Sphaleron Rate in the Minimal Standard Model

Abstract

We use large-scale lattice simulations to compute the rate of baryon number violating processes (the sphaleron rate), the Higgs field expectation value, and the critical temperature in the Standard Model across the electroweak phase transition temperature. While there is no true phase transition between the high-temperature symmetric phase and the low-temperature broken phase, the crossover is sharply defined at Tc = (159 ± 1) GeV. The sphaleron rate in the symmetric phase (T > Tc) is Γ/T 4 = (18 ± 3)α 5 W , and in the broken phase in the physically interesting temperature range 130 GeV < T < Tc it can be parametrized as log(Γ/T 4 ) = (0.83 ± 0.01)T /GeV − (147.7 ± 1.9). The freeze-out temperature in the early Universe, where the Hubble rate wins over the baryon number violation rate, is T * = (131.7 ± 2.3) GeV. These values, beyond being intrinsic properties of the Standard Model, are relevant for e.g. low-scale leptogenesis scenarios. Introduction:The current results from the LHC are in complete agreement with the Standard Model of particle physics: a Higgs boson with the mass of 125 -126 GeV has been discovered [1], and no evidence of exotic physics has been observed. If the Standard Model is indeed the complete description of the physics at the electroweak scale, the electroweak symmetry breaking transition in the early Universe was a smooth cross-over from the symmetric phase at T > T c , where the (expectation value of the) Higgs field was approximately zero, to the broken phase at T < T c GeV where it is finite, reaching the experimentally determined value |φ| ≃ 246/ √ 2 GeV at zero temperature. The cross-over temperature T c is somewhat larger than the Higgs mass. The nature of the transition was settled already in 1995-98 using lattice simulations [2][3][4][5], which indicate a first-order phase transition at Higgs masses < ∼ 72 GeV, and a cross-over otherwise.A smooth cross-over means that the standard electroweak baryogenesis scenarios [6,7] are ineffective. These scenarios produce the matter-antimatter asymmetry of the Universe through electroweak physics only, and they require a strong first-order phase transition, with supercooling and associated out-of-equilibrium dynamics. Thus, the origin of the baryon asymmetry must rely on physics beyond the Standard Model.Baryogenesis at the electroweak scale is possible in the first place through the existence of the chiral anomaly relating the baryon number of fermions to the topological Chern-Simons number N cs of the electroweak SU(2) gauge fields

NA62 sensitivity to heavy neutral leptons in the low scale seesaw model

“…The Yukawa couplings F ai generally violate CP, and the interactions of the ν R in the early universe can potentially generate a matter-antimatter asymmetry in the primordial plasma. At temperatures above T sph = 130 GeV [8] this asymmetry can be converted into a net baryon number by weak sphalerons [9]. This process called leptogenesis can either occur during the freeze out and decay of the ν R [10] ("freeze out scenario") or during their production [11][12][13] ("freeze in scenario").…”

Leptogenesis constraints on B − L breaking Higgs boson in TeV scale seesaw models

“…of eq. (2.2), this extra process could significantly dilute the RHN number density before the sphaleron decoupling temperature T c 131.7 GeV [53], thus potentially making type-I seesaw freeze-out leptogenesis ineffective, as we show below. 4 In general, the dilution effect depends on the RHN mass m N , the scalar mass m H, A , the effective Yukawa coupling f H,A and other model parameters such as the effective neutrino mass m ≡ v 2 (Y † Y ) 11 /m N (or Dirac Yukawa coupling) and the CP asymmetry ε CP , as well as the CP property of the extra scalar.…”

One-loop considerations for coexisting vacua in the CP conserving 2HDM

“…The model also allows the possibility of other sources of CP violation [8,9], a feature that gets even richer when more doublet copies are added [10]. Finally, a more complex scalar sector can generate a strong enough EW first-order phase transition [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27], a property that is lacking in the SM [28][29][30][31][32][33] but is necessary to explain the matter-antimatter asymmetry of our universe.…”