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.