arXiv subjects

S. S. Gousheh

Publications and source records attributed to S. S. Gousheh.

At least 19 recordsLinked to original sources

arXiv2026

Fermion Zero Modes and Fermion number $1/2$ of the 't Hooft-Polyakov Monopole

Fermion bound states in the background of the 't Hooft-Polyakov SU(2) monopole are investigated for various values of gauge coupling constant $g$, the Higgs self-coupling constant $λ$, and the Yukawa coupling constant $y_q$. Numerical solutions to the set of coupled differential equations for various selected points in the parameter space reveal only a zero mode, for which we also present an analytic argument. We show that the monopole profile functions and the zero mode wave function become more localized with increasing $g$ and $λ$, while the right-handed component of the latter decreases with $g$. However, as expected, this component increases with $y_q$. We find that the zero mode in the limit $g\to 0$ differs from the zero mode held by the Higgs alone, highlighting the nonlinear and nonperturbative character of the system. Finally, we prove the spectral mirror symmetry of the fermion, whence, together with the existence of the zero mode, we infer the fermion number $1/2$ of the 't Hooft-Polyakov monopole.

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arXiv2026

Global charge conservation in the symmetric phase of the early Universe

In the Standard Model at high temperatures, anomalous effects contribute to the violation of baryon number ($B$) and lepton number ($L$), separately, while $B-L$ remains conserved. There are also corresponding changes in the helicity of the hypermagnetic field ($h_B$) and the Chern-Simons numbers of the non-Abelian gauge fields ($N_{\rm CS,w}$ and $N_{\rm CS,s}$). In this study, we investigate a baryogenesis process in the symmetric phase of the early Universe by taking into account the Abelian and non-Abelian anomalous effects as well as the perturbative chirality-flip processes of all fermions. We calculate the time evolution of all relevant physical quantities, including the asymmetries of all fermions and the Higgs, as well as $h_B$ and $N_{\rm CS,w}$. We present a method to compute the latter, for which it is crucial to consider the minute departure from equilibrium of the sphaleron processes. We then verify explicitly the conservation of a global charge, involving the total matter-antimatter asymmetry $B+L$, the hypermagnetic helicity $h_B$ and $N_{\rm CS,w}$, the existence of which had been inferred earlier. In particular we show that, in the scenario that we study, an initial $h_B$ decays mostly to $N_{\rm CS,w}$, with only $10^{-3}$ conversion ratio into $B+L$ asymmetry.

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arXiv2026

On the Fermion Level Crossing in the Electroweak Instanton Background

We investigate fermion level crossing in the electroweak instanton background, taking into account the Euclidean-time dependence of the fermion energy throughout our analysis, from the field equations to the spectral flow of fermion energy levels. Modifying the standard fermion ansatzes, we show that, irrespective of the model parameters, the duration over which the fermion energy spectrum flows from one continuum to another corresponds to exactly one unit change in the Chern--Simons number of the instanton. We further demonstrate that incorporating this time dependence is essential for establishing a one-to-one correspondence between the number of fermion zero modes and the instanton winding number, providing a numerical confirmation of the index theorem in the context of instanton backgrounds.

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arXiv2025

Thermal Fermion Propagators and Flavor-Changing via Loop Corrections in the Early Universe

We present the Minimally Extended Standard Model in the mass basis in the symmetric phase of the early Universe, demonstrating that the CP-violating CKM and PMNS matrices emerge not only in the weak interactions but also in the Yukawa interactions. This is due to the presence of all four components of the Higgs field. Specifically, left-handed fermions acquire additional thermal mass contributions involving the CKM and PMNS matrix elements. Most notably, the structure of Yukawa interactions enables flavor-changing and CP-violating conversions among left-handed fermions, such as $u_L\leftrightarrow c_L$, which do not occur in the broken phase. In contrast, the right-handed fermions retain their mass eigenstates, leading to distinct thermal masses. Additionally, we identify novel CP-violating scattering processes, such as $u_L\bar{c}_L\rightarrow 2A_3$, which are exclusive to the symmetric phase.

