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A. Bashir

Publications and source records attributed to A. Bashir.

At least 37 records · Page 2Linked to original sources
arXiv2023

Light-front Wave Functions of Vector Mesons in an Algebraic Model

Inspired by the recent development of an algebraic model which provides an adequate and unified description of the internal structure of the lowest-lying pseudo-scalar mesons, belonging both to the light quarks sector and to the one of heavy quarks, we perform its first extension to the vector-meson case. The algebraic model describes meson's structure in terms of the spectral density function that appears in a Nakanishi integral representation of the covariant quark-antiquark bound-state amplitude, \emph{i.e.}, the Bethe-Salpeter amplitude. We compute the leading-twist light-front wave functions of the $ρ(770)$, $ϕ(1020)$, $J/ψ$ and $Υ(1S)$ mesons through their connection with the parton distribution amplitudes. Among the results we present, the following are of particular interest: (i) transverse light-front wave functions can be obtained algebraically from the corresponding parton distribution amplitudes, whereas that is not the case for longitudinal light-front wave functions, which requires an intermediate step where a spectral density function must be derived from the particular parton distribution amplitude; (ii) the derived spectral density functions show marked differences between light and heavy vector mesons, the latter being narrower as compared to the former; these are also non-positive definite, although the integral over the entire curve is larger than zero as expected; and (iii) the longitudinal and transverse light-front wave functions of vector mesons with light quark content exhibit steep $x$- and $p_\perp^2$-dependence, while those of the $J/ψ$ and $Υ(1S)$ mesons are characterized by narrow distributions in the $x$-range but, comparatively, much more gradual fall-offs with respect to the $p_\perp^2$-range depicted.

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arXiv2023

Electromagnetic Form Factors and Charge Radii of Pseudoscalar and Scalar Mesons: A Comprehensive Contact Interaction Analysis

We carry out a comprehensive survey of electromagnetic form factors of all light, heavy and heavy-light ground-state pseudoscalar and scalar mesons. Our analysis is based upon a Schwinger-Dyson equations treatment of a vector $\times$ vector contact interaction. It incorporates confinement and ensures axial vector and vector Ward-Takahashi identities are satisfied along with the corresponding corollaries such as the Goldberger-Treiman relations. The algebraic simplicity of the model allows us to compute the form factors at arbitrarily large virtualities of the probing photon momentum squared with relative ease. Wherever possible and insightful, we compare our results for the electromagnetic form factors and the charge radii with those obtained earlier through Schwinger-Dyson equations, lattice and with experimental observations available. We also comment on the scope and shortcomings of the model.

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arXiv2022

Electron-Photon Vertex and Dynamical Chiral Symmetry Breaking in Reduced QED: An Advanced Study of Gauge Invariance

We study the effect of a refined electron-photon vertex on the dynamical breaking of chiral symmetry in reduced quantum electrodynamics. We construct an educated {\em ansatz} for this vertex which satisfies the required discrete symmetries under parity, time reversal and charge conjugation operations. Furthermore, it reproduces its asymptotic perturbative limit in the weak coupling regime and ensures the massless electron propagator is multiplicatively renormalizable in its leading logarithmic expansion. Employing this vertex {\em ansatz}, we solve the gap equation to compute dynamically generated electron mass whose dependence on the electromagnetic coupling is found to satisfy Miransky scaling law. We also investigate the gauge dependence of this dynamical mass as well as that of the critical coupling above which chiral symmetry is dynamically broken. As a litmus test of our vertex construction, both these quantities are rendered virtually gauge independent within a certain interval of values considered for the covariant gauge parameter.

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arXiv2022

Pseudo-scalar mesons: light front wave functions, GPDs and PDFs

We develop a unified algebraic model which satisfactorily describes the internal structure of pion and kaon as well as heavy quarkonia ($η_c$ and $η_b$). For each of these mesons, we compute their generalized parton distributions (GPDs), built through the overlap representation of their light-front wave function, tightly constrained by the modern and precise knowledge of their quark distribution amplitudes. From this three-dimensional knowledge of mesons, we deduce parton distribution functions (PDFs) as well as electromagnetic form factors and construct the impact parameter space GPDs. The PDFs for mesons formed with light quarks are then evolved from the hadronic scale of around 0.3 GeV to 5.2 GeV, probed in experiments. We make explicit comparisons with experimental results available and with earlier theoretical predictions.

