arXiv subjects

Faisal Akram

Publications and source records attributed to Faisal Akram.

At least 19 recordsLinked to original sources

arXiv2026

Landau-Khalatnikov-Fradkin Transformations in Reduced Quantum Electrodynamics: Perturbative and Nonperturbative Dynamics of the Fermion Propagator

We present a comprehensive analysis of the Landau-Khalatnikov-Fradkin transformations for the charged fermion propagator in reduced quantum electrodynamics (RQED). Starting from the propagator in a reference gauge, we perform a gauge transformation to obtain its analytical expression valid to all orders in an arbitrary covariant gauge and also applicable in a nonperturbative context. This work complements and extends previous studies of quantum electrodynamics in various spacetime dimensions, for both massless and massive fermions. At the perturbative level, we expand the resulting expressions up to two-loop order for both massless and massive cases, and compare our results with those available in the literature wherever possible. We argue that the most suitable choice of the reference covariant gauge in RQED is $\xi=1/3$, as in this case the leading logarithmic contribution to the massless wave-function renormalization vanishes at one-loop order. This choice provides a direct connection between perturbation theory and the constraints imposed by multiplicative renormalizability on the massless fermion propagator. We also investigate the implications of the Landau-Khalatnikov-Fradkin transformations for the dynamically generated mass function of the fermion propagator. Finally, through numerical computation, we demonstrate that both the chiral fermion condensate and the fermion pole mass are gauge-invariant quantities.

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arXiv2025

Masses of Light Flavor Mesons using Bethe-Salpeter Approach

This work employs the approach based on the Bethe-Salpeter and Dyson-Schwinger equations to study the light meson spectrum. The Dyson-Schwinger equation of the quark propagator is truncated using the Maris-Tandy model for the dressed gluon propagator, which incorporates both the infrared enhancement and the perturbatively correct ultraviolet behavior. Additionally, for the dressed quark-gluon vertex, we apply its bare form and the Ball-Chiu model, which minimally satisfies the constraint imposed by the gauge symmetry through its Ward-Green-Takahashi identity. Consistent truncation of both Bethe-Salpeter and Dyson-Schwinger equations requires that axial-vector Ward-Takahashi identity, arising from chiral symmetry of the Lagrangian of quantum chromodynamics, must not be violated. We utilize this identity as an additional constraint to truncate the Bethe-Salpeter equation and examine the impact of two choices of quark-gluon vertex, along with the application of the Maris-Tandy model on the light meson spectrum. To extract the masses of flavored and unflavored light mesons, we solve the inhomogeneous Bethe-Salpeter equation using the Pad$\acute{e}$ approximation, which enables us to locate the poles of the Bethe-Salpeter amplitude without requiring a numerical solution in the timelike region of momentum space. We find that truncations of the Bethe-Salpeter equation based on bare and Ball-Chiu vertices, coupled with the Maris-Tandy model, yield consistent results.

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arXiv2025

Production cross sections of charm-beauty mesons in proton-nucleus and nucleus-nucleus collisions at LHC

In this work, we calculate the production cross sections of the 1S and 1P states of the $B_{c}$ meson for proton-nucleus and nucleus-nucleus colliding beam experiments at LHC and RHIC. We provide estimates for the Au nucleus at RHIC energies and for the Pb and Xe nuclei at LHC energies. Previous estimates of these cross sections have ignored quark anti-quark annihilation diagrams and are confined to S states for Pb and Au nuclei. The cross sections of the P states are also equally important as these states lie below the BD threshold and cascade into $B_{c}$ ground states with 100\% probability. In addition to calculating the $p_{T}$, rapidity, and pseudo-rapidity distributions of the cross sections, we also determine the nuclear modification factors $R_{pA}$ and $R_{AA}$ for $A=\textrm{Pb}$, $\textrm{Xe}$, and $\textrm{Au}$. The results provide a baseline for the upcoming experimental studies of $B_{c}$ mesons in pp, pA, and AA collisions in RUN III of LHC and could help develop experimental strategies for identification of hitherto undiscovered states of the $B_{c}$ meson.

