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Standard Model Baryogenesis CERN-TH. 7368/94. LPTHE Orsay-94/71 HD-THEP-94-24 hep-ph/yymmnnn Standard Mo del Baryogenesis M.B. Gavela, P.Hernandez, J. Orlo and O.Pene Contribution to the XXIXth Rencontre de Moriond, \Electroweak Interactions and Uni ed Theories". Presented byM.B.Gavela CERN, TH Division, CH-1211, Geneva 23, Switzerland Abstract Simply on CP arguments, we argue against a Standard Mo del ex- planation of baryogenesis via the charge transp ort mechanism. A CP- asymmetry is found in the re ection co ecients of quarks hitting the electroweak phase b oundary created during a rst order phase transi- tion. The problem is analyzed b oth in an academic zero temp erature case and in the realistic nite temp erature one. At nite temp era- ture, a crucial role is played by the damping rate of quasi-quarks in a hot plasma, which induces loss of spatial coherence and suppresses re ection on the b oundary even at tree-level. The resulting baryon asymmetry is many orders of magnitude b elow what observation re- quires. We commentaswell on related works. HEP-PH-9407403 1 Intro duction The baryon number to entropy ratio in the observed part of the universe 11 is estimated to b e n =s (4 6)10 [1] . In 1967, A.D. Sakharov [2] B established the three building blo cks required from any candidate theory of baryogenesis: a) Baryon numb er violation, b) C and CP violation, c) Departure from thermal equilibrium. The Standard Mo del (SM) contains a)[3 ] and b)[4], while c) could also b e large enough [5][6], if a rst order SU (2) U (1) phase transition to ok place in the evolution of the universe [7]. An explanation within the SM would b e avery economical solution to the baryon asymmetry puzzle. Unfortunately, intuitive arguments lead to an asymmetry many orders of magnitude b elow observation [8][9]. However, the study of quantum e ects in the presence of a rst order phase transition is rather delicate, and traditional intuition may fail. The authors of ref.[10]have recently studied this issue in more detail and claim that, in the nite temp erature charge transp ort mechanism [11], the SM is close to pro duce enough CP violation as to explain the observed n =s B ratio. In this talk, we summarize our study [12] of the Standard Mo del C and CP e ects in an electroweak baryogenesis scenario. Even if one assumes an optimal sphaleron rate and a strong enough rst order phase transition, we discard this scenario as an explanation of the observed baryon number to entropy ratio. υ=0 υ=/ 0 ψ R inc ψ L ref ψ tr Figure 1: Artistic view of the charge transport mechanism, as describedin the text. The hungry \pacman"represents rapid sphalerons processes. The wiggly lines stand for col lisions with thermal gluons in the nite temperature case; they are absent in the academic T =0 model. Only electroweak loops are depicted, represented by dotted lines. A rst order phase transition can b e describ ed in terms of bubbles of \true" vaccuum (with an inner vaccuum exp ectation value of the Higgs eld v 6= 0) app earing and expanding in the preexisting \false" vaccuum (with v = 0 throughout). We can \zo om" into the vicinity of one of the bubbles. There the curvature of its wall can b e neglected and the world is divided in two zones: on the left hand side, say, v = 0; on the right v 6=0. The actual bubble expands from the broken phase (v 6=0)towards the unbroken one (v = 0). Wework in the wall rest frame in which the plasma ows in the opp osite direction. Consider thus a baryonic ux hitting the wall from the unbroken phase. The heart of the problem lies in the re ection and transmission prop erties of quarks bumpimg on the bubble wall. CP violation distinguishes particles from antiparticles and it is a pr ior i p ossible to obtain a CP asymmetry on the re ected baryonic current, . The induced baryon CP 2 asymmetry is at most n =s 10 ,inavery optimistic estimation of B CP the non-CP ingredients [13][10]. The symmetries of the problem have b een analyzed in detail [14] for a generic bubble. The analytical results corresp ond to the thin wall scenario. The latter provides an adequate physical description for typical momentum of the incoming particles j~pj smaller than the inverse wall thickness l , i.e., j~pj 1=l . For higher momenta, cuto e ects would show up, but it is reasonable