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arXiv2022

Elastic meson form factors in a unified scheme

The extraction of elastic form factors for mesons in the context of the contact interaction model is revisited in this manuscript. The dressed masses of quarks and mesons are determined through the gap and Bethe-Salpeter equations. The generic elastic scattering process $Mγ\to M$ is studied for the meson $M$ formed of two differently flavored quarks. The charge radii of scalar, pseudoscalar, vector and axial-vector mesons are also extracted by virtue of explicit calculation of the meson elastic form factors.

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arXiv2021

Mesons and Baryons: Parity Partners

We calculate masses of light and heavy mesons as well as baryons of negative parity containing $u,d,s,c$ and $b$ quarks. It is an extension of our previous work where we had studied the positive parity baryons. We adopt a quark-diquark picture of baryons where the diquarks are non-pointlike with a finite spatial extension. The mathematical foundation for this analysis is implemented through a symmetry-preserving Schwinger-Dyson equations treatment of a vector-vector contact interaction, which preserves key features of quantum chromodynamics, such as confinement, chiral symmetry breaking, axial vector Ward-Takahashi identity and low-energy Goldberger-Treiman relations. This treatment simultaneously describes mesons and provides attractive correlations for diquarks in the $\overline{3}$ representation. Employing this model, we compute the spectrum and masses of all spin-1/2 and spin-3/2 baryons of negative parity, supplementing our earlier evaluation of positive parity baryons, containing 1, 2 or 3 heavy quarks. In the process, we calculate masses of a multitude of mesons and corresponding diquarks. Wherever possible, we make comparisons of our results with known experimental observations as well as theoretical predictions of several models and approaches including lattice quantum chromodynamics, finding satisfactory agreement. We also make predictions for heavier states not yet observed in the experiment.

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arXiv2020

The anomalous magnetic moment of the muon in the Standard Model

We review the present status of the Standard Model calculation of the anomalous magnetic moment of the muon. This is performed in a perturbative expansion in the fine-structure constant $α$ and is broken down into pure QED, electroweak, and hadronic contributions. The pure QED contribution is by far the largest and has been evaluated up to and including $\mathcal{O}(α^5)$ with negligible numerical uncertainty. The electroweak contribution is suppressed by $(m_μ/M_W)^2$ and only shows up at the level of the seventh significant digit. It has been evaluated up to two loops and is known to better than one percent. Hadronic contributions are the most difficult to calculate and are responsible for almost all of the theoretical uncertainty. The leading hadronic contribution appears at $\mathcal{O}(α^2)$ and is due to hadronic vacuum polarization, whereas at $\mathcal{O}(α^3)$ the hadronic light-by-light scattering contribution appears. Given the low characteristic scale of this observable, these contributions have to be calculated with nonperturbative methods, in particular, dispersion relations and the lattice approach to QCD. The largest part of this review is dedicated to a detailed account of recent efforts to improve the calculation of these two contributions with either a data-driven, dispersive approach, or a first-principle, lattice-QCD approach. The final result reads $a_μ^\text{SM}=116\,591\,810(43)\times 10^{-11}$ and is smaller than the Brookhaven measurement by 3.7$σ$. The experimental uncertainty will soon be reduced by up to a factor four by the new experiment currently running at Fermilab, and also by the future J-PARC experiment. This and the prospects to further reduce the theoretical uncertainty in the near future-which are also discussed here-make this quantity one of the most promising places to look for evidence of new physics.

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arXiv2020

Existence of global solutions and blow-up of solutions for coupled systems of fractional diffusion equations

We study the Cauchy problem for a system of semi-linear coupled fractional-diffusion equations with polynomial nonlinearities posed in $% \mathbb{R}_{+}\times \mathbb{R}^{N}$. Under appropriate conditions on the exponents and the orders of the fractional time derivatives, we present a critical value of the dimension N, for which global solutions with small data exist, otherwise solutions blow-up in finite time. Furthermore, the large time behavior of global solutions is discussed.

math.AP↗
arXiv2020

Contribution of neutral pseudoscalar mesons to $a_μ^{HLbL}$ within a Schwinger-Dyson equations approach to QCD

