Electroweak Baryon Research Articles

Dynamics of Electroweak Phase Transition in the 3-3-1-1 Model

The bubble nucleation in the framework of 3-3-1-1 model is studied. Previous studies show that first order electroweak phase transition occurs in two periods. In this paper we evaluate the bubble nucleation temperature throughout the parameter space. Using the stringent condition for bubble nucleation formation we find that in the first period, symmetry breaking from \(SU(3)\rightarrow SU(2)\), the bubble is formed at the nucleation temperature $T=150$ GeV and the lower bound of the scalar mass is 600 GeV. In the second period, symmetry breaking from \((SU(2)\rightarrow U(1)\), only subcritical bubbles are formed. This constraint eliminates the electroweak baryon genesis in the second period of the model.

Topological Dark Matter from the Theory of Composite Electroweak Symmetry Breaking**Supported by National Science Foundation of China (NSFC) under Grant Nos. 11273013, 11475071, 11547308, and the Seeds Funding of Jilin University, the National Science Foundation of Jilin Province under Grant No. 20180101228JC

The lightest electroweak baryon as a topological object is investigated by using a general effective Lagrangian of composite electroweak symmetry breaking and the spin-independent electroweak baryon-nucleon scattering cross section is calculated. We explicitly show the masses of the electroweak baryons and the cross section as functions of the Peskin-Takeuchi S parameter and the ratio of the masses of axial-vector and vector composite bosons. We find that it is acceptable to regard the electroweak baryon as a dark matter candidate and the even number of technicolor is favored.

Indications on the mass of the lightest electroweak baryon

In general, an effective low-energy Lagrangian model of composite electroweak symmetry breaking contains soliton solutions that may be identified with technibaryons. We recall how the masses of such states may be related to the coefficients of fourth-order terms in the effective Lagrangian, and review the qualitative success of this approach for baryons in QCD. We then show how the current theoretical and phenomenological constraints on the corresponding fourth-order coefficients in the electroweak theory could be used to estimate qualitative lower and upper bounds on the lightest electroweak baryon mass. We also discuss how the sensitivity of the LHC experiments could enable these bounds to be improved.

Dynamical simulations of electroweak baryogenesis with fermions

We perform real-time numerical lattice simulations of a one-family version of the Standard Model. We model the quantum fermions using the ensemble method and treat the bosonic scalar and non-abelian gauge fields classically. Our main interest is electroweak baryogenesis, and we test the approach by considering Standard Model baryon number violation through the chiral anomaly, a truly quantum phenomenon. We find that the method correctly reproduces the anomaly, and perform the first dynamical simulations of electroweak baryon number violation including fermions.

Bödeker’s effective theory: From Langevin dynamics to Dyson–Schwinger equations

The dynamics of weakly coupled, non-abelian gauge fields at high temperature is non-perturbative if the characteristic momentum scale is of order | k | ∼ g 2 T . Such a situation is typical for the processes of electroweak baryon number violation in the early Universe. Bödeker has derived an effective theory that describes the dynamics of the soft field modes by means of a Langevin equation. This effective theory has been used for lattice calculations so far [G.D. Moore, Nucl. Phys. B568 (2000) 367. Available from: <hep-ph/9810313>; G.D. Moore, Phys. Rev. D62 (2000) 085011. Available from: <hep-ph/0001216>]. In this work we provide a complementary, more analytic approach based on Dyson–Schwinger equations. Using methods known from stochastic quantitation, we recast Bödeker’s Langevin equation in the form of a field theoretic path integral. We introduce gauge ghosts in order to help control possible gauge artefacts that might appear after truncation, and which leads to a BRST symmetric formulation and to corresponding Ward identities. A second set of Ward identities, reflecting the origin of the theory in a stochastic differential equation, is also obtained. Finally, Dyson–Schwinger equations are derived.

Anomalous commutators and electroweak baryogenesis

Electroweak vacuum transition processes (sphalerons) in the early Universe provide a possible explanation of the baryon asymmetry. Combining this physics with the anomalous commutators of Adler and Boulware and renormalization group invariance, we argue that electroweak baryon number violation also induces a “topological condensate” in the vacuum. QCD sphaleron processes act to distribute the baryon number violation between both left- and right-handed quarks and induce a spin independent component in this “condensate”.

An upper bound on the total cross-section for electroweak baryon number violation

An upper bound on the total cross-section of s-wave electroweak instanton/sphaleron induced baryon plus lepton number violating processes is presented. It is obtained by exploiting a recently reported lower bound on the corresponding tunneling suppression exponent and by estimating the pre-exponential factor. We find that the present knowledge about electroweak baryon plus lepton number violating processes still allows their eventual observability at the Very Large Hadron Collider, even as pure s-wave scattering. A possibly observable rate at cosmic ray facilities and neutrino telescopes is presently not excluded, but requires a substantial contribution from higher partial waves.

