Twin Higgs at finite temperature

Studying a Twin Higgs model at finite temperature indicates that spontaneously broken electroweak symmetry will get restored, even in Standard Model extensions with same-spin partners.

Presentation given at:
* Tri-Institute Summer School on Elementary Particles (TRISEP) 2015
* Theoretical Advanced Studies Institute (TASI) 2016

Transcript

1. Twin Higgs at finite temperature
   Decreasing coolness implies increasing conformity
   Sivaramakrishnan Swaminathan
   Theory Group, Department of Physics and Texas Cosmology Center,
   The University of Texas at Austin, Austin, TX 78712 U.S.A.
   Acknowledgements
   This work is done in collaboration with Can Kilic. This research is supported by the
   National Science Foundation under Grant Numbers PHY-1315983 and PHY-1316033.
   References
   [1] J. R. Espinosa, M. Losada and A. Riotto, Phys. Rev. D 72, 043520 (2005)
   [2] Z. Chacko, H. S. Goh and R. Harnik, Phys. Rev. Lett. 96, 231802 (2006)
   [3] J. I. Kapusta and C. Gale, Cambridge, UK: Univ. Pr. (2006) 428 p
   Can A Broken Phase of Electroweak Symmetry Exist At High Temperature In Models With Same-Spin Partners?
   Boson-fermion cancellations protecting Higgs mass naturalness at zero temperature fail to extend to finite temperature. This miscancellation is
   expected to drive symmetry restoration at high temperatures. In alternative paradigms (SM extensions with same-spin partners) the possibility of
   non-restoration of electroweak symmetry at high temperatures is left open. It was argued in [1] that a Little Higgs model has a symmetry broken phase
   at high temperature, using a truncated high-temperature approximation of the effective potential. However, we believe that it is important to keep
   track of the higher order terms, which point to a restoration of symmetry at high temperature, in a Twin Higgs inspired model we consider.
   A Twin-Higgs inspired model
   Twin the standard model [2]: SMA
   Z2 symmetry
   ←
   −
   −
   −
   −
   −
   → SMB
   SM Higgs doublet h among the SU(4)/SU(3) pNGBs
   V (H) =
   λ
   4
   |H|2 − f2
   2
   , H ≡
   HA
   HB
   =
   
   
   
   if h
   √
   h†h
   sin
   √
   h†h
   f
   if h
   √
   h †h
   cos
   √
   h†h
   f
   
   
   
   One-loop corrections to the Higgs effective potential from the scalar
   sector must respect the SU(4) symmetry
   Z2
   symmetry ensures that Λ2 contributions from fermions and gauge
   bosons respect SU(4) symmetry
   V1
   (H) ⊃ −
   3y2Λ2
   8π2
   +
   9g2Λ2
   64π2
   H†
   A
   HA
   + H†
   B
   HB
   HA H†
   A
   HB H†
   B
   h h
   y
   y
   h
   h
   × yf
   − y
   2f
   +
   h
   h
   ×
   yf
   − y
   2f
   No quadratically divergent contribution to mass of Higgs particle!
   Phenomenological considerations prefer a small hierarchy vEW
   f;
   break the Z2
   symmetry softly with L ⊃ µH†
   A
   HA
   HB
   HA
   vEW
   √
   2
   v
   √
   2
   f
   Note that the partners have no SM charges. In particular, the top
   partner is uncoloured.
   Finite temperature effective potential
   Finite temperature effective potential (see [3] for details)
   ∆V T
   1
   (φ, T) ≡ STr
   T4
   2π2
   Jb/f
   m2(φ)
   T2
   For T > m(φ), we can expand these as an asymptotic series in x,
   with af
   = π2e−2γE+3
   2 and ab
   = 16π2e−2γE+3
   2
   Jb
   (x) = −
   π2
   45
   +
   x
   12
   −
   πx3
   2
   6
   −
   x2
   32π2
   log
   x
   ab
   + . . .
   −Jf
   (x) = −
   7π2
   360
   +
   x
   24
   +
   x2
   32π2
   log
   x
   af
   + . . .
   Finite temperature breaks SUSY, but same-spin cancellation
   mechanisms carry through to finite temperature
   bosons: +
   Λ2
   16π2
   −→ +
   T2
   12
   fermions: −
   Λ2
   16π2
   −→ +
   T2
   24
   .
   Therefore, subleading terms could play an important role!
   Complexities due to IR divergences and non-perturbative effects.
   δm2
   T
   ∼ {λ, g2, y2}T2
   Conclusion: Electroweak symmetry does get restored
   A numerical study of the one-loop effective potential indicates symmetry restoration,
   driven by the log term. Truncating the same to O(T2) completely misses the transition.
   In the UV completed linear theory, the radial mode VEV is driven to the origin at high
   temperature, so VEV of the Goldstones is rendered moot.
   Restoration of electroweak symmetry seems a robust conclusion, since two broad
   paradigms for enforcing naturalness: supersymmetry and pNGB mechanisms, both lead
   to symmetry restoration.
   

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