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In the centre of mass frame, we have investigated the process of Higgs production in association with a pair of fermions, $e^{+}e^{-}\rightarrow f\bar{f} H$, at the leading order inside an intense electromagnetic field with circular polarization. Our analytical calculations are based on the Narrow Width Approximation (NWA), which is valid in the leading order. We have considered only the initial particles inside the laser field as a first step. In the second part, we have embedded both initial and final particles in the laser field. We have analyzed the angular distribution of the produced Higgs boson as a function of the laser parameters in both cases. We have found that in the case where both initial and final particles are embedded in the laser field, the order of magnitude of the differential cross-section of the process $e^{+}e^{-}\rightarrow\mu^{+}\mu^{-}H$ is reduced more significantly, while that of the process $e^{+}e^{-}\rightarrow\nu\bar{\nu}H$ is enhanced., Comment: 7 pages, 4 figures

In the framework of Higgs triplet model (HTM), we study the pair production process of doubly charged Higgs bosons via $e^{+}e^{-}$ annihilation in the presence of a laser field with circular polarization . We begin our work by presenting the theoretical calculation of the differential cross section in the centre of mass frame including both $Z$ and $\gamma$ diagrams. Then, from the numerical analysis of the production cross section's dependence on the laser field parameters, we have shown that the laser-assisted total cross section decreases as far as the electromagnetic field intensity enhances or by decreasing its frequency. Finally, we analyze the variation of the total cross section versus the mass of the doubly charged Higgs boson by fixing the laser field parameters and the centre of mass energy, and we have found that the order of magnitude of the cross section decreases as long as $M_{H^{\pm\pm}}$ increases., Comment: 18 pages, 6 figures

In the centre of mass frame, we have investigated the process of Higgs production in association with a pair of fermions, $e^{+}e^{-}\rightarrow f\bar{f} H$, at the leading order inside an intense electromagnetic field with circular polarization. Our analytical calculations are based on the Narrow Width Approximation (NWA), which is valid in the leading order. We have considered only the initial particles inside the laser field as a first step. In the second part, we have embedded both initial and final particles in the laser field. We have analyzed the angular distribution of the produced Higgs boson as a function of the laser parameters in both cases. We have found that in the case where both initial and final particles are embedded in the laser field, the order of magnitude of the differential cross-section of the process $e^{+}e^{-}\rightarrow\mu^{+}\mu^{-}H$ is reduced more significantly, while that of the process $e^{+}e^{-}\rightarrow\nu\bar{\nu}H$ is enhanced., Comment: 7 pages, 4 figures

In the framework of Higgs triplet model (HTM), we study the pair production process of doubly charged Higgs bosons via $e^{+}e^{-}$ annihilation in the presence of a laser field with circular polarization . We begin our work by presenting the theoretical calculation of the differential cross section in the centre of mass frame including both $Z$ and $\gamma$ diagrams. Then, from the numerical analysis of the production cross section's dependence on the laser field parameters, we have shown that the laser-assisted total cross section decreases as far as the electromagnetic field intensity enhances or by decreasing its frequency. Finally, we analyze the variation of the total cross section versus the mass of the doubly charged Higgs boson by fixing the laser field parameters and the centre of mass energy, and we have found that the order of magnitude of the cross section decreases as long as $M_{H^{\pm\pm}}$ increases., Comment: 18 pages, 6 figures

In this research paper, we investigate the decay of the proton into neutron, positron and electron neutrino in the presence of an external electromagnetic field with circular polarization. Different physical quantities related to this decay process, such as proton's decay rate and its lifetime, are calculated based on the S-matrix approach. The proton and positron are treated as Dirac-Volkov states, while the neutron and electron neutrino are free-states. We have found that, though it can not occur in vacuum, the proton's decay process into neutron, positron and electron neutrino becomes possible in the presence of laser field with high intensities near or close to the Schwinger limit. In addition, near this limit and for some frequencies, the proton's lifetime can be comparable to that of the neutron, and the required laser strength, from which this decay becomes possible, depends on the chosen laser source., Comment: 10 pages, 2 figures