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arXiv2025

The generation of baryon asymmetry and hypermagnetic field by the chiral vortical effect in the presence of sphalerons

We show how the temperature-dependent chiral vortical effect can generate hypermagnetic fields and matter-antimatter asymmetries, in the symmetric phase of the early Universe, in the temperature range $100\mbox{GeV} \le T\le 10\mbox{TeV}$, even in the presence of the weak sphaleron processes. We take into account all perturbative chirality-flip processes, as well as the nonperturbative Abelian and non-Abelian anomalous effects for all three generations. Using the constraints and conservation laws in the plasma, we reduce the number of required evolution equations. We also simplify the anomalous transport coefficients, accordingly. We consider both monochromatic and continuous spectra for the hypermagnetic and velocity fields to solve the anomalous magnetohydrodynamics equations. We then show that overlapping small transient fluctuations in the temperature of some matter degrees of freedom and vorticity of the plasma can generate a chiral vortical current, resulting in the generation of strong hypermagnetic fields and matter-antimatter asymmetries, all starting from zero initial values. We obtain the baryon asymmetry $η_{B}\simeq 5\times10^{-10}$ and a positive helicity hypermagnetic field with amplitude $B_{Y}(x)\simeq10^{19}G$, at the onset of the electroweak phase transition. Although the sphaleron processes tend to washout the generated $(\rm B +L)$ asymmetry, the anomalous processes prevail and the baryogenesis and leptogenesis occur without $(\rm B-L)$ violation.

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arXiv2023

Contribution of the thermal mass to the chiral vortical effect and magnetobaryogenesis

We show that the chiral vortical effect can exist in a nonchiral electroweak plasma in thermal equilibrium using the effective thermal masses of the fermions in the symmetric phase. We use a nonperturbative formula for the vortical current, which has been recently obtained and is a functional of the dispersion relation. Then, taking into account the effect of fermion thermal mass in the dispersion relation, we show that the corresponding hyperelectric vortical current receives implicit thermal corrections proportional to T2, from both the gauge and Yukawa interactions of the fermion. We show that the contributions of gauge interactions to the thermal masses in the total hyperelectric vortical current cancel out due to the gauge symmetries, while those of the Yukawa interactions do not cancel out. We finally show that, due to this current, only small transient vorticity fluctuations about the zero background value in a nonchiral electroweak plasma in thermal equilibrium can activate the chiral vortical effect, leading to the generation of hypermagnetic fields and matter-antimatter asymmetries in the symmetric phase of the early Universe, in the temperature range 100GeV<T<10TeV, all starting from zero initial values, even in the presence of the weak sphaleron processes.

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arXiv2023

Casimir free energy for massive scalars: a comparative study of various approaches

We compute the Casimir thermodynamic quantities for a massive real scalar field between two parallel plates with the Dirichlet boundary conditions, using three different general approaches and present explicit solutions for each. The Casimir thermodynamic quantities include the Casimir Helmholtz free energy, pressure, energy, and entropy. The three general approaches that we use are based on the fundamental definition of Casimir thermodynamic quantities, the analytic continuation method, and the zero temperature subtraction method. Within the analytic continuation approach, we use two distinct methods which are based on the utilization of the zeta function and the Schlomilch summation formula. We include the renormalized versions of the latter two approaches as well, whereas the first approach does not require one. Within each general approach, we obtain the same results in a few different ways to ascertain the selected cancellations of infinities have been done correctly. We show that, as expected, the results based on the zeta function and the Schlomilch summation formula are equivalent. We then do a comparative study of the three different general approaches and their results and show that they are in principle not equivalent to each other, and they yield equivalent results only in the massless case. In particular, we show that the Casimir energy calculated only by the first approach has all three properties of going to zero as the temperature, mass of the field or the distance between the plates increases. Moreover, we show that in this approach the Casimir entropy reaches a positive constant in the high temperature limit, which can explain the linear term in the Casimir free energy.

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arXiv2022

Electroweak phase transition in the presence of hypermagnetic field and the generation of gravitational waves

We investigate the effects of a large-scale background hypermagnetic field on the electroweak phase transition. We propose a model in which an effective weak angle varies during the electroweak phase transition and upon its use we show that, although for the majority of the parameter space the phase transition is a crossover, there are tiny regions in which the phase transition occurs in two steps and can be first-order. We obtain all of the important quantities characterizing the details of the first-order phase transition, including the latent heat, transition temperature and duration. We then calculate the gravitational wave energy spectrum generated during the first-order part of the electroweak phase transition and find that, for strong enough background hypermagnetic fields, these signals can be detected by the Ultimate-DECIGO interferometer.

