This study provides an extensive investigation of the mass spectra, and their strong decays and M1 transitions, of D-mesons in a Relativistic Independent Quark Model (RIQM). The quark-antiquark interaction is described by an equal components of scalar and vector potentials of square-root form, supplemented with essential corrections arising from center-of-mass motion, gluon-exchange effects and pionic contributions. These refinements enable accurate reproduction of the ground- and excited-state masses, which exhibit reasonable agreement with experimental and lattice QCD results. The radial and orbital excitations, covering the 5S, 3P and 3D states, have been systematically computed. The obtained spin-averaged masses and fine-structure splitting correspond closely with those reported by PDG and LHCb. Employing the momentum-space wave functions, the pseudoscalar and vector decay constants are evaluated, yielding results reasonably consistent with those obtained from lattice QCD and QCD sum-rule calculations. The two-body strong decay widths of various charmed resonances are evaluated through the Heavy Quark Effective Theory (HQET) in combination with the chiral Lagrangian approach. The magnetic-dipole (M1) transitions are also examined. The predicted strong decay widths for highly excited states follow the observed experimental and theoretical results. Additionally, the vector-pseudoscalar-pseudoscalar (VPP) coupling constants are extracted, offering valuable understanding of meson-meson interaction. Overall, the consistency of the present results indicates that this relativistic potential model provides a phenomenologically consistent description of the spectroscopic and decay properties of heavy-light D-mesons.

We study a phenomenological framework to investigate the properties of nuclear matter using a modified relativistic Dirac formalism. The model incorporates scalar and vector linear confinement potentials for quarks inside neutron, with quantum corrections including center-of-mass motion, gluonic, and pionic contributions. This approach enables the calculation of key nucleon properties and the nucleon mass in vacuum. Extending the model, we introduce interactions of quarks with the σ, ω, and ρ mesons in dense matter to compute the mass of the neutron in-medium, relevant for neutron star environments. The formalism is further employed to explore essential nuclear matter characteristics such as the equation of state (EOS), binding energy, symmetry energy, and thermodynamic instabilities. A systematic analysis of the correlation between symmetry energy and its density dependence offers insights for improving existing nuclear models and understanding matter in beta equilibrium at finite densities. Additionally, the model is applied to examine the mass-radius relationship of neutron stars, providing critical implications for astrophysical observations and the study of matter under extreme conditions.

In this paper, we study the DS meson's radial and angular resonance states using the relativistic independent quark potential model with scalar and vector components of square root confinement. The model parameters are set phenomenologically, with a=0.885 GeV, U0=-1.115 GeV, and the leading predictions, 13S1 (2.112GeV) and 11S0 (1.903GeV), are well in accord with PDG results. To explore radial and angular resonance states, we adjust U0=-1.314 GeV while keeping "a" remains constant. Our computations, 23S1 (2.707GeV), 21S0 (2.687GeV), 33S1 (3.336GeV), 31S0 (3.327GeV), 13P2 (2.568GeV), 13P1 (2.535GeV), 13P0 (2.314GeV), 11P1 (2.467GeV), 23P1 (3.098GeV), and 13D3 (2.866GeV), are nearly matching with both experiment and other theoretical results. Further, we calculate the pseudoscalar and vector meson decay constant, magnetic transitions (M1 transition), non-leptonic, and semileptonic decay widths and branching fractions of DS-meson. The findings are in reasonable accord with Lattice QCD computations, experimental data, and other theoretical projections. The current calculated values of fp and fV, are nearly identical with the PDG and QCDSR values. The predicted magnetic transition aligns well with experimental and other computed theoretical values. The calculated non-leptonic decay widths, like, DS ->rho 0 pi+, DS -> k0 pi+, DS ->phi pi+, DS ->eta pi+ shows good agreement with experimental values. Furthermore, we figure out the semileptonic decay widths and branching fractions of DS-mesons, such as DS ->eta ' e+nu e, DS -> K & lowast;e+nu e, DS ->pi+e+nu e, and shows good agreement with the PDG results. Our findings are consistent with Lattice QCD computations, experimental observations, and other theoretical predictions.

In this paper, we examine the radially excited states of B-mesons: [Formula: see text] and [Formula: see text]-mesons. Our investigation uses the relativistic independent quark model, which relies on a flavor-independent average potential expressed in the scalar and vector square root form. We make phenomenological fit the potential model parameters, [Formula: see text] [Formula: see text]GeV, [Formula: see text] [Formula: see text]GeV for calculation of 1S state of B-mesons: [Formula: see text] (5.329[Formula: see text]GeV), [Formula: see text] [Formula: see text], which aligns well with theoretical and experimental data. For higher radially excited states (2S, 3S, 4S, 5S), we adjust [Formula: see text] [Formula: see text]GeV while keeping “a” fixed, yielding results consistent with other theoretical models. With these parameters, we compute the pseudoscalar and vector meson decay constants, magnetic transition rates, non-leptonic decay widths, branching fractions, rare decay widths, and semileptonic decay widths and branching fractions of the B-mesons. Our findings show reasonable agreement with lattice QCD calculations, experimental results and other theoretical predictions. For instance, our predicted radiative decay width for [Formula: see text] (1S) [Formula: see text] [Formula: see text](1S)[Formula: see text], sensitive to the [Formula: see text] and [Formula: see text], mass difference, can aid in experimentally determining the [Formula: see text], mass. Predicted non-leptonic branching fractions, such as [Formula: see text] [Formula: see text] and [Formula: see text], align with PDG values of [Formula: see text] and [Formula: see text]. Additionally, we calculate the dileptonic decays of [Formula: see text] and [Formula: see text], which agrees with CMS, LHCb and PDG results. Our semileptonic decays of [Formula: see text] and [Formula: see text] mesons are computed and compared with PDG results. Furthermore, the results obtained for mass difference, [Formula: see text] and [Formula: see text], mixing parameters, [Formula: see text] and [Formula: see text], [Formula: see text] (0.1866 and 0.4993) of [Formula: see text] and [Formula: see text] oscillations, shows good agreement with PDG data, validating our model.