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arXiv2025

Study of excited $D$ and $D_s$ mesons in a relativized quark model

We use a modified relativistic quark model to study the properties of excited charmed and charmed strange mesons. We calculate the masses and wave functions of conventional charmed and charmed strange mesons incorporating both spin and $S$-$D$ mixing effects and fit parameters of the potential model with known experimental states using differential evolution technique. Using Leading Born-Oppenheimer expansion, we also compute the spectrum and wave functions of first gluonic excited state of charmed and charmed strange mesons. We examine the effects of gluonic excitation on the spectrum of resultant hybrid mesons. By using our calculated spectrum and wave functions, we determine the radiative transitions of the conventional and hybrid open charm mesons. We compare our calculations with experimental data and other works. We expect our results will be beneficial in the detection of the charmed and charmed strange conventional and hybrids mesons.

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arXiv2025

Strong Decays of Charmonia

In this work, we calculate the charmonium spectrum and strong decay widths of cc states. The calculations are performed using the quark potential model with which incorporates the relativistic effects. The resulting cc spectrum exhibits a good agreement with experimental data. The open flavor strong decay widths are calculated employing the 3P0 model. We adopt two choices of wave functions to determine the observables: the first involves the utilization of realistic wave functions obtained by solving relativistic Schrodinger equation, while the second employs Simple harmonic oscillator (SHO) wave functions whose parameters are fitted to the realistic wave functions. We find that the decay widths of higher charmonia states above the threshold value of open charm mesons are well described with these wave functions. We provide a comprehensive analysis of the strong decay widths and assigned specific charmonium states: X(3940) is assigned to the {\eta}c(3S) state, Y (4660) to the {\psi}(5S) state, X(3915) to the \c{hi}0(2P) state, Zc(3900) to the hc(2P) state, X(4350) to the \c{hi}2(3P) state, and X(3842) to the {\psi}3(1D) state. We also compare our results with available experimental data and theoretical predictions of other models.

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arXiv2025

Landau-Khalatnikov-Fradkin Transformations in Quantum Electrodynamics: For Perturbation Theory and Dynamical Mass Generation

We carry out a comprehensive analysis of the Landau-Khalatnikov-Fradkin transformations for a charged fermion propagator at the two-loop level in quantum electrodynamics (QED). Starting with an arbitrary covariant gauge $\xi$ and space-time dimension $d$, we provide its explicit expressions in three and four-dimensional QED. We begin with the tree-level fermion propagator in the Landau gauge and gauge-transform it to obtain an analytical expression for an all order result in an arbitrary covariant gauge. We expand it out to two-loops both for the massless and massive propagators in three and four space-time dimensions. In addition to comparing with all earlier results in the literature wherever possible, we also study constraints of multiplicative renormalizabilty of our results in four-dimensional QED which are logarithmically divergent. Finally, we analyze representative solutions of the fermion propagator which correspond to dynamical chiral symmetry breaking and mass generation in QED. We study the gauge dependence of these emergent solutions, that of the Euclidean pole mass and the chiral fermion condensate.

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arXiv2024

$Υ$ absorption cross sections by nucleons

The cross sections of $Υ$\ absorption by nucleons are calculated in meson-baryon exchange model using an effective hadronic Lagrangian. Calculated cross sections are found to peak near threshold followed by an increase which tends to settle at large center of mass energy. Peak values are found in range about 1.8 to 4 mb when cutoff parameter of monopole form factor is varied from 1.2 to 1.8 GeV. The results disagree with pQCD calculations but are consistent with the effective value of the absorption cross section extracted from p-A scattering data in E772 experiment at $\sqrt{s_{NN}}=39$ GeV. We use this data value to find a best fit of the cutoff parameter which enables us provide definite predictions for the values of $Υ$ absorption cross sections by nucleons for upcoming p-A scattering experiments at RHIC and LHC energies for zero rapidity $b\bar{b}$ states. The results could be useful in studying the effect of $Υ$ absorption by nucleons at its production stage in relativistic heavy-ion collision experiments. We also find that thermal averaged values of total absorption cross sections are small enough to rule out the effect of absorption of $Υ$ by the comovers in the hadronic matter.

nucl-th↗

arXiv2023

Effect of the Quark-Gluon Vertex on Dynamical Chiral Symmetry Breaking

In this work, we investigate how the details of the quark-gluon interaction vertex affect the quantitative description of chiral symmetry breaking through the gap equation for quarks. We start from two gluon propagator models widely used in literature and constructed in direct connection with our gradually improved understanding of infrared quantum chromodynamics coupled with its exact one-loop limit. The gap equation is then solved by employing a variety of vertex \emph{Ansätze}, which have been constructed in order to implement some of the key aspects of quantum chromodynamics, namely, multiplicative renormalizability of the quark propagator, gauge invariance, matching with perturbation theory in the weak coupling regime, independence from unphysical kinematic singularities as well as manifestly correct transformation properties under charge conjugation and parity operations. On general grounds, all truncation schemes exhibit the same qualitative and quantitative pattern of chiral symmetry breaking, ensuring the overall robustness of this approach and its potentially reliable description of the hadron spectrum and properties.