In this paper, we have investigated the elementary particle reaction ${e}^{+} {e}^{-} \rightarrow{\mu}^{+} {\mu}^{-}$ that results from the electron-positron interaction, at the leading order, with an intense laser wave of circular polarization. We have derived, by annalytical means, the laser-assisted differential cross section expression by using the scattering matrix approach. We have analyzed the energy and the number of exchanged photons dependence of muon pair production in electron-positron annihilation at different centre of mass energies including the $Z$-boson peak. For this reason, a wide range of high centre of mass energies relevant to future $e^{+}e^{-}$ collider were covered to study the cross section behavior. We have found that, for a given number of exchanged photons, laser field strength and frequency, the circularly polarized laser field decreases the total cross section by several orders of magnitudes., Comment: 17 pages, 10 figures

The production of a pair of charged Higgs bosons from $e^{+}e^{-}$ annihilation in the presence of a circularly polarized laser field is investigated in Inert Higgs doublet Model (IHDM) at ${e}^{+}{e}^{-}$ colliders. We have derived the analytical expression for the laser-assisted differential cross section by using the Dirac-Volkov formalism at leading order including the $Z$ and $\gamma$ diagrams. Since the laser-free cross section of this process depends, in the lowest order, only on the mass of the charged Higgs boson and the energy of the center of mass, we have analyzed the dependence of the total laser-assisted cross section on these parameters and also on the laser parameters such as the number of photons exchanged, the laser field intensity and its frequency. The results found indicate that the electromagnetic field decreases the order of magnitude of the total cross section as much as the laser field intensity increases or by decreasing its frequency. Moreover, it becomes high for low charged Higgs masses and low center of mass energies., Comment: 16 pages, 5 figures

In the framework of the Inert Higgs Doublet model (IHDM), we have investigated, in the center of mass frame, the neutral Higgs-boson pair production in the presence of an intense and circularly polarized laser field via ${e}^{+} {e}^{-}$ annihilation $({e}^{+} {e}^{-}\rightarrow H^{0}A^{0})$ at the lowest order. By using the scattering matrix method, we have derived the analytical expression of the differential cross section. The latter is numerically integrated over the solid angle to obtain the total cross section. Then, we have shown how this total cross section depends on the outgoing particles mass for different number of exchanged photons. Next, we have illustrated its variation as a function of the centre of mass energy for different neutral Higgs-boson masses. Finally, we have indicated how it changes as a function of the laser field amplitudes for both different number of exchanged photons and different neutral Higgs-bosons masses., Comment: 10 pages, 6 figures

In the centre of mass frame, we have studied theoretically the $Z$-boson resonant production in the presence of an intense laser field via the weak process $e^+e^- \to \mu^+\mu^-$. Dressing the incident particles by a Circularly Polarized laser field (CP-laser field), at the first step, shows that for a given laser field's parameters, the $Z$- boson cross section decreases by several orders of magnitude. We have compared the the Total Cross Section (TCS) obtained by using the scattering matrix method with that given by the Breit-Wigner approach in the presence of a CP-laser field and the results are found to be very consistent. This result indicates that Breit-Wigner formula is valid not only for the laser-free process but also in the presence of a CP-laser field. The dependence of the laser-assisted differential cross section on the Centre of Mass Energy (CME) for different scattering angles proves that it reaches its maximum for small and high scattering angles. At the next step and by dressing both incident and scattered particles, we have shown that the CP-laser field largely affects the TCS, especially when its strength reaches $10^{9}\,V.cm^{-1}$. This result confirms that obtained for the elastic electron-proton scattering in the presence of a CP-laser field [I. Dahiri et al., arXiv:2102.00722v1]. It is interpreted by the fact that heavy interacting particles require high laser field's intensity to affect the collision's cross section., Comment: 26 pages, 8 figures

In this paper, we have theoretically studied the neutral Higgs pair production in Two Higgs Doublet Model (THDM) in the presence of a circularly polarized laser field. The laser-assisted differential partial cross section is derived in the centre of mass frame at the leading order including $Z$ diagram. The total cross section is computed numerically by integrating the differential cross section over the solid angle $d\Omega$. Two benchmark points are discussed for the THDM parameters. In the first step, we have analyzed the total cross section of ${e}^{+}{e}^{-}\rightarrow h^{0}A^{0}$ by considering $H^{0}$ as the standard model-like Higgs boson. Then, the process ${e}^{+}{e}^{-}\rightarrow H^{0}A^{0}$ is studied by taking $h^{0}$ as the Higgs boson of the standard model. For both benchmark points, the laser-assisted total cross section of the studied processes depends on the produced neutral Higgs masses, the centre of mass energy and the laser field parameters. In addition, the maximum cross section occurs at high centre of mass energy for the process ${e}^{+}{e}^{-}\rightarrow H^{0}A^{0}$ as compared to that of ${e}^{+}{e}^{-}\rightarrow h^{0}A^{0}$., Comment: 18 pages, 10 figures