A continuum approach to Quantum Chromodynamics (QCD), based upon Schwinger-Dyson (SD) and Bethe-Salpeter (BS) equations, is employed to provide a tightly constrained prediction for the $γ^{*} γ^{*} \rightarrow \{ π^0, η, η', η_c, η_b \}$ transition form factors (TFFs) and their corresponding pole contribution to the hadronic light-by-light (HLbL) piece of the anomalous magnetic moment of the muon ($a_μ$). This work relies on a practical and well-tested quark-photon vertex Ansatz approach to evaluate the TFFs for arbitrary space-like photon virtualities, in the impulse approximation. The numerical results are parametrized meticulously, ensuring a reliable evaluation of the HLbL contributions to $a_μ$. We obtain: $a_μ^{π^0-\textrm{pole}} = (6.14 \pm 0.21) \times 10^{-10}$, $a_μ^{η-\textrm{pole}} = (1.47 \pm 0.19) \times 10^{-10}$, $a_μ^{η'-\textrm{pole}} = (1.36 \pm 0.08) \times 10^{-10}$, yielding a total value of $a_μ^{π^0+η+η'-\textrm{pole}} = (8.97 \pm 0.48) \times 10^{-10}$, compatible with contemporary determinations. Notably, we find that $a_μ^{η_c+η_b-\textrm{pole}} \approx a_μ^{η_c-\textrm{pole}} = (0.09 \pm 0.01) \times 10^{-10}$, which might not be negligible once the percent precision in the computation of the light pseudoscalars is reached.

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arXiv2018

Transverse Takahashi Identities and Their Implications for Gauge Independent Dynamical Chiral Symmetry Breaking

In this article, we employ transverse Takahashi identities to impose valuable non-perturbative constraints on the transverse part of the fermion-photon vertex in terms of new form factors, the so called $Y_i$ functions. We show that the implementation of these identities is crucial in ensuring the correct local gauge transformation of the fermion propagator and its multiplicative renormalizability. Our construction incorporates the correct symmetry properties of the $Y_i$ under charge conjugation operation as well as their well-known one-loop expansion in the asymptotic configuration of incoming and outgoing momenta. Furthermore, we make an explicit analysis of various existing constructions of this vertex against the demands of transverse Takahashi identities and the previously established key features of quantum electrodynamics, such as gauge invariance of the critical coupling above which chiral symmetry is dynamically broken. We construct a simple example in its quenched version and compute the mass function as we vary the coupling strength and also calculate the corresponding anomalous dimensions $γ_m$. There is an excellent fit to the Miransky scalling law and we find $γ_m=1$ rather naturally in accordance with some earlier results in literature, using arguments based on Cornwall-Jackiw-Tomboulis effective potential technique. Moreover, we numerically confirm the gauge invariance of this critical coupling.

nucl-th↗
arXiv2018

Structure of the orbital excited $N^*$ from the Schwinger-Dyson equations

We present progress in the evaluation of $γ^* N \rightarrow N^*(1535)$ transition form factors in a quark-diquark picture of these baryons. Our analysis is based upon the fully-consistent treatment of a vector $\times$ vector contact interaction, embedded in the interlaced formalism of Schwinger-Dyson and Bethe-Salpeter equations.

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arXiv2018

A fresh look at the (non-)Abelian Landau-Khalatnikov-Fradkin transformations

The Landau-Khalatnikov-Fradkin transformations (LKFTs) allow to interpolate $n$-point functions between different gauges. We first offer an alternative derivation of these LKFTs for the gauge and fermions field in the Abelian (QED) case when working in the class of linear covariant gauges. Our derivation is based on the introduction of a gauge invariant transversal gauge field, which allows a natural generalization to the non-Abelian (QCD) case of the LKFTs. To our knowledge, within this rigorous formalism, this is the first construction of the LKFTs beyond QED. The renormalizability of our setup is guaranteed to all orders. We also offer a direct path integral derivation in the non-Abelian case, finding full consistency.

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arXiv2017

Heavy quarkonia in a contact interaction and an algebraic model: mass spectrum, decay constants, charge radii and elastic and transition form factors

For the flavor-singlet heavy quark system of bottomonia, we compute the masses of the ground state mesons in four different channels, namely, pseudo-scalar ($η_{b}(1S)$), vector ($Υ(1S)$), scalar ($χ_{b_0}(1P)$) and axial vector ($χ_{b_{1}}(1P)$). We also calculate the weak decay constants of the $η_{b}(1S)$ and $Υ(1S)$ as well as the charge radius of $η_{b}(1S)$. It complements our previous study of the corresponding charmonia systems: $η_c(1S)$, $J/Ψ(1S)$, $χ_{c_0}(1P)$) and ($χ_{c_{1}}(1P)$). The unified formalism for this analysis is provided by a symmetry-preserving Schwinger-Dyson equations treatment of a vector$\times$vector contact interaction. Whenever a comparison is possible, our results are in fairly good agreement with experimental data and model calculations based upon Schwinger-Dyson and Bethe-Salpeter equations involving sophisticated interaction kernels. Within the same framework, we also report the elastic and transition form factors to two photons for the pseudo-scalar channels $η_{c}(1S)$ and $η_{b}(1S)$ in addition to the elastic form factors for the vector mesons $J/Ψ$ and $Υ$ for a wide range of photon momentum transfer squared ($Q^2$). For $η_{c}(1S)$ and $η_{b}(1S)$, we also provide predictions of an algebraic model which correlates remarkably well between the known infrared and ultraviolet limits of these form factors.