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arXiv2022

Charmonium spectrum in an unquenched quark model

The effects of virtual light quark pairs on the charmonium spectrum are studied. Pair creation is modelled with a ``$^{3}P_{0}$" vertex and intermediate states are summed up to 2S excitations. Quark model parameters are obtained by fitting to 12 well-known charmonium states, allowing for feedback between the decaying particle and the induced mass shifts. Both of these technical steps are new and improve agreement with the experimental spectrum. In general, the masses receive small shifts once model parameters are refit. This is true in almost cases except the $χ_{cJ}(2P)$ multiplet, which experiences upwards mass shifts of order 150 MeV, has the ordering of the multiplet rearranged, and pushes the erstwhile $c\bar{c}$ ${2}^3P_1$ state well above $D^*\bar{D}$ threshold--observations that clarify the nature of the enigmatic $X(3872)$

hep-ph↗

arXiv2022

Quarkonium in a spin dependent quark anti-quark potential at finite temperature

We study the states of $c\bar{c}$ and $b\bar{b}$ system in a non-relativistic a spin dependent potential model at finite temperature. The potential incorporate color screening effect through a parameter $μ$. The parameter $μ$ along with strong coupling constant $α_s$ and string tension $σ$ are taken temperature dependent and their values are fitted to the Lattice data of quark anti-quark potential available at different values of temperature. The applied potential include spin-spin, spin-orbital, tensor interactions which allow us to study spin singlet and triplet states of quarkonia. By solving non-relativistic Schr{ö}dinger equation, we find the spectrum of quarkonium states at different temperature and also determine the critical temperature at which each state is dissolved. We find the critical temperature is decreased with orbital and radial excitations, however, for spin singlet and triplet states it remains same.

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arXiv2019

Properties of excited charmed-bottom mesons

We calculate the spectrum of $B_c$ mesons using a non-relativistic quark potential model. Using the calculated wave functions, we compute the radiative widths of $B_c$ excited states. The strong decay widths are calculated in a modified $^3P_0$ model, assuming harmonic oscillator wave functions. The hadronic transition rates of $B_c$ mesons are calculated using the Kuang-Yan approach. These results are used to determine branching ratios of possible decay channels of several $B_c$ excited states. Calculated branching ratios are then combined with production cross section of $B_c$ states at the LHC to suggest strategies to find missing excited states of $B_c$ mesons.

hep-ph↗

arXiv2018

Conventional and Hybrid $B_c$ Mesons in an Extended Potential Model

Using our analytical expressions that well model the lattice simulations of the gluonic excitations, we use the extended quark potential model to study the effects of orbital and radial excitations on the masses and sizes of conventional and hybrid $B_c$ mesons. A non relativistic formalism is used to numerically calculate the wave functions using the shooting method; this allows us also calculating the $E1$, $M1$ radiative partial widths for conventional meson to meson and hybrid to hybrid transitions. We incorporate spin mixing and compare our calculated spectrum and decay widths with the available experimental $B_c$ masses and the theoretically predicted spectra and the decay widths by other groups. Our results can help consider both conventional and hybrid quantum numbers to $B_c$ mesons as experimental results become available.

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arXiv2018

The Effect of the Earth Matter on Three Neutrino Oscillations and Sensitivity to CP Phase Parameter

We find an analytical expression of neutrino evolution operator in the Earth matter using perturbative approach in the context of three neutrino oscillations. We find that our analytical expression is highly accurate by comparing its results with the numerical solutions of neutrino evolution equation at energy scales relevant for solar, reactor, atmospheric, and accelerator neutrinos. Using our analytical approach we study the accuracy of hypothesis of treating the Earth density piecewise constant. We also study how the Earth matter effect can change the sensitivity to CP phase parameter $δ_{CP}$. Through nadir angle averaged conversion probabilities of neutrino and anti-neutrino, we find that the sensitivity to $δ_{CP}$ is maximum in the energy range 0.2 to 1 GeV and through energy averaged conversion probabilities, we find that the sensitivity is maximum about nadir angle $72.5^{\text{o}}$ for neutrinos oscillating in the Earth matter.

