Electroweak baryogenesis fails in the SM because of too small CP violation
and the lack of a strong first-order phase transition. It has been shown that
supersymmetric models allow for successful baryogenesis, where the Higgsinos
play an important role in the transport processes that generate the asymmetry.
I will demonstrate that also non-supersymmetric models can provide the observed
baryon asymmetry. The top quark takes the role of the Higgsinos. Focusing on
the two-Higgs doublet model, I will discuss details of the phase transition and
consequences for Higgs physics and EDM searches.Comment: 5 pages, 2 figures. Proceedings of Moriond 2006, Electroweak Session.
  11-18 March, La Thuile (Italy

Huber, Stephan J.

English

arXiv

Electroweak baryogenesis fails in the SM because of too small CP violation and the lack of a strong first-order phase transition. It has been shown that supersymmetric models allow for successful baryogenesis, where the Higgsinos play an important role in the transport processes that generate the asymmetry. I will demonstrate that also non-supersymmetric models can provide the observed baryon asymmetry. The top quark takes the role of the Higgsinos. Focusing on the two-Higgs doublet model, I will discuss details of the phase transition and consequences for Higgs physics and EDM searches

CERN Document Server

arXiv:hep-ph/0606009v1  1 Jun 2006Electroweak Baryogenesis in a Two-Higgs Doublet ModelStephan J. HuberCERN, Theory Division, CH-1211 Geneva 23, SwitzerlandElectroweak baryogenesis fails in the SM because of too small CP violation and the lack of astrong first-order phase transition. It has been shown that supersymmetric models allow forsuccessful baryogenesis, where the Higgsinos play an important role in the transport processesthat generate the asymmetry. I will demonstrate that also non-supersymmetric models canprovide the observed baryon asymmetry. The top quark takes the role of the Higgsinos.Focusing on the two-Higgs doublet model, I will discuss details of the phase transition andconsequences for Higgs physics and EDM searches.1 IntroductionThe baryon asymmetry may have been generated at temperatures much higher than the elec-troweak scale, e.g. through the decay of superheavy right-handed neutrinos 1 or even squarks 2.While these proposals seem to be perfectly viable, they are now, and may remain for some time,very difficult to test. Electroweak baryogenesis, on the other hand, relies on physics which willbe probed at future colliders, at the first place the LHC.In recent years, electroweak baryogenesis has mostly been studied in the context of super-symmetric models, such as the MSSM 3,4 or the NMSSM 5. The CP-violating interactions ofthe Higgsinos with the expanding bubble walls generate source terms in the Boltzmann equa-tions which drive the baryogenesis process. It is an interesting question if non-supersymmetricmodels can also generate the observed baryon asymmetry. It was the result of refs. 6,7 that thisis possible in a general effective field theory approach, where the SM Higgs sector is augmentedby dimension-six operators to induce a first-order phase transition and to provide additional CPviolation. Here we show that a simple two-Higgs doublet model (2HDM) can explain the baryonasymmetry, without being in conflict with collider bounds on the Higgs mass or electric dipolemoment (EDM) searches 8.300320340360380400420440120 130 140 150 160 170 180 190mHmhξ = 1.0ξ = 1.5ξ = 2.0ξ = 2.5Lw = 2/TcLw = 3/TcLw = 5/TcLw = 10/TcLw = 15/Tc∆ = 0.5Figure 1: Lines of constant ξ and Lw in the mh–mH plane for µ23 = 10000 GeV2 and φ = 0.2. In addition, theline of the relative size of the one-loop corrections ∆ = max |δλi/λi| = 0.5 is shown. The Higgs masses are givenin units of GeV.2 The phase transitionWe consider a 2HDM of type II, where the discrete symmetry, introduced to eliminate flavorviolation at the tree-level, is softly broken. The most general potential takes the formV0(H1,H2) = −µ21H†1H1 − µ22H†2H2 − µ23(eiφH†1H2 + h.c.)