Fermions in electroweak baryogenesis

We study the chiral anomaly by solving the Dirac equation for fermions in parallel electric and magnetic fields. In such case, only the lowest-energy Landau levels are relevant to the anomaly. Specifically, for massless fermions, the chiral anomaly is a result of the production of particles of one chirality, and no creation of particles of the other chirality. For massive fermions, we find that the chiral anomaly equation can be simply obtained via a proper regularization of the range of the momentum. We extend the method to anomaly cancellation, and conclude that the conservation of the baryon number plus lepton number must be violated as a quantum anomaly in the context of the Standard Model. Accordingly, such baryon number non-conservation can play a vital role during the electroweak transition to achieve the baryon asymmetry of the Universe. Through real-time lattice simulations, we refine the implementation of ensemble fermions for a cold electroweak transition, involving the SU (2) gauge field, Higgs field and one generation of fermions. We find that the dynamics and most observables converge quickly with a reasonable number of fermion realizations, and the method of ensemble fermions for the entire electroweak sector becomes numerically tractable. We apply the method to the computation of the effective preheating temperature during a fast electroweak transition, relevant for Cold Electroweak Baryogenesis. We find that the fermion temperature is never below 20 GeV, and this can indirectly rule out Standard Model CP -violation as the origin of the baryon asymmetry of the Universe, as Standard Model cold baryogenesis requires a temperature of at most of order of 1 GeV. For this reason, new CP -violation source from physics beyond the Standard Model is required in order to explain the baryon asymmetry. We further present a first-principles numerical computation of the baryon asymmetry in electroweak-scale baryogenesis, where the CP -violation is obtained as a consequence of including another Higgs doublet. For one particularly favourable scalar potential that could provide a high sphaleron transition rate, we calculate the asymmetry through large-scale computer simulations. The numerical signal is at the boundary of what is numerically discernible with the available computer resources, but we tentatively find an asymmetry of |η| ≤ 3.5 × 10−7 . We also find it is attainable to include the complete electroweak SU (2) × U (1) gauge fields in the reduced Standard Model that we are using in practical simulations, so that in further studies we can measure the cosmic magnetic field generated during the electroweak phase transition

Simulations of Cold Electroweak Baryogenesis: finding the optimal quench time

We revisit the numerical computation of the baryon asymmetry from Cold Electroweak Baryogenesis given the physical Higgs mass. We investigate the dependence of the asymmetry on the speed at which electroweak symmetry breaking takes place. The maximum asymmetry does not occur for arbitrarily fast quenches, but at quench times of about τq ≃ 16m_H^−1, with no asymmetry created for quenches slower than τq > 30m_H^−1. Curiously, we also find that the overall sign of the asymmetry depends on the quench time

Polarized Deep Inelastic Scattering Off the "Neutron" From Gauge/String Duality

We investigate deep inelastic scattering off the polarized "neutron" using gauge/string duality. The "neutron" corresponds to a supergravity mode of the neutral dilatino. Through introducing the Pauli interaction term into the action in $\textrm{AdS}_{5}$ space, we calculate the polarized deep inelastic structure functions of the "neutron" in supergravity approximation at large t' Hooft coupling $\lambda$ and finite $x$ with $\lambda^{-1/2}\ll x<1$. In comparison with the charged dilatino "proton," which has been obtained in the previous work by Gao and Xiao, we find the structure functions of the "neutron" are power suppressed at the same order as the ones of the "proton." Especially, we find the Burkhardt-Cottingham-like sum rule, which is satisfied in the work by Gao and Xiao, is broken due to the Pauli interaction term. We also illustrate how such a Pauli interaction term can arise naturally from higher dimensional fermion-graviton coupling through the usual Kaluza-Klein reduction.Comment: 21pages,5figures, published versio

Optimisation of Thimble Simulations and Quantum Dynamics of Multiple Fields in Real Time

We apply the Generalised Thimble approach to the computation of exact path integrals and correlators in real-time quantum field theory. We first investigate the details of the numerical implementation and ways of optimizing the algorithm. We subsequently apply the method to an interacting two-field system in 0+1 dimensions, illustrating the scope for addressing realistic physical processes using real-time Generalised Thimble computations.Comment: 22 page

Optimisation of Thimble simulations and quantum dynamics of multiple fields in real time

We apply the Generalised Thimble approach to the computation of exact path integrals and correlators in real-time quantum field theory. We first investigate the details of the numerical implementation and ways of optimizing the algorithm. We subsequently apply the method to an interacting two-field system in 0+1 dimensions, illustrating the scope for addressing realistic physical processes using real-time Generalised Thimble computations

Simulations of Cold Electroweak Baryogenesis: hypercharge U(1) and the creation of helical magnetic fields

We perform numerical simulations of Cold Electroweak Baryogenesis, including for the first time in the Bosonic sector the full electroweak gauge group SU(2)×U(1) and CP-violation. We find that the maximum generated baryon asymmetry is reduced by a factor of three relative to the SU(2)-only model, but that the quench time dependence is very similar. In addition, we compute the magnitude of the helical magnetic fields, and find that it is proportional to the strength of CP-violation and dependent on quench time, but is not proportional to the magnitude of the baryon asymmetry as proposed in the literature. Astrophysical signatures of primordial magnetic helicity can therefore not in general be used as evidence that electroweak baryogenesis has taken place

Simulations of “tunnelling of the 3rd kind”

We consider the phenomenon of ``tunnelling of the 3rd kind" \cite{third}, whereby a magnetic field may traverse a classically impenetrable barrier by pair creation of unimpeded quantum fermions. These propagate through the barrier and generate a magnetic field on the other side. We study this numerically using quantum fermions coupled to a classical Higgs-gauge system, where we set up a magnetic field outside a box shielded by two superconducting barriers. We examine the magnitude of the internal magnetic field, and find agreement with existing perturbative results within a factor of two

Simulations of cold electroweak baryogenesis: dependence on the source of CP-violation

We compute the baryon asymmetry created in a tachyonic electroweak symmetry breaking transition, focusing on the dependence on the source of effective CP-violation. Earlier simulations of Cold Electroweak Baryogenesis have almost exclusively considered a very specific CP-violating term explicitly biasing Chern-Simons number. We compare four different dimension six, scalar-gauge CP-violating terms, involving both the Higgs field and another dynamical scalar coupled to SU(2) or U(1) gauge fields. We find that for sensible values of parameters, all implementations can generate a baryon asymmetry consistent with observations, showing that baryogenesis is a generic outcome of a fast tachyonic electroweak transition