Observing B-violation in relativistic heavy-ion collisions

Under certain situations, partons formed in heavy-ion collision experiments may expand out forming a shell-like structure. The partons in the outer shell subsequently hadronize, leaving a bubble of pure deconfined vacuum for a first-order quark-hadron phase transition. The bubble collapses and may eventually decay into particles which may thermalize to temperatures exceeding the electroweak transition temperature (100 GeV) at LHC. This will lead to the possibility of unsuppressed electroweak baryon number violating processes.

Spectral flow of chiral fermions in nondissipative Yang-Mills gauge field backgrounds

Real-time anomalous fermion number violation is investigated for massless chiral fermions in spherically symmetric SU(2) Yang-Mills gauge field backgrounds which can be weakly dissipative or even nondissipative. Restricting consideration to spherically symmetric fermion fields, the zero-eigenvalue equation of the time-dependent effective Dirac Hamiltonian is studied in detail. For generic spherically symmetric SU(2) gauge fields in Minkowski spacetime, a relation is presented between the spectral flow and two characteristics of the background gauge field. These characteristics are the well-known ``winding factor,'' which is defined to be the change of the Chern-Simons number of the associated vacuum sector of the background gauge field, and a new ``twist factor,'' which can be obtained from the zero-eigenvalue equation of the effective Dirac Hamiltonian but is entirely determined by the background gauge field. For a particular class of (weakly dissipative) Luscher-Schechter gauge field solutions, the level crossings are calculated directly and nontrivial contributions to the spectral flow from both the winding factor and the twist factor are observed. The general result for the spectral flow may be relevant to electroweak baryon number violation in the early universe.

High temperature color conductivity at next-to-leading log order

The non-Abelian analogue of electrical conductivity at high temperature has previously been known only at leading logarithmic order --- that is, neglecting effects suppressed only by an inverse logarithm of the gauge coupling. We calculate the first sub-leading correction. This has immediate application to improving, to next-to-leading log order, both effective theories of non-perturbative color dynamics, and calculations of the hot electroweak baryon number violation rate.

Nonperturbative dynamics of hot non-Abelian gauge fields: Beyond the leading log approximation

Many aspects of high-temperature gauge theories, such as the electroweak baryon number violation rate, color conductivity, and the hard gluon damping rate, have previously been understood only at leading logarithmic order (that is, neglecting effects suppressed only by an inverse logarithm of the gauge coupling). We discuss how to systematically go beyond leading logarithmic order in the analysis of physical quantities. Specifically, we extend to next-to-leading-log order (NLLO) the simple leading-log effective theory due to B\"odeker that describes non-perturbative color physics in hot non-Abelian plasmas. A suitable scaling analysis is used to show that no new operators enter the effective theory at next-to-leading-log order. However, a NLLO calculation of the color conductivity is required, and we report the resulting value. Our NLLO result for the color conductivity can be trivially combined with previous numerical work by Moore to yield a NLLO result for the hot electroweak baryon number violation rate.

From hard thermal loops to Langevin dynamics

In hot non-Abelian gauge theories, processes characterized by the momentum scale g 2 T (such as electroweak baryon number violation in the very early universe) are non-perturbative. An effective theory for the soft (| p| ∼ g 2T) field modes is obtained by integrating out momenta larger than than g 2 T. Starting from the hard thermal loop effective theory, which is the result of integrating out the scale T, it is shown how to integrate out the scale gT in an expansion in the gauge coupling g. At leading order in g, one obtains Vlasov-Boltzmann equations for the soft field modes, which contain a Gaussian noise and a collision term. The 2-point function of the noise and the collision term are explicitly calculated in a leading logarithmic approximation. In this approximation the Boltzmann equation is solved. The resulting effective theory for the soft field modes is described by a Langevin equation. It determines the parametric form of the hot baryon number violation rate as Γ = κg 10 log(1/ g) gT 4, and it allows for a calculation for κ on the lattice.

Longitudinal subtleties in diffusive Langevin equations for non-Abelian plasmas

B\"odeker has recently argued that non-perturbative processes in very high temperature non-Abelian plasmas (such as electroweak baryon number violation in the very hot early Universe) can be quantitatively described, to leading logarithmic accuracy, by a simple diffusive effective theory. B\"odeker's effective theory is intended to describe the long-distance transverse electric and magnetic fields which are responsible for non-perturbative dynamics. His effective theory, however, also contains long-wavelength longitudinal electric fields. We discuss several subtleties in the treatment of longitudinal dynamics which were not closely examined in B\"odeker's original treatment. Somewhat to our surprise, we find that within its domain of validity B\"odeker's effective theory does correctly describe both longitudinal and transverse fluctuations. We also show that, as far as the transverse dynamics of interest is concerned, B\"odeker's effective theory could be replaced by a transverse-only theory that removes the longitudinal dynamics altogether. In the process, we discuss several interesting aspects of stochastic field theories.