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arXiv2022

Casimir free energy for massive fermions: a comparative study of various approaches

We compute the Casimir thermodynamic quantities for a massive fermion field between two parallel plates with the MIT boundary conditions, using three different general approaches and present explicit solutions for each. The Casimir thermodynamic quantities include the Casimir Helmholtz free energy, pressure, energy and entropy. The three general approaches that we use are based on the fundamental definition of Casimir thermodynamic quantities, the analytic continuation method represented by the zeta function method, and the zero temperature subtraction method. We include the renormalized versions of the latter two approaches as well, whereas the first approach does not require one. Within each general approach, we obtain the same results in a few different ways to ascertain the selected cancellations of infinities have been done correctly. We then do a comparative study of the three different general approaches and their results, and show that they are in principle not equivalent to each other and they yield, in general, different results. In particular, we show that the Casimir thermodynamic quantities calculated only by the first approach have all three properties of going to zero as the temperature, the mass of the field, or the distance between the plates increases.

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arXiv2021

The generation of matter-antimatter asymmetries and hypermagnetic fields by the chiral vortical effect of transient fluctuations

We study the contribution of temperature-dependent chiral vortical effect to the generation and evolution of the hypermagnetic fields and the matter-antimatter asymmetries, in the symmetric phase of the early Universe, in the temperature range $100\mbox{GeV} \le T\le 10\mbox{TeV}$. Our most important result is that, due to the chiral vortical effect, small overlapping transient fluctuations in the vorticity field in the plasma and temperature of matter degrees of freedom can lead to the generation of strong hypermagnetic fields and matter-antimatter asymmetries, all starting from zero initial values. We show that, either an increase in the amplitudes of the fluctuations of vorticity or temperature, or a decrease in their widths, leads to the production of stronger hypermagnetic fields, and therefore, larger matter-antimatter asymmetries. We have the interesting result that fluctuating vorticity fields are more productive, by many orders of magnitude, as compared to vorticities that are constant in time.

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arXiv2021

The effects of non-helical component of hypermagnetic field on the evolution of the matter-antimatter asymmetry, vorticity, and hypermagnetic field

We study the evolution of the matter-antimatter asymmetry (η), the vorticity, and the hypermagnetic field in the symmetric phase of the early Universe, and in the temperature range 100 GeV < T < 10 TeV. We assume a configuration for the hypermagnetic field which includes both helical and non-helical (Bz) components. Consequently, the hypermagnetic field and the fluid vorticity can directly affect each other, the manifestations of which we explore in three scenarios. In the first scenario, we show that in the presence of a small vorticity and a large ηeR, helicity can be generated and amplified for an initially strong Bz. The generation of the helical seed is due to the chiral vortical effect (CVE) and/or the advection term, while its growth is mainly due to the chiral magnetic effect (CME) which leads to the production of the baryon asymmetry, as well. The vorticity saturates to a nonzero value which depends on Bz, even in the presence of the viscosity, due to the back-reaction of Bz on the plasma. Increasing the initial vorticity, makes the values of the helicity, ηs, and vorticity reach their saturation curves sooner, but does not change their final values at the onset of the electroweak phase transition. The second scenario is similar to the first except we assume that all initial ηs are zero. We find that much higher initial vorticity is required for the generation process. In the third scenario, we show that in the presence of only a strong hypermagnetic field, ηs and vorticity can be generated and amplified. Increasing the initial helicity, increases the final ηs and vorticity. We find that although the presence of a nonzero initial Bz is necessary in all three scenarios, its increase only increases the final values of vorticity.

