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A. Bashir

Publications and source records attributed to A. Bashir.

At least 55 records · Page 3Linked to original sources
arXiv2014

QCD: Restoration of Chiral Symmetry and Deconfinement for Large N_f

Exploiting the recent lattice results for the infrared gluon propagator with light dynamical quarks, we solve the gap equation for the quark propagator. We thus model the chiral symmetry breaking mechanism with increasing number of flavours and study confinement (intimately tied with the analytic properties of QCD Schwinger functions) order parameters. We obtain, with this approach, clear signals of chiral symmetry restoration and deconfinement when the number of light quark flavors exceeds a critical value of $N_f^c \approx 8 \pm 1$, in agreement with the state-of-the-art direct lattice analysis of chiral symmetry restoration in QCD.

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arXiv2013

Multiple solutions for the fermion mass function in QED3

Theories that support dynamical generation of a fermion mass gap are of widespread interest. The phenomenon is often studied via the Dyson-Schwinger equation (DSE) for the fermion self energy; i.e., the gap equation. When the rainbow truncation of that equation supports dynamical mass generation, it typically also possesses a countable infinity of simultaneous solutions for the dressed-fermion mass function, solutions which may be ordered by the number of zeros they exhibit. These features can be understood via the theory of nonlinear Hammerstein integral equations. Using QED3 as an example, we demonstrate the existence of a large class of gap equation truncations that possess solutions with damped oscillations. We suggest that there is a larger class, quite probably including the exact theory, which does not. The structure of the dressed-fermion--gauge-boson vertex is an important factor in deciding the issue.

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arXiv2013

Studies of Nucleon Resonance Structure in Exclusive Meson Electroproduction

Studies of the structure of excited baryons are key to the N* program at Jefferson Lab. Within the first year of data taking with the Hall B CLAS12 detector following the 12 GeV upgrade, a dedicated experiment will aim to extract the N* electrocouplings at high photon virtualities Q2. This experiment will allow exploration of the structure of N* resonances at the highest photon virtualities ever yet achieved, with a kinematic reach up to Q2 = 12 GeV2. This high-Q2 reach will make it possible to probe the excited nucleon structures at distance scales ranging from where effective degrees of freedom, such as constituent quarks, are dominant through the transition to where nearly massless bare-quark degrees of freedom are relevant. In this document, we present a detailed description of the physics that can be addressed through N* structure studies in exclusive meson electroproduction. The discussion includes recent advances in reaction theory for extracting N* electrocouplings from meson electroproduction off protons, along with QCD-based approaches to the theoretical interpretation of these fundamental quantities. This program will afford access to the dynamics of the non-perturbative strong interaction responsible for resonance formation, and will be crucial in understanding the nature of confinement and dynamical chiral symmetry breaking in baryons, and how excited nucleons emerge from QCD.

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arXiv2012

Vacuum Polarization and Dynamical Chiral Symmetry Breaking: Phase Diagram of QED with Four-Fermion Contact Interaction

We study chiral symmetry breaking for fundamental charged fermions coupled electromagnetically to photons with the inclusion of four-fermion contact self-interaction term. We employ multiplicatively renormalizable models for the photon dressing function and the electron-photon vertex which minimally ensures mass anomalous dimension = 1. Vacuum polarization screens the interaction strength. Consequently, the pattern of dynamical mass generation for fermions is characterized by a critical number of massless fermion flavors above which chiral symmetry is restored. This effect is in diametrical opposition to the existence of criticality for the minimum interaction strength necessary to break chiral symmetry dynamically. The presence of virtual fermions dictates the nature of phase transition. Miransky scaling laws for the electromagnetic interaction strength and the four-fermion coupling, observed for quenched QED, are replaced by a mean-field power law behavior corresponding to a second order phase transition. These results are derived analytically by employing the bifurcation analysis, and are later confirmed numerically by solving the original non-linearized gap equation. A three dimensional critical surface is drawn to clearly depict the interplay of the relative strengths of interactions and number of flavors to separate the two phases. We also compute the beta-function and observe that it has ultraviolet fixed point. The power law part of the momentum dependence, describing the mass function, reproduces the quenched limit trivially. We also comment on the continuum limit and the triviality of QED.

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arXiv2012

Quark flavour effects on gluon and ghost propagators

We compute the full non-perturbative ghost and gluon two-point Green functions by using gauge field configurations with $\nf=2$ and $\nf=2+1+1$ twisted-mass quark flavours. We use simulations with several different light quark masses, heavy quark masses close to that of the strange and charm quarks, and lightest pseudoscalar masses ranging from 270 to 510 [MeV]. Quark flavour effects on both the gluon and the ghost propagators are then investigated in a wide range of momenta, bridging the deep infrared and intermediate momenta domain of QCD interactions in the presence of dynamical quarks. The ghost-gluon vertex is also indirectly probed through a consistency requirement among the lattice data for the gluon and ghost propagators and the ghost propagator Schwinger-Dyson equation. The effective full QCD coupling is finally constructed, and its dependence on the presence of dynamical fermions scrutinized.