Effective dynamics of hot, soft non-Abelian gauge fields: Color conductivity and log(1/α)effects

B\"odeker has recently argued that non-perturbative processes in very high temperature non-Abelian plasmas (such as electroweak baryon number violation in the very hot early Universe) are logarithmically enhanced over previous estimates and take place at a rate per unit volume of order ${\ensuremath{\alpha}}^{5}{T}^{4}\mathrm{ln}(1/\ensuremath{\alpha})$ for small coupling. We give a simple physical interpretation of B\"odeker's qualitative and quantitative results in terms of Lenz's Law---the fact that conducting media resist changes in the magnetic field---and earlier authors' calculations of the color conductivity of such plasmas. In the process, we resolve some confusion in the literature about the value of the color conductivity and present an independent calculation. We also discuss the issue of whether the classical effective theory proposed by B\"odeker has a good continuum limit.

Effective dynamics of soft non-Abelian gauge fields at finite temperature

We consider time dependent correlation functions of non-Abelian gauge fields at finite temperature. An effective theory for the soft (p∼g2T) field modes is derived by integrating out the field modes with momenta of order T and of order gT in a leading logarithmic approximation. In this effective theory the time evolution of the soft fields is determined by a local Langevin-type equation. As an application, the rate for hot electroweak baryon number violation is estimated as Γ∼g2log(1/g)(g2T)4. Furthermore, possible consequences for non-perturbative lattice computations of unequal time correlation functions are discussed.

The hot baryon violation rate isO(αw5T4)

The rate per unit volume for anomalous electroweak baryon number violation at high temperatures, in the symmetric phase, has been estimated in the literature to be $O({\ensuremath{\alpha}}_{\mathrm{w}}^{4}{T}^{4})$ based on simple scaling arguments. We argue that damping effects in the plasma suppress the rate by an extra power of ${\ensuremath{\alpha}}_{\mathrm{w}}$ to give $O({\ensuremath{\alpha}}_{\mathrm{w}}^{5}{T}^{4})$. We show how to understand this effect in a variety of ways ranging from an effective description of the long-distance modes responsible for baryon number violation to a microscopic picture of the short-distance modes responsible for damping. In particular, we resolve an old controversy as to whether damping effects are relevant. Finally, we argue that similar damping effects should occur in numerical simulations of the rate in classical thermal field theory on a spatial lattice, and we point out a potential problem with simulations in the literature that have not found such an effect.

Электрослабое несохранение барионного числа в ранней Вселенной и в столкновениях частиц при высоких энергиях

Электрослабое несохранение барионного числа в ранней Вселенной и в столкновениях частиц при высоких энергиях, Рубаков В.А., Шапошников М.Е.

Baryon and lepton number assignment in E6 models.

In ${\mathrm{E}}_{6}$ models there are new particles whose baryon number is not uniquely assigned. We point out that the baryon and lepton number assignment to these particles can change the baryogenesis scenario significantly. We consider a left-right symmetric extension of the standard model in which the (B-L) quantum number is gauged. The identification of (B-L) with a generator of ${\mathrm{E}}_{6}$ is used to define the baryon and lepton numbers for the exotic particles in a way that the electroweak baryon and lepton number anomaly corresponding to the SU(2${)}_{\mathit{L}}$ group vanishes; i.e., there is no nonperturbative baryon or lepton number violation during the electroweak phase transition. We study some consequences of the new assignment.

Monte Carlo simulation of baryon and lepton number violating processes at high energies

We report results obtained with the first complete event generator for electroweak baryon and lepton number violating interactions at supercolliders. We find that baryon number violation would be very difficult to establish, but lepton number violation can be seen provided at least a few hundred L violating events are available with good electron or muon identification in the energy range 10 GeV to 1 TeV.

Total cross section for anomalous fermion-number violation via dispersion relation

We investigate the behaviour of the total cross section for electroweak baryon and lepton number violation (in association with multi-W and multi-Higgs production) at low energies (√ s < O(10)TeV) by means of a dispersion relation. The imaginary part of the relevant forward elastic scattering amplitude is calculated in a saddle-point approximation, systematically introduced by the so-called valley method. Taking into account the first correction to the basic instanton result (and neglecting the higher order corrections) we find that the total cross section does not get exponentially large. The question whether the cross section becomes of observable size remains still open, however.