Electroweak bubble nucleation, nonperturbatively

Moore, Guy D.; Rummukainen, Kari

doi:10.1103/physrevd.63.045002

Cited by 103 publications

(144 citation statements)

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“…This method has been successfully used to measure the sphaleron rate in pure gauge theory [24] and in the Standard Model [12,25], but not yet using the physical Higgs mass. It has also been used to study the bubble nucleation rate in first-order electroweak phase transition [26] at unphysically small Higgs mass.…”

Section: Introductionmentioning

confidence: 99%

Sphaleron Rate in the Minimal Standard Model

2014

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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

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Section: Introductionmentioning

confidence: 99%

Sphaleron Rate in the Minimal Standard Model

2014

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“…where Γ sph is the diffusion rate of the Chern-Simons number as measured by lattice simulations [16]: Γ sph = (20 ± 2)α 5 w T . The exponential accounts for sphaleroninduced relaxation of the baryon asymmetry back to zero due to restoration of thermal equilibrium, in the limit of a very slowly moving wall.…”

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confidence: 99%

New Source for Electroweak Baryogenesis in the Minimal Supersymmetric Standard Model

2000

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One of the most experimentally testable explanations for the origin of the baryon asymmetry of the universe is that it was created during the electroweak phase transition, in the minimal supersymmetric standard model. Previous efforts have focused on the current for the difference of the two Higgsino fields, H1 − H2, as the source of biasing sphalerons to create the baryon asymmetry. We point out that the current for the orthogonal linear combination, H1 + H2, is larger by several orders of magnitude. Although this increases the efficiency of electroweak baryogenesis, we nevertheless find that large CP-violating angles ≥ 0.15 are required to get a large enough baryon asymmetry. PACS: 98.80.Cq 1. A highly constrained proposal for the origin of baryonic matter in the universe is electroweak baryogenesis in the minimal supersymmetric standard model (MSSM) [1][2][3][4][5][6]. Unlike many other baryogenesis mechanisms, this one has strong prospects for being falsified in upcoming experiments, due to its need for some light exotic particles, notably a right-handed top squark which is lighter than the top quark [7,8].The basic mechanism [9] is intuitively clear: particles interact in a CP-violating manner with bubble walls, which form during the first order electroweak phase transition, when the temperature of the universe was near T = 100 GeV. This causes a buildup of a left-handed quark density in excess of that of the corresponding antiquarks, and an equal and opposite right-handed asymmetry, so that there is initially no net baryon number. The left-handed quark asymmetry biases anomalous sphaleron interactions, present within the standard model, to violate baryon number preferentially to create a net quark density. The resulting baryon asymmetry of the universe (BAU) soon falls inside the interiors of the expanding bubbles, where the sphaleron interactions are shut off, and thus baryon number is safe from subsequent sphaleron-induced relaxation to zero.Despite the simplicity of this idea, a quantitatively accurate calculation is difficult to carry out. Various approximations have been made, leading to a variety of formalisms which give somewhat conflicting predictions for the dependence of the BAU on the parameters of the MSSM. Although most authors agree on the diffusion equations which govern the generation of the left-handed quark asymmetry, there is less consensus about how to derive the source terms which appear in these equations.In a previous paper [5], we advocated an approach based on the classical force on particles [10,11] due to their spatially varying masses as inside the bubble wall. It is straightforward to solve for this force, put it into the Boltzmann equations, and derive corresponding diffusion equations. No ad hoc assumptions are needed; one only requires that the width of the wall be significantly larger than thermal de Broglie wavelengths of particles in the plasma, to justify an expansion in derivatives of the background Higgs field, which constitutes the bubble wall. Detailed calculations o...

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“…In order to address the question of hadronization after a first-order transition in a heavy ion collision picture, one should then perform finite-size real-time lattice simulations. In fact, lattice methods have been successfully applied to the study of homogeneous nucleation in different contexts [2,27,28]. One can thereby avoid the drawbacks implied by analytical approximations, such as the thin-wall hypothesis.…”

Section: ∼ O(10mentioning

confidence: 99%

Finite-size constraints on nucleation of hadrons in a quark-gluon plasma

Fraga

Venugopalan

2004

Braz. J. Phys.

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We discuss finite-size effects on homogeneous nucleation in first-order phase transitions. We study their implications for cosmological phase transitions and to the hadronization of a quark-gluon plasma generated in high-energy heavy ion collisions.Finite-size scaling has achieved an immense success in the study of equilibrium critical phenomena. On the other hand, systematic studies of finite size effects in the case of metastable decays and other nonequilibrium processes are rare [1,2]. In this paper, we discuss finite size effects on the dynamics of homogeneous nucleation in a first-order temperature-driven transition (For more details, see [3]). In particular, we consider the case of cosmological phase transitions in the early universe [4], and that of a quark-gluon plasma (QGP) decay into hadronic matter in a high-energy heavy ion collision [5,6]. The former might provide sensible mechanisms to explain the baryon number asymmetry in the universe and primordial nucleosynthesis [7,8], whereas the latter is expected to be observed [9] at BNL Relativistic Heavy Ion Collider (RHIC). The length and time scales involved in each of these cases differ by several orders of magnitude.In the usual description of homogeneous nucleation [1], there are two ways in which the finite size of the system can affect the formation and evolution of bubbles and, consequently, the dynamics of phase conversion. Firstly, one has to consider the effects on the nucleation rate and the early stage growth of the bubbles. As will be shown below, this correction comes about through an intrinsic uncertainty in the determination of the supercooling undergone by the system. For the cases considered here, it brings only minor modifications to a description which assumes an infinite system. The second and, in general, most important finite-size effect is its influence on the domain coarsening process, or late-stage growth of the bubbles. The relevant length scales here are the typical size of the system, the radius of the critical bubble and the correlation length.In a continuum description of a first-order phase transition, it is common to consider a coarse-grained free energy, F , of the Landau-Ginzburg form with temperaturedependent coefficients [1]. (In the case of QCD, such a free energy can be obtained, for instance, from the oneloop effective potential of a linear sigma model coupled to quarks [10,11].) The nucleation rate can be expressed as Γ = P e −F b /T , where F b is the free energy of a critical bubble, with radius R c , and the prefactor P measures statistical and dynamical fluctuations about the saddle point of the Euclidean action in functional space. It is convenient to write the prefactor P as a product of the bubble's growth rate and a factor proportional to the ratio of the determinant of the fluctuation operator around the bubble configuration relative to that around the homogeneous metastable state [12]. For the relativistic case, in the thin-wall limit, we have [13]:Here, η and ξ are respectively the shear viscosity and ...

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Electroweak bubble nucleation, nonperturbatively

Cited by 103 publications

References 84 publications

Sphaleron Rate in the Minimal Standard Model

Sphaleron Rate in the Minimal Standard Model

New Source for Electroweak Baryogenesis in the Minimal Supersymmetric Standard Model

Finite-size constraints on nucleation of hadrons in a quark-gluon plasma

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