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arXiv2011

Dynamical chiral symmetry breaking and the fermion--gauge-boson vertex

We present a workable model for the fermion-photon vertex, which is expressed solely in terms of functions that appear in the fermion propagator and independent of the angle between the relative momenta, and does not explicitly depend on the covariant-gauge parameter. It nevertheless produces a critical coupling for dynamical chiral symmetry breaking that is practically independent of the covariant-gauge parameter and an anomalous magnetic moment distribution for the dressed fermion that agrees in important respects with realistic numerical solutions of the inhomogeneous vector Bethe-Salpeter equation.

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arXiv2011

pi- and rho-mesons, and their diquark partners, from a contact interaction

We present a unified Dyson-Schwinger equation treatment of static and electromagnetic properties of pseudoscalar and vector mesons, and scalar and axial-vector diquark correlations, based upon a vector-vector contact-interaction. A basic motivation for this study is the need to document a comparison between the electromagnetic form factors of mesons and those diquarks which play a material role in nucleon structure. This is an important step toward a unified description of meson and baryon form factors based on a single interaction. A notable result, therefore, is the large degree of similarity between related meson and diquark form factors. The simplicity of the interaction enables computation of the form factors at arbitrarily-large spacelike-Q^2, which enables us to expose a zero in the rho-meson electric form factor at z_Q^ρ~ Sqrt[6] m_ρ. Notably, r_ρ*z_Q^ρ~ r_D*z_Q^D, where r_ρ, r_D are, respectively, the electric radii of the rho-meson and deuteron.

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arXiv2011

Critical Number of Flavours in QED

We demonstrate that in unquenched quantum electrodynamics (QED), chiral symmetry breaking ceases to exist above a critical number of fermion flavours $N_f$. This is a necessary and sufficient consequence of the fact that there exists a critical value of electromagnetic coupling $α$ beyond which dynamical mass generation gets triggered. We employ a multiplicatively renormalizable photon propagator involving leading logarithms to all orders in $α$ to illustrate this. We study the flavour and coupling dependence of the dynamically generated mass analytically as well as numerically. We also derive the scaling laws for the dynamical mass as a function of $α$ and $N_f$. Up to a multiplicative constant, these scaling laws are related through $(α, α_c) \leftrightarrow (1/N_f, 1/N_f^c)$. Calculation of the mass anomalous dimension $γ_m$ shows that it is always greater than its value in the quenched case. We also evaluate the $β$-function. The criticality plane is drawn in the $(α,N_f)$ phase space which clearly depicts how larger $N_f$ is required to restore chiral symmetry for an increasing interaction strength.

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arXiv2010

Abelian anomaly and neutral pion production

We show that in fully-self-consistent treatments of the pion; namely, its static properties and elastic and transition form factors, the asymptotic limit of the product Q^2 G_{γ* γπ^0}(Q^2), determined a priori by the interaction employed, is not exceeded at any finite value of spacelike momentum transfer. Furthermore, in such a treatment of a vector-vector contact-interaction one obtains a γ* γ-> π^0 transition form factor that disagrees markedly with all available data. We explain that the contact interaction produces a pion distribution amplitude which is flat and nonvanishing at the endpoints. This amplitude characterises a pointlike pion bound-state. Such a state has the hardest possible form factors; i.e., form factors which become constant at large momentum transfers and hence are in striking disagreement with completed experiments. On the other hand, interactions with QCD-like behaviour produce soft pions, a valence-quark distribution amplitude that vanishes as ~(1-x)^2 for x~1, and results that agree with the bulk of existing data. Our analysis supports a view that the large-Q^2 data obtained by the BaBar Collaboration is not an accurate measure of the γ* γ-> π^0 form factor.

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arXiv2010

The anapole moment in scalar quantum electrodynamics

The anapole moment of a charged scalar particle is studied in a model independent fashion, using the effective Lagrangian technique, as well as radiatively within the context of scalar quantum electrodynamics (SQED). It is shown that this gauge structure is characterized by a non renormalizable interaction, which is radiatively generated at the one--loop. It is found that the resulting anapole moment for off-shell particles, though free of ultraviolet divergences, is gauge dependent and thus it is not a physical observable. We also study some of its kinematical limits. In particular, it is shown that its value comes out to be zero when all particles are on--shell.

