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Walaa I. Eshraim

Publications and source records attributed to Walaa I. Eshraim.

At least 19 recordsLinked to original sources
arXiv2025

Hamilton-Jacobi Treatment of The Scalar Field Coupled to Two Fermions

The constrained filed system, the scalar field coupled to two flavours of fermions through Yukawa couplings, is treated by using the Hamilton-Jacobi approach. The equations of motion are obtained as total differential equations in many variables. The equations of motion are in exact agreement with those equations obtained using Dirac's method. Due to the Hamilton-Jacobi quantization, the path integral of the scalar field coupled to two fermions is obtained directly as an integration over the canonical phase space without using any gauge fixing condition.

physics.gen-ph↗
arXiv2025

Hamilton-Jacobi Treatment of Constraint Field Systems

Motivated by the Hamilton$-$Jacobi approach of fields with constraints, we analyse the classical structure of three different constrained field systems: (i) the scalar field coupled to two flavors of fermions through Yukawa couplings (ii) the scalar field coupled minimally to the vector potential (iii) the electromagnetic field coupled to a spinor. The equations of motion are obtained as total differential equations in many variables. The integrability conditions are investigated. The second and third constrained systems are quantized using canonical path integral formulation based on the Hamilton$-$Jacobi treatment.

physics.gen-ph↗
arXiv2023

Treatment of Landau-Ginzburg Theory with Constraints

Treatment of a singular Lagrangian with constraints using the canonical Hamiltonian approach is studied. We investigate Landau-Ginzburg theory as a constrained system using the Euler-Lagrange equation for the field system and the canonical approach. The equations of motion are obtained as total differential equations in many variables. It is shown that the simultaneous solutions of the Landau-Ginzburg theory with constraints by canonical approach lead to obtaining canonical phase space coordinates and the reduced phase space Hamiltonian without introducing Lagrange multipliers and without any additional gauge fixing condition.

physics.gen-ph↗
arXiv2023

Quantization of Non-Abelian Yang-Mills Theories

A non-Abelian theory of fermions interacting with gauge bosons, the constrained system, is studied. The equations of motion for a singular system are obtained as total differential equations in many variables. The integrability conditions are investigated and the set of equations of motion is integrable. The Senjanovic and the canonical methods are used to quantize the system, and the integration is taken over the canonical phase space coordinates.

physics.gen-ph↗
arXiv2023

Decay of the pseudoscalar glueball into vector, axial-vector, scalar and pseudoscalar mesons

We resume the investigation of the ground-state pseudoscalar glueball, $J^{PC}=0^{-+}$, by computing its two- and three-body decays into vector and axial-vector quark-antiquark meson fields additional to scalar and pseudoscalar mesons through the construction of an interaction chiral Lagrangian that produces these decays. We evaluate the branching ratio, via a parameter-free calculation, by setting the mass of the pseudoscalar glueball to $2.6$ GeV as predicted by lattice QCD simulations. We duplicate the computation for the branching ratios for a pseudoscalar glueball mass $2.37$ GeV which matches to the measured mass of the resonance $X(2370)$ in the BESIII experiment. The present channels and states are potentially reached and are interesting for the running BESIII and Belle-II experiments and the planned PANDA experiment at FAIR/GSI which will be able to detect the pseudoscalar glueball within the accessible energy range.

hep-ph↗
arXiv2022

Masses of vector and pseudovector hybrid mesons in a chiral symmetric model

We enlarge the chiral model, the so-called extended Linear Sigma Model (eLSM), by including the low-lying hybrid nonet with exotic quantum numbers $J^{PC}=1^{-+}$ and the nonet of their chiral partners with $J^{PC}=1^{+-}$ to a global $U(3)_r \times U(3)_l$ chiral symmetry. We use the assignment of the $π_1^{hyb}= π_1(1600)$ as input to determine the unknown parameters. Then, we compute the lightest vector and pseudovector hybrid masses that could guide ongoing and upcoming experiments in searching for hybrids.

hep-ph↗
arXiv2020

Hybrid phenomenology in a chiral approach

We calculate masses and decays of the (lightest) hybrid nonet with exotic quantum numbers $J^{PC}=1^{-+}$ and the nonet of their chiral partners with $J^{PC}=1^{+-}$ in the framework of the extended Linear Sigma Model (eLSM). As an input, we identify $π_{1}^{hyb}=π_{1}(1600)$ as a low-lying hybrid. We investigated interaction terms which fulfil chiral symmetry. For what concerns $π_{1}^{hyb},$ the most important decays are $π_{1}^{hyb}\rightarrow b_{1}π,$ $π_{1}(1600)\rightarrowρπη,$ $π_{1}^{hyb}% \rightarrowρπ,$ and $π_{1}^{hyb}\rightarrow KK^{\ast}(892).$ The decays $π_{1}^{hyb}\rightarrowηπ$ and $π_{1}^{hyb}\rightarrowη^{\prime }π$ are expected to be small but non-zero: they follow from a chirally symmetric interaction term that breaks explicitly the axial anomaly. For all the other members of the two hybrid nonets (for which no experimental candidates exist yet) we report decay ratios that may guide ongoing and future experiments.