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arXiv2020

Contribution of the chiral vortical effect to the evolution of the hypermagnetic field and the matter-antimatter asymmetry in the early Universe

In this paper, we study the contribution of the chiral vortical effect, in addition to that of the chiral magnetic effect, to the evolution of the hypermagnetic field and the matter-antimatter asymmetry in the symmetric phase of the early Universe in the temperature range 100GeV < T < 10TeV. We choose a fully helical Chern-Simons wave configuration for the velocity and the hypermagnetic vector potential fields. The latter makes the plasma force-free in the absence of viscosity. We show that the most pronounced effect of the chiral vorticity is the production and initial growth of the hypermagnetic field. In particular, we show that in the presence of a non-zero matter asymmetry, the hypermagnetic field can grow from zero initial value only in the presence of a non-zero vorticity field. Moreover, we show that larger initial growths not only result in larger maximum values of the hypermagnetic field, but also cause the saturation of the hypermagnetic field and the conversion of the lepton-baryon asymmetry to occur more quickly, i.e., at a higher temperature. We show that the damping of the vorticity due to the presence of viscosity, which typically occurs extremely rapidly, does not significantly affect the evolution.

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arXiv2020

Fermion Number 1/2 of Sphalerons and Spectral Mirror Symmetry

We present a rederivation of the baryon and lepton numbers $\frac{1}{2}$ of the $SU(2)_L$ S sphaleron of the standard electroweak theory based on spectral mirror symmetry. We explore the properties of a fermionic Hamiltonian under discrete transformations along a noncontractible loop of field configurations that passes through the sphaleron and whose endpoints are the vacuum. As is well known, CP transformation is not a symmetry of the system anywhere on the loop, except at the endpoints. By augmenting CP with a chirality transformation, we observe that the Dirac Hamiltonian is odd under the new transformation precisely at the sphaleron, and this ensures the mirror symmetry of the spectrum, including the continua. As a consistency check, we show that the fermionic zero mode presented by Ringwald in the sphaleron background is invariant under the new transformation. The spectral mirror symmetry which we establish here, together with the presence of the zero mode, are the two necessary conditions whence the fermion number $\frac{1}{2}$ of the sphaleron can be inferred using the reasoning presented by Jackiw and Rebbi or, equivalently, using the spectral deficiency $\frac{1}{2}$ of the Dirac sea. The relevance of this analysis to other solutions is also discussed.

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arXiv2019

A Minimal System Including Weak Sphalerons for Investigating the Evolution of Matter Asymmetries and Hypermagnetic Fields

We study simultaneous evolution of large scale hypermagnetic fields and the asymmetries of quarks, leptons and Higgs boson in the temperature range from 10TeV to 100GeV. Above 10TeV, we identify all of the major fast interactions and use the associated conservation laws as constraints on the initial conditions at 10TeV. Below 10TeV, we identify the major processes which fall out of equilibrium or emerge as non-negligible processes and derive the relevant evolution equations. These include the Abelian anomalies which violate fermion numbers, direct and inverse Higgs decays that change the chiralities of fermions, and weak sphalerons which violate the left-handed fermion numbers. We also consider the contributions of all fermionic chemical potentials to the UY(1) Chern-Simons term which affects the evolution through the AMHD equations. Thus, we present a minimal set of self-consistent initial conditions and evolution equations which respect all constraints coming from conservation laws, fast processes and charge neutrality of the plasma. We solve the coupled evolution equations and find that initial large hypermagnetic field can produce matter asymmetries starting from zero initial value, and vice versa provided an initial seed of hypermagnetic field is present and the rate of the electron Yukawa processes is lower. We find that our model yields acceptable values for baryon asymmetry and magnetic field. However, the scale of the magnetic field obtained is much smaller than the observational data, even when the turbulence driven inverse cascade mechanism in the broken phase is taken into account.

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arXiv2018

Electroweak baryogenesis via chiral gravitational waves

We propose a new mechanism for electroweak baryogenesis based on gravitational waves generated by helical magnetic fields that are present during a first order electroweak phase transition. We generate a net lepton number through the gravitational chiral anomaly which appears due to the chiral gravitational waves produced by these magnetic fields. The observed value of baryon asymmetry can be obtained in our mechanism within parameter space of scenarios with an inverse cascade evolution for magnetic fields which can also be candidates for large-scale magnetic fields.