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arXiv2010

Pion form factor from a contact interaction

In a Poincare'-covariant vector-boson-exchange theory, the pion possesses components of pseudovector origin, which materially influence its observable properties. For a range of such quantities, we explore the consequences of a momentum-independent interaction, regularised in a symmetry-preserving manner. The contact interaction, whilst capable of describing pion static properties, produces a form factor whose: evolution for Q^2>0.17GeV^2 disagrees markedly with experiment; and asymptotic power-law behaviour conflicts strongly with perturbative-QCD.

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arXiv2009

On the Compton scattering vertex for massive scalar QED

We investigate the Compton scattering vertex of charged scalars and photons in scalar quantum electrodynamics (SQED). We carry out its non perturbative construction consistent with Ward-Fradkin-Green-Takahashi identity (WFGTI) which relates 3-point vertices to the 4-point ones. There is an undetermined part which is transverse to one or both the external photons, and needs to be evaluated through perturbation theory. We present in detail how the transverse part at the 1-loop order can be evaluated for completely general kinematics of momenta involved in covariant gauges and dimensions. This involves the calculation of genuine 4-point functions with three massive propagators, the most non-trivial integrals reported in this paper. We also discuss possible applications of our results.

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arXiv2009

Gauge invariance of a critical number of flavours in QED3

The fermion propagator in an arbitrary covariant gauge can be obtained from the Landau gauge result via a Landau-Khalatnikov-Fradkin transformation. This transformation can be written in a practically useful form in both configuration and momentum space. It is therefore possible to anticipate effects of a gauge transformation on the propagator's analytic properties. These facts enable one to establish that if a critical number of flavours for chiral symmetry restoration and deconfinement exists in noncompact QED3, then its value is independent of the gauge parameter. This is explicated using simple forms for the fermion-photon vertex and the photon vacuum polarisation. The illustration highlights pitfalls that must be avoided in order to arrive at valid conclusions. Landau gauge is seen to be the covariant gauge in which the propagator avoids modification by a non-dynamical gauge-dependent exponential factor, whose presence can obscure truly observable features of the theory.

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arXiv2008

Gauge Covariance Relations and the Fermion Propagator in Maxwell-Chern-Simons QED3

We study the gauge covariance of the fermion propagator in Maxwell-Chern-Simons planar quantum electrodynamics (QED$_3$) considering four-component spinors with parity-even and parity-odd mass terms both for fermions and photons. Starting with its tree level expression in the Landau gauge, we derive a non perturbative expression for this propagator in an arbitrary covariant gauge by means of its Landau-Khalatnikov-Fradkin transformation (LKFT). We compare our findings in the weak coupling regime with the direct one-loop calculation of the two-point Green function and observe perfect agreement up to a gauge independent term. We also reproduce results derived in earlier works as special cases of our findings.

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arXiv2008

Regarding confinement and dynamical chiral symmetry breaking in QED3

We establish that QED3 can possess a critical number of flavours, N_f^c, associated with dynamical chiral symmetry breaking if, and only if, the fermion wave function renormalisation and photon vacuum polarisation are homogeneous functions at infrared momenta when the fermion mass function vanishes. The Ward identity entails that the fermion-photon vertex possesses the same property and ensures a simple relationship between the homogeneity degrees of each of these functions. Simple models for the photon vacuum polarisation and fermion-photon vertex are used to illustrate these observations. The existence and value of N_f^c are contingent upon the precise form of the vertex but any discussion of gauge dependence is moot. We introduce an order parameter for confinement. Chiral symmetry restoration and deconfinement are coincident owing to an abrupt change in the analytic properties of the fermion propagator when a nonzero scalar self-energy becomes insupportable.

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arXiv2007

Truncated Schwinger-Dyson Equations and Gauge Covariance in QED3

We study the Landau-Khalatnikov-Fradkin transformations (LKFT) in momentum space for the dynamically generated mass function in QED3. Starting from the Landau gauge results in the rainbow approximation, we construct solutions in other covariant gauges. We confirm that the chiral condensate is gauge invariant as the structure of the LKFT predicts. We also check that the gauge dependence of the constituent fermion mass is considerably reduced as compared to the one obtained directly by solving SDE.

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arXiv2007

$\barψ ψ$-condensate in constant magnetic fields

We solve Dirac equation in the presence of a constant magnetic field in (3+1)- and (2+1)-dimensions. Quantizing the fermion field, we calculate $\barψ ψ$-condensate from first principles for parity conserving and violating Lagrangians for arbitrary field strength. We make comparison with the results already known in the literature for some particular cases and point out the relevance of our work for possible physical applications.

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