+λ12(H†1H1)2 +λ22(H†2H2)2 + λ3(H†1H1)(H†2H2)+λ4|H†1H2|2 +λ52((H†1H2)2 + h.c.). (1)The model allows us to introduce a single CP-violating phase, which can be attributed to thesoft mass parameter µ23eiφ. In addition to the SM Higgs, the 2HDM contains two extra neutraland charged Higgs particles. In the presence of CP violation, the 3 neutral Higgs states aremixtures, with a scalar and pseudoscalar content, and masses m2Hi .To reduce the number of parameters, we focus on the case where the extra Higgs states areheavy and degenerate in mass, i.e. mH = mH2 = mH3 = mH± . These states will obtain theirlarge masses from order unity self couplings λi. There is also a lighter SM-like Higgs, with amass mh = mH1 that has to fulfill the standard LEP bound of 114 GeV. With this choice largeoblique corrections are avoided. We also fix the Higgs vev ratio at tanβ = 1. There is also alower limit on the charged Higgs mass from b→ sγ 9 which will be automatically satisfied in ourparameter region of interest. To V0 we add the one-loop Coleman–Weinberg corrections of theheavy Higgs states and the top quark. The Higgs masses are computed from the full one-looppotential.To study the electroweak phase transition, we have to compute the finite-temperature effec-tive potential. We include the one-loop corrections of the heavy Higgs states, the top quark andthe gauge bosons. Since the high-temperature approximation is not valid for the heavy Higgses,we rather use an interpolation to the full one-loop results.The strength of the resulting electroweak phase transition is shown in fig. 18 for a particularparameter set. Here ξ =√v21c + v22c/Tc should be larger than 1, so that the phase transition isstrong enough to avoid baryon number washout. As mH increases, the phase transition becomesstronger. This somewhat counter-intuitive result is due to the fact that the larger Higgs massescome from larger quartic couplings. So this limit actually does not lead to the decoupling ofthe heavy states. At some point perturbation theory will finally break down. We find thatin our example the phase transition becomes sufficiently strong for mH & 300 GeV, wherethe size of the zero-temperature one-loop corrections relative to the tree-level terms is about15%, so that perturbation theory is well under control. Fig. 1 also shows the line where thecorrections become 50%. Even for light Higgs masses of mh ∼ 200 GeV the phase transitioncan be sufficiently strong 8. So there is a wide parameter range, where the phase transition isconsistent with electroweak baryogenesis. These results agree with the findings of ref. 11.The CP-violating phase φ has only a minor impact on the phase transition. We also showthe thickness of the expanding bubble walls, Lw. As the phase transition gets stronger, the wallsbecome thinner. In the largest part of the parameter space the walls are thick, i.e. LwTc ≫ 1.Along the bubble wall also the relative complex phase between the two Higgs vevs, θ, changes.In principle one has to numerically solve the field equations of the Higgs fields, using an algorithmsuch as the one recently proposed in ref. 10. In an approximation, we compute the θ-profile byminimizing the thermal potential at Tc with respect to v2 and θ, at fixed values of v1, betweenthe symmetric and broken phase. For example, we find that for mh = 150 GeV, mH = 350 GeV,µ23 = 10000 GeV2 and φ = 0.2 the phase changes from θsym = −0.29 to θbrk = −0.068. Later onwe will approximate the profiles of vi and θ by a kink ansatz with common wall thickness Lw.3 The baryon asymmetryThe CP-violating interactions of particles in the plasma with the bubble wall create an excess ofleft-handed quarks over the corresponding