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MSSM Finite-Temperature Higgs Potential for Phase Transition
Mikhail Dolgopolov (Samara State University)
Dubinin M. (SINP MSU) Rykova E. (SSU)

· · · ·

Introduction Finite-temperature corrections of squarks Thermal evolution and the critical temperature Conclusions

Outline

[ M. Dolgopolov, M. Dubinin, E. Rykova Threshold corrections to the MSSM finitetemperature Higgs potential. Jan 2009. 26pp. e-Print: arXiv:0901.0524v1 ; Physics of Atomic Nuclei, 2010, Vol. 73, No. 6, pp. 10321036] Golitsyno, Russia, QFTHEP 2010, September 10
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The absence of antimatter in the Universe, a small ratio of the observed number of baryons to the observed number of photons and the absence of light CP-even Higgs boson signal at LEP2 and Tevatron energies lay a specific claims to models of particle physics · Two problems in the Standard Model First order phase transition requires mh< 50 GeV Need new sources of CP violation · Minimal Supersymmetric Standard Model 1st order phase transition is possible if mt~R 160GeV New CP violating phases
Light stop window: M. Carena, M. Quiros, C.E.M. Wagner, Phys.Lett. B380 (1996) 81; M. Carena, G. Nardini, M. Quiros and C.E.M.Wagner JHEP 10 (2008) 062; M. Carena, G. Nardini, M. Quiros, C.E.M. Wagner. Nucl.Phys. B812: 243-263, 2009. M. Dolgopolov, M. Dubinin, E. Rykova Threshold corrections to the MSSM finitetemperature Higgs potential. e-Print: arXiv:0901.0524v2 In the MSSM we calculate the 1-loop FT corrections from the squarks-Higgs bosons sector, reconstruct the effective two-Higgs-doublet potential and study possibilities of the EWPT in the full MSSM (mH±, tg, At,b, µ, mQ, mU, mD) parameter space.
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MODEL [QFTHEP'2003, 2004]

THDM: Fields
Georgi: A Model Of Soft CP Violation. 1978 Lee: A Theory Of Spontaneous T Violation. 1973

GeV
Ilya F. Ginzburg, M. Krawczyk, Symmetries of two Higgs doublet model and CP violation. Phys.Rev.D72,2005. Akhmetzyanova E.N., D M.V., Dubinin M.N. 3 Higgs Bosons in the Two-Doublet Model with CP Violation Phys.Rev.D71.2005. Violation of CP invariance in the two-doublet Higgs sector of the MSSM. Phys.Part.Nucl.37,2006.

Effective THDM potential with explicit CP violation
General hermitian renormalized SU(2)xU(1) invariant potential:

5, 6,
complex =arg(
6, 7

12

2

,
7

)

=arg( 5 )/2

One-loop (t, b)CP U eff contributions mtop

at the MS

USY

U is CP-invariant =0 scale, because
µ - massscale
4

SUSY Eff. potential method energy or Feynman diags (temperature T)

M

Scalar sector for MSSM
The main contribution to self-couplings due to Yukawa 3 generation couplings. The corresponding potential with CPV sources
rd

5

Threshold corrections (left and central diagram) and diagram contributing to the wave-function renormalization (right)

"Fish" diagrams

6

The surface of minima for zero-temperature two-doublet Higgs potential at the scale MSUS

Y

8

Integration and summation method
In the finite temperature field theory Feynman diagrams with boson propagators, containing Matsubara frequencies, lead to structures of the form

temperature

Integration and summation method

Parameters of the effective potential (forms of contribitions)

Parameters of the effective potential (forms of contribitions)

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1
0,8 0,6

Temperature-dependent parameters with various quantum corrections in CPX-like scenario At=Ab=1000 GeV, µ=2000 GeV

0,4
0,2 0 -0,2 -0,4 -0,6 -0,8 -1 Msusy=500GeV, T=0. Msusy=500GeV, T=200GeV. mQ=500GeV, mU=800 GeV, mD=200GeV,T=0. mQ=500GeV, mU=800 GeV, mD=200GeV,T=200GeV. mQ=500GeV, mU=800 GeV, mD=200GeV,T=200GeV, Log

T, GeV CPX: M.Carena, J.Ellis, A.Pilaftsis, C.Wagner, PL B495 (2000) 155

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The surfaces of minima for effective potential U(v1,v2) at the critical temperature T=120 GeV, = =0

Phase transitions of the first order can occur along the going down hollow. In other directions minima at nonzero v1,2 will be above the minimum at v1=v2=0.

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The surfaces of minima for effective potential U(v1,v2) at the critical temperature T=120 GeV and nonzero

At nonzero there are directions always along which the first order phase transition exists.

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Effective potential at finite temperature

Mass term

Critical temperature determination

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Evolution of the critical parameters

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Effective potential U(v1,v2) at the critical temperature and nonzero

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The thermal evolution of the CP-even Higgs bosons h and H is expressed by

where is the mixing angle of the CP-even states h and H.
[ Akhmetzyanova E.N., Dolgopolov M.V., Dubinin M.N. Higgs Bosons in the TwoDoublet Model with CP Violation // Phys.Rev.D. V.71. N7. 2005. P.075008. (hepph/0405264) ]
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Higgs bosons masses
v,

T,

=180
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Conclusions
1. In the MSSM we calculate the 1-loop finite-temperature corrections from the squarks-Higgs bosons sector, reconstruct the effective two-Higgs-doublet potential in the full MSSM parameter space (mH±, tg, At,b, µ, mQ, mU, mD). 2. At large values of A and µ of around 1 TeV, favored indirectly by LEP2 and Tevatron data, the threshold finite-temperature corrections from triangle and box diagrams with intermediate third generation squarks are very substantial. 3. High sensitivity of the low-temperature evolution to the effective two-doublet and the MSSM squark sector parameters is observed, but rather extensive regions of the full MSSM parameter space allow the first-order electroweak phase transition respecting the phenomenological constraints at zero temperature.
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Perspectives
· The topology analysis of extended Higgs potentials · viable models: THDM, MSSM, Singlet models: many possibilities · Electroweak baryogenesis is still viable in extended Higgs sectors · It would offer the possibiliy to compute the baryon asymmetry from parameters measured in collider experiments · If the result would match the observations, we could claim to understand the early universe up to electroweak temperature · Strong constraints on CP phases from EDM's
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