In this study, we have investigated the production of a charged Higgs boson in assiciation with a charged weak $W$-boson ($H^{\pm}W^{\mp}$) at tree level via $e^{+}e^{-}$ annihilation in the presence of a laser field with circular polarization. At first step and by using analytical techniques, we have derived the expression of the differential cross section involving both $Z$ and $\gamma$ diagrams. Next, we have shown that the cross section of this process inside the laser field is proportional to the form factor $F_{HWV}$, and it depends on the mass of the charged Higgs boson and the energy of the center of mass. Then, we have analyzed the dependence of the total laser-assisted cross section on the number of photons exchanged for two different cases of form factor. Finally, we have found that the maximum number of photons that can be transferred depends only on the laser parameters., Comment: 16 pages, 6 figures. arXiv admin note: text overlap with arXiv:2109.05530

In the framework of the electroweak standard model, we investigated, in the center of mass frame, the Higgs boson production in the presence of an intense laser field via ${e}^{+} {e}^{-}$ annihilation $({e}^{+} {e}^{-}\rightarrow ZH)$. By comparing our results with those obtained by Djouadi \cite{1} for laser-free process, we show that the circularly polarized laser field affects significantly the $s$-channel Higgs boson production. We find that for a given number of exchanged photons, laser field strength and frequency, the total cross section decreases by several orders of magnitude. These effects of laser field on cross section are found to be consistent with what was found for muon pair production via QED process in the presence of a circularly polarized laser field \cite{2}., Comment: 17 pages, 11 figures

In this paper, we have theoretically studied the neutral Higgs pair production in Two Higgs Doublet Model (THDM) in the presence of a circularly polarized laser field. The laser-assisted differential partial cross section is derived in the centre of mass frame at the leading order including $Z$ diagram. The total cross section is computed numerically by integrating the differential cross section over the solid angle $d\Omega$. Two benchmark points are discussed for the THDM parameters. In the first step, we have analyzed the total cross section of ${e}^{+}{e}^{-}\rightarrow h^{0}A^{0}$ by considering $H^{0}$ as the standard model-like Higgs boson. Then, the process ${e}^{+}{e}^{-}\rightarrow H^{0}A^{0}$ is studied by taking $h^{0}$ as the Higgs boson of the standard model. For both benchmark points, the laser-assisted total cross section of the studied processes depends on the produced neutral Higgs masses, the centre of mass energy and the laser field parameters. In addition, the maximum cross section occurs at high centre of mass energy for the process ${e}^{+}{e}^{-}\rightarrow H^{0}A^{0}$ as compared to that of ${e}^{+}{e}^{-}\rightarrow h^{0}A^{0}$., Comment: 18 pages, 10 figures

In this study, we have investigated the production of a charged Higgs boson in assiciation with a charged weak $W$-boson ($H^{\pm}W^{\mp}$) at tree level via $e^{+}e^{-}$ annihilation in the presence of a laser field with circular polarization. At first step and by using analytical techniques, we have derived the expression of the differential cross section involving both $Z$ and $\gamma$ diagrams. Next, we have shown that the cross section of this process inside the laser field is proportional to the form factor $F_{HWV}$, and it depends on the mass of the charged Higgs boson and the energy of the center of mass. Then, we have analyzed the dependence of the total laser-assisted cross section on the number of photons exchanged for two different cases of form factor. Finally, we have found that the maximum number of photons that can be transferred depends only on the laser parameters., Comment: 16 pages, 6 figures. arXiv admin note: text overlap with arXiv:2109.05530

