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.