hep-ph↗

arXiv2018

Decays and spectrum of bottom and bottom strange mesons

The strong decay amplitudes and radiative partial widths of orbital and radially excited states of $B$ and $B_s$ mesons are presented. These results are obtained with a nonrelativistic potential quark model, the nonrelativistic reduction of the electromagnetic transition operator, and the "$^3P_0$" model of strong decays. The predictions are compared to experiment where possible and assignments for the recently discovered states, $B_1(5721)$, $B_2^*(5747)$, $B_J(5840)$, $B_J(5970)$, $B_{s1}(5830)$, and $B_{s2}^*(5840)$, are made.

hep-ph↗

arXiv2018

$ρJ/Ψ$ Scattering in an Improved Many Body Potential

We calculate the cross-sections for the processes $ρJ/ψ\rightarrow D^0\bar{D}^0$, $ρJ/ψ\rightarrow D^0\bar{D}^{0*}$ ($D^{0*}\bar{D}^{0}$) and $ρJ/ψ\rightarrow D^{0*}\bar{D}^{0*}$ using a QCD-motivated many-body overlap factor to modify the usual sum of two-body interaction model. The realistic Cornell potential has been used for pairwise interaction in the four quark Hamiltonian and noted to give lesser cross-sections as compared to the quadratic potential. The Resonating group method is employed along with the Born approximation which decouples its integral equations. It is pointed out that the additional QCD effect (a gluonic field ovelap factor) result in a significant suppression in the cross sections as compared to the more popular sum of two-body interaction.

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arXiv2017

Interactions of $B_{c}$ Meson in Relativistic Heavy-Ion Collisions

We calculate the absorbtion cross-sections of $B_{c}$ mesons by $π$ and $ρ$ mesons including anomalous processes using an effective hadronic Lagrangian. The enhancement of Bc production is expected due to QGP formation in heavy-ion experiments. However it is also expected that the production rate of Bc meson can be affected due to the interaction with comovers. These processes are relevant for experiments at RHIC. Thermal average cross-sections of $B_{c}$ are evaluated with form factor when a cut off parameter in it is 1 and 2 GeV. Using these thermal average cross-sections in the kinetic equation we investigate the time evolution of $B_{c}$ mesons due to dissociation in the hadronic matter formed at RHIC.

nucl-th↗

arXiv2017

Higher Hybrid Bottomonia in an Extended Potential Model

Using our extension of the quark potential model to hybrid mesons that fits well to the available lattice results, we now calculate the masses, radii, wave functions at origin, leptonic and two photon decay widths, E1 and M1 radiative transitions for a significant number of bottomonium mesons. These mesons include both conventional and hybrid ones with radial and angular excitations. Our numerical solutions of the Schrodinger equation are related to QCD through the Born-Oppenheimer approach. Relativistic corrections in masses and decay widths are also calculated by applying the leading order perturbation theory. The calculated results are compared with available experimental data and the theoretical results by other groups. We also identify the states of $Υ(10860)$, $Υ(11020)$, and $Y_b(10890)$ mesons by comparing their experimental masses and decay widths with our results.

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arXiv2016

$\bar{D}^{0}D^{0}$ $(D^{0}\bar{D}^{0})$ System in QCD-Improved Many Body Potential

For a system of current interest (composed of charm, anticharm quarks and a pair of light ones), we show trends in phenomenological implications of QCD-based improvements to a simple quark model treatment. We employ resonating group method to render this difficult four-body problem manageable. We use a quadratic confinement so as to be able to improve beyond the Born approximation. We report the position of the pole corresponding to $\bar{D}^{0}D^{0*}$ molecule for the best fit of a model parameter to the relevant QCD simulations. We point out the interesting possibility that the pole can be shifted to $3872$ MeV by introducing another parameter $I_{0}$ that changes the strength of the interaction in this one component of $X(3872)$. The revised value of this second parameter can guide future trends in modeling of the full exotic meson $X(3872)$. We also report the changes with $I_{0}$ in the $S$-wave spin averaged cross sections for $\bar{D}^{0}D^{0*}\longrightarrowωJ/ψ$ and $\bar{D}^{0}D^{0*}\longrightarrowρJ/ψ$. These cross sections are important regarding the study of QGP (quark gluon plasma).

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