hep-ph↗
arXiv2020

Hamilton-Jacobi Treatment of Superstring and Quantization of Fields with Constraints

The Hamilton-Jacobi formalism of constrained systems is used to study superstring. That obtained the equations of motion for a singular system as total differential equations in many variables. These equations of motion are in exact agreement with those equations obtained using Dirac's method. Moreover, the Hamilton-Jacobi quantization of a constrained system is discussed. Quantization of the relativistic local free field with a linear velocity of dimension D containing second-class constraints is studied. The set of Hamilton-Jacobi partial differential equations and the path integral of these theories are obtained by using the canonical path integral quantization. We figured out that the Hamilton-Jacobi path integral quantization of this system is in exact agreement with that given by using Senjanovic method. Furthermore, Hamilton-Jacobi path integral quantization of the scalar field coupled to two flavours of fermions through Yukawa couplings is obtained directly as an integration over the canonical phase space. Hamilton-Jacobi quantization is applied to the constraint field systems with finite degrees of freedom by investigating the integrability conditions without using any gauge fixing condition.

physics.gen-ph↗
arXiv2019

Decay of the pseudoscalar glueball and its first excited state into scalar and pseudoscalar mesons and their first excited states

We expand the study of the pseudoscalar glueball and its first excited state by constructing an interaction Lagrangian which produces the two- and three-body decays of the pseudoscalar glueball, $J^{PC}=0^{-+}$, into the (pseudo)scalar and the excited (pseudo)scalar mesons as well as by constructing other two different chiral Lagrangians which describe the two- and three-body decays of the first excited pseudoscalar glueball, $J^{PC}=0^{*-+}$, into the (pseudo)scalar and the excited (pseudo)scalar mesons. We compute the decay channels for the ground state of a pseudoscalar glueball with a mass of $2.6$ GeV and for the first excited pseudoscalar glueball with a mass $3.7$ GeV, following predictions from Lattice QCD in the quenched approximation. These states and channels are within reach of PANDA experiment at the upcoming FAIR facility experiment and ongoing BESIII experiment. In our approach, the various branching ratios are a parameter-free prediction.

hep-ph↗
arXiv2019

Phenomenology of a pseudoscalar glueball and charmed mesons

We study the vacuum properties of the pseudoscalar glueball and charmed mesons by using the so-called extended Linear Sigma Model (eLSM). This model includes scalar and pseudoscalar mesons, as well as vector and axial-vector mesons. We calculate the mesonic and baryonic decays of the pseudoscalar glueball, where we fixed its mass to $2.6$ GeV, as predicted by lattice-QCD simulations, and take a closer look at the scalar-isoscalar decay channel. As a second step, we enlarge the so-called extended linear Sigma model (eLSM) by including the charm quark to a global $U(4)_r\times U(4)_l$ chiral symmetry. Most of the parameters of the model have been determined in a previous work by fitting hadron properties involving three quark flavours. Only three new parameters, all related to the current charm quark mass, appear when introducing charmed mesons. We compute charmed mesons masses, weak decay constants, and strong decay widths of (open and hidden) charmed mesons. Moreover, we calculate the decay width of a pseudoscalar ground state charmonium $η_c$ into a pseudoscalar glueball and the decay widths of a scalar charmonium $χ_{c0}$ into the scalar glueball.

hep-ph↗
arXiv2018

Hadronic decays of the (pseudo-)scalar charmonium states $η_c$ and $χ_{c0}$ in the extended Linear Sigma Model

We study the phenomenology of the ground-state (pseudo-)scalar charmonia $η_c$ and $χ_{c0}$ in the framework of a $U(4)_r \times U(4)_l$ symmetric linear sigma model with (pseudo-)scalar and (axial-) vector mesons. Based on previous results for the spectrum of charmonia and the spectrum and (OZI-dominant) strong decays of open charmed mesons, we extend the study of this model to OZI-suppressed charmonia decays. This includes decays into 'ordinary' mesons but also particularly interesting channels with scalar-isoscalar resonances $f_0(1370),\, f_0(1500),\, f_0(1710)$ that may include sizeable contributions from a scalar glueball. We study the variation of the corresponding decay widths assuming different mixings between glueball and quark-antiquark states. We also compute the decay width of the pseudoscalar $η_c$ into a pseudoscalar glueball. In general, our results for decay widths are in reasonable agreement with experimental data where available. Order of magnitude predictions for as yet unmeasured states and channels are potentially interesting for BESIII, Belle II, LHCb as well as the future PANDA experiment at the FAIR facility.

