∗ 2 h∗ 3 h1 h2 h3 h0 ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎡ ⎣ ⎢ ⎢ ⎢ 0 0 0 f ⎤ ⎦ ⎥ ⎥ ⎥ SU(4) Λ2 m2 h
15. SU(4)/SU(3) SU(4)/SU(3) NLSM (2) NLSM (2) H [ ] = ≈ [ ] − → − − − − − − − − − − − − − − − − − Exploit [ ] SU(2) A SU(2) B |⟨ ⟩| HA |⟨ ⟩| HB ⎡ ⎣ ⎢ f sin ( ) v f f cos ( ) v f ⎤ ⎦ ⎥ v f − v2 2f What happens to ? 3 : eaten by gauge bosons 3 : eaten by gauge bosons 1 : heavy radial �uctuation 1 : "magnitude" of the SM Higgs H R SU(2) A R SU(2) B R R
16. A caricature model A caricature model Twin image of SM (A B) Forget the gauge bosons for now (Set ) Focus on the top quark sector (forget all other fermions) ⟷ = 0 gi Top sector Top sector = y [ (ϵ ) + (ϵ ) ] + h.c. Lup-type yukawa Q ¯ A HA UA Q ¯ B HB UB Yukawas break but have twin symmetry SU(4) (A ↔ B)
17. Twin mechanism Twin mechanism Discrete symmetry causes quadratic terms to mimic symmetry (which is otherwise broken) Z2 SU(4) − ( + ) = − 3y2Λ2 8π2 H† A HA H† B HB 3y2 8π2 Λ2|H|2
18. High temperature behaviour High temperature behaviour
19. Observations Observations Symmetry does get restored! f = 450GeV, μ = 90GeV, = 1500GeV Tmax
20. Insights Insights The leading dependence cancels away ( just like ) Subleading temperature dependence ( ) restores symmetry Those corrections are unavoidable, since terms are what give the Higgs a �nite mass ( ), in such models T T 2 Λ2 log T log Λ 125GeV
21. Thank you! Thank you!