antiquarks. This excess diffuses into the symmetricphase, where the left-handed quark density biases the sphaleron transitions to generate a netbaryon asymmetry. Since the bubble walls are thick, we can apply the WKB formalism 12,3,7,and obtain different dispersion relations for particles and antiparticles in the space-time depen-dent background of the Higgs expectation values. The dispersion relations then lead to forceterms in the transport equations.In the 2HDM, baryogenesis is driven by top transport. The top quark dispersion relation tofirst order in gradients is given by 7,13E = E0 ±∆E = E0 ±θ′tm2t2E0E0z, (2)where E0 =√p2 +m2t and E0z =√p2z +m2t , in terms of the kinetic momentum, and θt isthe phase of the top quark mass. The prime denotes the derivative with respect to z, thecoordinate perpendicular to the bubble wall. The upper and the lower sign corresponds toparticles and antiparticles, respectively. In ref. 7 this dispersion relation was derived from theone-particle Dirac equation, and shown to match the result of the more rigorous Schwinger–Keldysh formalism13. The change in θt along the bubble wall is given by ∆θt = ∆θ/(1+tan2 β),assuming that tan β is constant along the wall 14. So there is an additional suppression of ∆θtfor large tan β.The transport processes in the hot plasma are described by Boltzmann equations. Top andbottom quarks, and the Higgs bosons are the most important particle species. The other quarkflavors and the leptons can be neglected thanks to their small Yukawa couplings.We use a fluidansatz for the particle distribution functions. The CP-violating top dispersion relations enteras force terms that source the transport equations. We take into account W -scatterings, thetop Yukawa interaction, the strong sphalerons, the top helicity flips and Higgs number violationwith rates ΓW , Γy, Γss, Γm and Γh, respectively, where the latter two are only present in the 300 320 340 360 380 400 120  130  140  150  160  170  180  190ηB=5ηB=10ηB=20ηB=40ηB=60mHmhξ=1Figure 2: Contours of constant ηB in the mh–mH plane for µ23 = 10000 GeV2 and φ = 0.2. The Higgs masses aregiven in units of GeV and ηB in units of 10−11.broken phase. The explicit expressions of the transport equations are given in ref. 8 and followref. 7.In fig. 2 we show the baryon asymmetry ηB = nB/s in the mh–mH plane, fixing againµ23 = 10000 GeV2 and φ = 0.2. The observational value is 15 ηB = (8.7 ± 0.3) × 10−11. Foreach mass combination we determine all relevant properties of the phase transition, such as ξ,Lw, θsym and θbrk to put them into the transport equations. There is only a mild dependenceof the baryon asymmetry on the wall velocity, so we consider only a single value, vw = 0.1. Inaddition, the (ξ=1)-contour of fig. 1 is also shown for orientation. As we increase mH , leavingmh fixed, the asymmetry becomes larger. This behavior results from the m2t ∼ ξ2 dependenceof the top source term. Accordingly the baryon asymmetry becomes larger for a stronger phasetransition. If we increase mh, leaving the heavy Higgs mass fixed, ηB becomes smaller andreaches a minimum at mh ≈ 150–160 GeV, similar to the behavior of Lw. But in general thereis only a minor dependence on the light Higgs mass. In this parameter setting it is possible togenerate the observed baryon asymmetry for a heavy Higgs mass between 320 and 330 GeV anda light Higgs mass up to 160 GeV. Since ηB is more or less proportional to the CP-violatingphase φ, the measured value can also be explained for other values of the parameters if we adjustφ.One can also compute the EDMs of the electron and neutron, induced by scalar–pseudoscalarmixing in the neutral Higgs sector. The dominant contributions are arise from two-loop Barr–Zeetype diagrams. Since there is only a single complex phase in the model, we can predict |de| and|dn| in terms of the baryon asymmetry and the