hep-ph↗
arXiv2016

Decay modes of the excited pseudoscalar glueball

We study three different chiral Lagrangians that describe the two- and three-body decays of an excited pseudoscalar glueball, $J^{PC}=0^{*-+}$, into light mesons and charmonium states as well as into a scalar and pseudoscalar glueball. We compute the decay channels for an excited pseudoscalar glueball with a mass of $3.7$ GeV and consider a ground state pseudoscalar glueball of mass $2.6$ GeV, following predictions from lattice QCD simulations. These states and channels are in reach of the ongoing BESIII experiment and the PANDA experiments at the upcoming FAIR facility experiment. We present the resulting decay branching ratios with a parameter-free prediction.

hep-ph↗
arXiv2015

Phenomenology of charmed mesons in the extended Linear Sigma Model

We study the so-called extended linear sigma model for the case of four quark flavors. This model is based on global chiral symmetry and dilatation invariance and includes, besides scalar and pseudoscalar mesons, vector and axial-vector mesons. Most of the parameters of the model have been determined in previous work by fitting properties of mesons with three quark flavors. Only three new parameters, all related to the current charm quark mass, appear when introducing charmed mesons. Surprisingly, within the accuracy expected from our approach, the masses of open charmed mesons turn out to be in quantitative agreement with experimental data. On the other hand, with the exception of $J/ψ$, the masses of charmonia are underpredicted by about 10\%. It is remarkable that our approach correctly predicts (within errors) the mass splitting between spin-0 and spin-1 negative-parity open charm states. This indicates that, although the charm quark mass breaks chiral symmetry quite strongly explicitly, this symmetry still seems to have some influence on the properties of charmed mesons.

hep-ph↗
arXiv2014

Vacuum properties of open charmed mesons in a chiral symmetric model

We present a $U(4)_R \times U(4)_L$ chirally symmetric model, which in addition to scalar and pseudoscalar mesons also includes vector and axial-vector mesons. A part from the three new parameters pertaining to the charm degree of freedom, the parameters of the model are fixed from the $N_f=3$ flavor sector. We calculate open charmed meson masses and the weak decay constants of nonstrange open charm $D$ and strange open charm $D_S$. We also evaluate the (OZI-dominant) strong decays of open charmed mesons. The results are turn out to be in quantitative agreement with experimental data.

hep-ph↗
arXiv2014

A pseudoscalar glueball and charmed mesons in the extended Linear Sigma Model

In the framework of the so-called extended linear sigma model (eLSM), we include a pseudoscalar glueball with a mass of 2.6 GeV (as predicted by Lattice-QCD simulations) and we compute the two- and three-body decays into scalar and pseudoscalar mesons. This study is relevant for the future PANDA experiment at the FAIR facility. As a second step, we extend the eLSM by including the charm quark according to the global $U(4)_R \times U(4)_L$ chiral symmetry. We compute the masses, weak decay constants and strong decay widths of open charmed mesons. The precise description of the decays of open charmed states is important for the CBM experiment at FAIR.

hep-ph↗
arXiv2014

Decays of open charmed mesons in the extended Linear Sigma Model

We enlarge the so-called extended linear Sigma model (eLSM) by including the charm quark according to the global $U(4)_r\times U(4)_l$ chiral symmetry. In the eLSM, besides scalar and pseudoscalar mesons, also vector and axial-vector mesons are present. Almost all the parameters of the model were fixed in a previous study of mesons below 2 GeV. In the extension to the four-flavor case, only three additional parameters (all of them related to the bare mass of the charm quark) appear. We compute the (OZI-dominant) strong decays of open charmed mesons. The results are compatible with the experimental data, although the theoretical uncertainties are still large.

hep-ph↗
arXiv2013

Decay of the pseudoscalar glueball into scalar and pseudoscalar mesons

We study a chiral Lagrangian which describes the two- and three-body decays of a pseudoscalar glueball into scalar and pseudoscalar mesons. The various branching ratios are a parameter-free prediction of our approach. We compute the decay channels for a pseudoscalar glueball with a mass of 2.6 GeV, as predicted by Lattice QCD in the quenched approximation, which is in the reach of the PANDA experiment at the upcoming FAIR facility. For completeness, we also repeat the calculation for a glueball mass of 2.37 GeV which corresponds to the mass of the resonance X(2370) measured in the BESIII experiment.

hep-ph↗