nucl-th↗
arXiv2017

Quark-gluon Vertex: A Perturbation Theory Primer and Beyond

There has been growing evidence that the infrared enhancement of the form factors defining the full quark-gluon vertex plays an important role in realizing a dynamical breakdown of chiral symmetry in quantum chromodynamics, leading to the observed spectrum and properties of hadrons. Both the lattice and the Schwinger-Dyson communities have begun to calculate these form factors in various kinematical regimes of momenta involved. A natural consistency check for these studies is that they should match onto the perturbative predictions in the ultraviolet, where non-perturbative effects mellow down. In this article, we carry out a numerical analysis of the one-loop result for all the form factors of the quark-gluon vertex. Interestingly, even the one-loop results qualitatively encode most of the infrared enhancement features expected of their non-perturbative counter parts. We analyze various kinematical configurations of momenta: symmetric, on-shell and asymptotic. The on-shell limit enables us to compute anomalous chromomagnetic moment of quarks. The asymptotic results have implications for the multiplicative renormalizability of the quark propagator and its connection with the Landau-Khalatnikov-Fradkin transformations, allowing us to analyze and compare various Ans$\ddot{a}$tze proposed so far.

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arXiv2016

Structure of the neutral pion and its electromagnetic transition form factor

The $γ^\ast γ\to π^0$ transition form factor, $G(Q^2)$, is computed on the entire domain of spacelike momenta using a continuum approach to the two valence-body bound-state problem in relativistic quantum field theory: the result agrees with data obtained by the CELLO, CLEO and Belle Collaborations. The analysis unifies this prediction with that of the pion's valence-quark parton distribution amplitude (PDA) and elastic electromagnetic form factor, and demonstrates, too, that a fully self-consistent treatment can readily connect a pion PDA that is a broad, concave function at the hadronic scale with the perturbative QCD prediction for the transition form factor in the hard photon limit. The normalisation of that limit is set by the scale of dynamical chiral symmetry breaking, which is a crucial feature of the Standard Model. Understanding of the latter will thus remain incomplete until definitive transition form factor data is available on $Q^2>10\,$GeV$^2$.

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arXiv2016

Constructing Scalar-Photon Three Point Vertex in Massless Quenched Scalar QED

Non perturbative studies of Schwinger-Dyson equations (SDEs) require their infnite, coupled tower to be truncated in order to reduce them to a practically solvable set. In this connection, a physically acceptable ansatz for the three point vertex is the most favorite choice. Scalar quantum electrodynamics (sQED) provides a simple and neat platform to address this problem. The most general form of the three point scalar-photon vertex can be expressed in terms of only two independent form factors, a longitudinal and a transverse one. Ball and Chiu have demonstrated that the longitudinal vertex is fixed by requiring the Ward-Fradkin-Green-Takahashi identity (WFGTI), while the transverse vertex remains undetermined. In massless quenched sQED, we construct the transverse part of the non perturbative scalar-photon vertex. This construction (i) ensures multiplicative renormalizability (MR) of the scalar propagator in keeping with the Landau-Khalatnikov-Fradkin transformations (LKFTs), (ii) has the same transformation properties as the bare vertex under charge conjugation, parity and time reversal, (iii) has no kinematic singularities and (iv) reproduces one loop asymptotic result in the weak coupling regime of the theory.

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arXiv2015

Local Gauge Transformation for the Quark Propagator in an SU(N) Gauge Theory

In an SU(N) gauge field theory, the n-point Green functions, namely, propagators and vertices, transform under the simultaneous local gauge variations of the gluon vector potential and the quark matter field in such a manner that the physical observables remain invariant. In this article, we derive this intrinsically non perturbative transformation law for the quark propagator within the system of covariant gauges. We carry out its explicit perturbative expansion till O(g_s^6) and, for some terms, till O(g_s^8). We study the implications of this transformation for the quark-anti-quark condensate, multiplicative renormalizability of the massless quark propagator, as well as its relation with the quark-gluon vertex at the one-loop order. Setting the color factors C_F=1 and C_A=0, Landau-Khalatnikov-Fradkin transformation for the abelian case of quantum electrodynamics is trivially recovered.

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