Higgs masses. We find that |dn| & 10−27e cm.For the smallest allowed values of mh and mH , |dn| can slightly exceed the experimental boundof 3× 10−26e cm. Improving the neutron EDM sensitivity by an order of magnitude would testa substantial part of the parameter space of the model. The electron EDM is typically one totwo orders of magnitude below the bound of 1.6 × 10−27e cm. These values are for tan β = 1.Extrapolating our results suggests that for tan β & 10, the 2HDM cannot produce the observedbaryon asymmetry without being in conflict with the EDM constraints. In any case, the 2HDMcan explain the baryon asymmetry for a considerable range of the model parameters.4 SummaryWe have studied electroweak baryogenesis in the 2HDM, focusing on the case of tanβ = 1 anddegenerate extra Higgs states. The phase transition is strengthened by the loop contributionsof the extra Higgs states, provided these are sufficiently strongly coupled. Taking µ23 = 10000GeV2, this happens for a common heavy Higgs mass mH & 300 GeV. The mass of the light,SM-like Higgs, mh, can be up to 200 GeV, or even larger. The Higgs potential allows us tointroduce of a single CP-violating phase, which induces a varying phase between the two Higgsvevs along the bubble wall. We compute the CP-violating source term of the top quark inthe WKB approximation and solve the resulting transport equations, using the formalism ofref. 7. We find that for typical parameter values the baryon asymmetry is in the range of theobserved value. Since there is only a single complex phase in the model, we can predict theelectric dipole moments in terms of the baryon asymmetry and the Higgs masses. We find that|dn| & 10−27e cm. Improving the neutron EDM sensitivity by an order of magnitude would testa substantial part of the parameter space of the model. The electron EDM is typically one totwo orders of magnitude below the bound. Large values of tanβ suppress the baryon asymmetry.AcknowledgementsI wish to thank L. Fromme and M. Seniuch for enjoyable collaboration on this project. I wouldalso like to thank the conference organizers and acknowledge the financial support of a MarieCurie grant.References1. M. Fukugita and T. Yanagida, Phys. Lett. B174 (1986) 45; W. Buchmu¨ller, R.D. Pecceiand T. Yanagida, Ann. Rev. Nucl. Part. Sci. 55 (2005) 311 [hep-ph/0502169].2. S.J. Huber, JCAP 0602 (2006) 008 [hep-ph/0508208].3. J.M. Cline, M. Joyce and K. Kainulainen, JHEP 0007 (2000) 018 [hep-ph/0006119]; Er-ratum added online, Oct/2/2001.4. S.J. Huber, P. John, M.G. Schmidt, Eur. Phys. J. C20 (2001) 695 [hep-ph/0101249];M. Carena, M. Quiros, M. Seco and C.E.M. Wagner, Nucl. Phys. B650 (2003) 24[hep-ph/0208043]; T. Konstandin, T. Prokopec, M.G. Schmidt and M. Seco, Nucl. Phys.B738 (2006) 1 [hep-ph/0505103].5. S.J. Huber and M.G. Schmidt, Nucl. Phys. B606 (2001) 183 [hep-ph/0003122]; A. Menon,D.E. Morrissey and C.E.M. Wagner, Phys. Rev. D70 (2004) 035005 [hep-ph/0404184].6. D. Bo¨deker, L. Fromme, S. J. Huber and M. Seniuch, JHEP 0502 (2005) 026[hep-ph/0412366].7. L. Fromme and S. J. Huber, hep-ph/0604159.8. L. Fromme, S. J. Huber and M. Seniuch, hep-ph/0605242.9. M. Neubert, Eur. Phys. J. C40 (2005) 165 [hep-ph/0408179].10. T. Konstandin and S.J. Huber, hep-ph/0603081.11. J.M. Cline and P.A. Lemieux, Phys. Rev. D55 (1997) 3873 [hep-ph/9609240].12. M. Joyce, T. Prokopec and N. Turok, Phys. Rev. Lett. 75 (1995) 1695, Erratum ibid. 75(1995) 3375 [hep-ph/9408339]; Phys. Rev. D53 (1996) 2958 [hep-ph/9410282].13. T. Prokopec, M.G. Schmidt and S. Weinstock, Ann. Phys. 314 (2004) 208[hep-ph/0312110]; Ann. Phys. 314 (2004) 267 [hep-ph/0406140].14. S.J. Huber, P. John, M. Laine and M.G. Schmidt, Phys. Lett. B475 (2000) 104[hep-ph/9912278].15. D.N. Spergel et al., astro-ph/0603449.

Electroweak Baryogenesis in a Two-Higgs Doublet Model

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