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arXiv2017

The effects of the U$_\textrm{Y}$(1) Chern-Simons term and its baryonic contribution on matter asymmetries and hypermagnetic fields

In this paper, we study the significance of the U$_\textrm{Y}$(1) Chern-Simons term in general, and its baryonic contribution in particular, for the evolution of the matter asymmetries and the hypermagnetic field in the temperature range $100$GeV$\leq T \leq 10$TeV. We show that an initial helical hypermagnetic field, denoted by $B_Y^{(0)}$, can grow matter asymmetries from zero initial value. However, the growth which is initially quadratic with respect to $B_Y^{(0)}$, saturates for values larger than a critical value. The inclusion of the baryonic contribution reduces this critical value, leading to smaller final matter asymmetries. Meanwhile, $B_Y(T_{EW})$ becomes slightly larger than $B_Y^{(0)}$. In the absence of the U$_\textrm{Y}$(1) Chern-Simons term, the final values of matter asymmetries grow without saturation. Conversely, we show that an initial matter asymmetry can grow an initial seed of hypermagnetic field, provided the Chern-Simons term is taken into account. The growth process saturates when the matter asymmetry drops abruptly. When the baryonic contribution is included, the saturation occurs at an earlier time, and $B_Y (T_{EW})$ becomes larger. We also show the results can be within the acceptable range of present day data, provided the inverse cascade process is also taken into account.

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arXiv2016

On the Contributions to the $\bf U_Y(1)$ Chern-Simons Term and the Evolution of Fermionic Asymmetries and Hypermagnetic Fields

We study simultaneous evolution of electron, neutrino and quark asymmetries, and large scale hypermagnetic fields in the symmetric phase of the electroweak plasma in the temperature range $100$GeV$\leq T\leq 10$TeV, taking into account the chirality flip processes via inverse Higgs decays and fermion number violation due to Abelian anomalies. We present a derivation of the coefficient of the Chern-Simons term for the hypercharge gauge field, showing that the left-handed and right-handed components of each fermion species contribute with opposite sign. This is in contrast to the results presented in some of the previous works. The $\textrm{U}_{\textrm{Y}}(1)$ Chern-Simons term affects the resulting anomalous magnetohydrodynamic (AMHD) equations. We solve the resulting coupled evolution equations for the lepton and baryon asymmetries, as well as the hypermagnetic field to obtain their time evolution along with their values at the electroweak phase transition ($T_{EW} \sim 100$GeV) for a variety of critical ranges for their initial values at $T=10$TeV. We first investigate the results of this sign change, by directly comparing our results with those obtained in one of the previous works and find that matter asymmetry generation increases considerably in the presence of a strong hypermagnetic field. Furthermore, we find that a strong hypermagnetic field can generate matter asymmetry starting from absolutely zero asymmetry, while matter asymmetry can generate a hypermagnetic field provided the initial value of the latter is nonzero.

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arXiv2016

Neutrino mixing matrix and masses from a generalized Friedberg-Lee model

The overall characteristics of the solar and atmospheric neutrino oscillation are approximately consistent with a tribimaximal form of the mixing matrix $U$ of the lepton sector. Exact tribimaximal mixing leads to $θ_{13}=0$. However, recent results from Daya Bay and RENO experiments have established a nonzero value for $θ_{13}$. Keeping the leading behavior of $U$ as tribimaximal, we use a generalized Fridberg-Lee neutrino mass model along with a complementary ansatz to incorporate a nonzero $θ_{13}$ along with CP violation. We generalize this model in two stages: In the first stage we assume $μ-τ$ symmetry and add imaginary components which leads to nonzero phases. In the second stage we add a perturbation with real components which breaks the $μ-τ$ symmetry and this leads to a nonzero value for $θ_{13}$. The combination of these two generalizations leads to CP violation. Using only two of the experimental data, we can fix all of the parameters of our model and predict not only values for the other experimental data, which agree well with the available data, but also the masses of neutrinos and the CP violating phases and parameters. These predictions include the following: $\langle m_{ν_e} \rangle\approx(0.033-0.037)~eV$, $\langle m_{ν_μ} \rangle\approx(0.043-0.048)~ eV$, $\langle m_{ν_τ} \rangle\approx(0.046-0.051)~ eV$, and $59.21^{\circ}\lesssim δ\lesssim 59.34^{\circ}$

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