to b elieve that the thin wall approximation pro duces an upp er b ound for the CP asymmetry.Wework in a simpli ed scenario with just one spatial direction, p erp endicular to the wall surface: phase space e ects in the 3 + 1 dimension case would further suppress the e ect. The precise questions to answer in the ab ove framework are : 1) the nature of the physical pro cess in terms of particles or quasi-particles resp onsible for CP violation, 2) the order in the electroweak coupling constant, , at which W an e ect rst app ears, 3) the dep endence on the quark masses and the nature of the GIM cancellations involved. We shall consider the problem in two steps: zero temp erature scenario (T = 0) in the presence of a wall with the non-equilibrium situation mim- icked by assuming a ux of quarks hitting the b oundary from just one phase, and nite temp erature case. Intuition indicates that an existing CP violating e ect already present at zero temp erature will diminish when the system is heated b ecause the e ective v.e.v. of the Higgs eld decreases and in con- sequence the fermion masses do as well (only the Yukawa couplings already presentat T = 0 remain unchanged). This intuition can b e misleading only if a new physical e ect, absentat T = 0 and relevant for the problem, app ears at nite temp erature. We discuss and compare the building blo cks of the analysis in b oth cases. The T = 0 case provides a clean analysis of the novel asp ects of the physics in a world with a two-phase vacuum. At nite temp erature, a plasma is an incoherent mixture of states. CP violation is a quantum phenomenon, and can only b e observed when quantum coherence is preserved over time scales larger than or equal to the electroweak time scales needed for CP violation. This is however not the case in the plasma, where the scattering of quasi-quarks with thermal gluons induces a large damping rate, . We show that tree-level re ection is suppressed for any light avour bya factor m=2 . The presently discussed CP-violation observable results from the convolution of this re ection e ect with electroweak lo ops in which the three generations must interfere coherently in order to pro duce an observable CP-violation. It follows that further factors of this typ e app ear in the nal result, which is many orders of magnitude b elow what observation requires and has an \a la Jarlskog"[8] typ e of GIM cancellations. The results of our analysis indicate that in the presence of a rst order 2 phase transition, a CP-asymmetry in the SM app ears at order , has a W conventional typ e of GIM cancellation and chiral limit, and it is well b elow what observation requires in order to solve the baryon asymmetry puzzle. 2 Zero temp erature The necessary CP-o dd couplings of the Cabibb o-Kobayashi-Maskawa (CKM) matrix are at work. Kinematic CP-even phases are also present, equal for particles and antiparticles, whichinterfere with the pure CP-o dd couplings to make them observable. These are the re ection co ecients of a given particle hitting the wall from the unbroken phase. They are complex when the particle energy is smaller than its (broken phase) mass. Finally, as shown in [12 ] [14] , the one lo op self-energy of a particle in the presence of the wall cannot b e completely renormalized away and results in physical transitions. Such an e ect is absent for on-shell particles in a world with just one phase. The di erence is easy to understand: the wall acts as an external source of momentum in the one-lo op pro cess. The transitions b etween anytwo avors of the same charge pro duce a CP violating baryonic ow for any given initial chirality. The essential non-p erturbative e ect is the wall itself. The propagation of any particle of the SM sp ectrum should b e exactly solved in its presence. And this we do for a free fermion, leading to a new Feynman propagator which replaces and generalizes the usual one. The propagator for quarks in the presence of the wall contains massless and massive p oles: ! ! 1 1 1 1 1 1 f i + + + S (q ;q )=1=2 f f f i f i i i =q =q =q m =q m q q +i q q i z z z z 1 1 1 1 z z f i f i =q m =q =q =q m " # m m m 0 1 (1) (1 ) z 0 f f 0 i i =q (=q m) E + p =q (=q m) z where wehave assumed for simplicity zero momentum parallel to the wall i i f f (q = q = q = q = 0).
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