In this paper, we have investigated the elementary particle reaction ${e}^{+} {e}^{-} \rightarrow{\mu}^{+} {\mu}^{-}$ that results from the electron-positron interaction, at the leading order, with an intense laser wave of circular polarization. We have derived, by annalytical means, the laser-assisted differential cross section expression by using the scattering matrix approach. We have analyzed the energy and the number of exchanged photons dependence of muon pair production in electron-positron annihilation at different centre of mass energies including the $Z$-boson peak. For this reason, a wide range of high centre of mass energies relevant to future $e^{+}e^{-}$ collider were covered to study the cross section behavior. We have found that, for a given number of exchanged photons, laser field strength and frequency, the circularly polarized laser field decreases the total cross section by several orders of magnitudes., Comment: 17 pages, 10 figures

In the framework of the Inert Higgs Doublet model (IHDM), we have investigated, in the center of mass frame, the neutral Higgs-boson pair production in the presence of an intense and circularly polarized laser field via ${e}^{+} {e}^{-}$ annihilation $({e}^{+} {e}^{-}\rightarrow H^{0}A^{0})$ at the lowest order. By using the scattering matrix method, we have derived the analytical expression of the differential cross section. The latter is numerically integrated over the solid angle to obtain the total cross section. Then, we have shown how this total cross section depends on the outgoing particles mass for different number of exchanged photons. Next, we have illustrated its variation as a function of the centre of mass energy for different neutral Higgs-boson masses. Finally, we have indicated how it changes as a function of the laser field amplitudes for both different number of exchanged photons and different neutral Higgs-bosons masses., Comment: 10 pages, 6 figures

The production of a pair of charged Higgs bosons from $e^{+}e^{-}$ annihilation in the presence of a circularly polarized laser field is investigated in Inert Higgs doublet Model (IHDM) at ${e}^{+}{e}^{-}$ colliders. We have derived the analytical expression for the laser-assisted differential cross section by using the Dirac-Volkov formalism at leading order including the $Z$ and $\gamma$ diagrams. Since the laser-free cross section of this process depends, in the lowest order, only on the mass of the charged Higgs boson and the energy of the center of mass, we have analyzed the dependence of the total laser-assisted cross section on these parameters and also on the laser parameters such as the number of photons exchanged, the laser field intensity and its frequency. The results found indicate that the electromagnetic field decreases the order of magnitude of the total cross section as much as the laser field intensity increases or by decreasing its frequency. Moreover, it becomes high for low charged Higgs masses and low center of mass energies., Comment: 16 pages, 5 figures

In the centre of mass frame, we have studied theoretically the $Z$-boson resonant production in the presence of an intense laser field via the weak process $e^+e^- \to \mu^+\mu^-$. Dressing the incident particles by a Circularly Polarized laser field (CP-laser field), at the first step, shows that for a given laser field's parameters, the $Z$- boson cross section decreases by several orders of magnitude. We have compared the the Total Cross Section (TCS) obtained by using the scattering matrix method with that given by the Breit-Wigner approach in the presence of a CP-laser field and the results are found to be very consistent. This result indicates that Breit-Wigner formula is valid not only for the laser-free process but also in the presence of a CP-laser field. The dependence of the laser-assisted differential cross section on the Centre of Mass Energy (CME) for different scattering angles proves that it reaches its maximum for small and high scattering angles. At the next step and by dressing both incident and scattered particles, we have shown that the CP-laser field largely affects the TCS, especially when its strength reaches $10^{9}\,V.cm^{-1}$. This result confirms that obtained for the elastic electron-proton scattering in the presence of a CP-laser field [I. Dahiri et al., arXiv:2102.00722v1]. It is interpreted by the fact that heavy interacting particles require high laser field's intensity to affect the collision's cross section., Comment: 26 pages, 8 figures

In the framework of the electroweak standard model, we investigated, in the center of mass frame, the Higgs boson production in the presence of an intense laser field via ${e}^{+} {e}^{-}$ annihilation $({e}^{+} {e}^{-}\rightarrow ZH)$. By comparing our results with those obtained by Djouadi \cite{1} for laser-free process, we show that the circularly polarized laser field affects significantly the $s$-channel Higgs boson production. We find that for a given number of exchanged photons, laser field strength and frequency, the total cross section decreases by several orders of magnitude. These effects of laser field on cross section are found to be consistent with what was found for muon pair production via QED process in the presence of a circularly polarized laser field \cite{2}., Comment: 17 pages, 11 figures