We sincerely thank the Editorial Board for forwarding the comments regarding our published paper [Panda et al 2024 Bulk properties of nuclear matter in a modified relativistic dirac formalism Phys. Scr. 99 105307], particularly those highlighting similarities with the earlier work [Barik et al 2013 Nuclear equation of state in a relativistic independent quark model with chiral symmetry and dependence on quark masses Phys. Rev. C - Nucl. Phys. 88 015206] and pointing out possible inaccuracies in our results. This Reply aims to clarify and responds to comments on our published study [Panda et al 2024 Bulk properties of nuclear matter in a modified relativistic dirac formalism Phys. Scr. 99 105307], which developed a Modified Relativistic Dirac Formalism (MRDF) for bulk nuclear matter using a QCD-motivated linear confinement potential, V r = 1 2 1 + γ 0 a 2 r + V 0 ,unlike the harmonic potential used in [Barik et al 2013 Nuclear equation of state in a relativistic independent quark model with chiral symmetry and dependence on quark masses Phys. Rev. C - Nucl. Phys. 88 015206]. Our formulation incorporates distinct eigenvalue equations, normalization conditions, and correction terms. The MRDF framework extends beyond [Barik et al 2013 Nuclear equation of state in a relativistic independent quark model with chiral symmetry and dependence on quark masses Phys. Rev. C - Nucl. Phys. 88 015206] by providing a self-consistent analysis of the symmetry energy, slope parameter, incompressibility, spin–orbit strength, and the neutron-star mass–radius relation. A minor plotting error in the binding-energy curve for m q = 300 MeV has been corrected; however, this adjustment does not affect any numerical results or physical conclusions. All results continue to satisfy the standard nuclear saturation conditions and remain consistent with QMC-type models. With the inclusion of the missing citation and the corrected figure, our conclusions remain valid, reaffirming that the MRDF is an independent and consistent model for describing nuclear matter. Below, we present point-by-point clarifications and a structured comparison to establish the integrity of our work.

We examine the properties of hyperons (Λ, Δ, Ξ) in dense baryon matter using a modified relativistic Dirac formalism (MRDF). In this approach, the quark–meson (σ, ω) couplings are derived self-consistently at the quark level, where quark confinement is modeled through a scalar-vector linear potential, and corrections are incorporated for center-of-mass motion, one-gluon exchange, and pionic contributions. We start by calculating the masses of baryons in a vacuum and then proceed to evaluate them within a medium. We also compute parameters, including the baryon charge radius, axial–vector coupling constant, pion coupling constant.

We look at the mass spectra of the [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] mesons using a relativistic square root potential. Before looking at the mass spectra, we have to figure out the model parameters, which are [Formula: see text][Formula: see text]GeV and [Formula: see text][Formula: see text]GeV. The calculated result of [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], findings of this study exhibit a notable concurrence with the experimental observations and pertinent theoretical projections. We estimate the decay constant, leptonic decay width, semileptonic decay width, and branching fractions of pseudoscalar and vector mesons, specifically B and D mesons, while keeping the model parameters unchanged. The pseudoscalar decay constants and partial decay widths of “B and D-mesons” reasonably agree with the theoretical predictions, lattice quantum chromodynamics (LQCD) calculations, and experimental data. Moreover, we have efficiently found the values for these mesons’ leptonic decay width and branching fraction, matching the experimental findings and theoretical forecasts. The calculated values of semileptonic decays are [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], [Formula: see text], [Formula: see text], the proximity of the observed results to experimental and certain theoretical models is evident.

Quark-gluon plasma (QGP) is a unique state of matter occurring at very high temperatures and densities, where quarks and gluons interact strongly. To explore the properties of QGP, we use an ideal confinement potential model and Mayer’s classical cluster expansion method to derive the equation of state for a quark–antiquark plasma within QGP. Our theoretical findings align reasonably with lattice QCD simulations, supporting our approach. Additionally, we calculate the pressure of an ideal quark-gluon plasma, considering contributions from both gluons and quark–antiquark pairs. We gauge the interaction strength among quarks and gluons by comparing non-ideal to ideal pressures. We also determine the energy density and mean particle number from the grand canonical partition function, enhancing our understanding of QGP’s thermodynamics. Our derived equations for the state, pressure, energy density, and particle number satisfy Euler’s equation, confirming the consistency of our theoretical model.

In this study, we employ a phenomenologically modified relativistic Dirac framework coupled with the sigma - omega quark-meson coupling model to look into the properties of nuclear matter. By combining scalar and vector linear potential forms and incorporating perturbative adjustments for various factors such as centre-of-mass motion, gluonic, and pionic effects, we aim to find the nucleon's mass in a vacuum. Then, we consider nucleon-nucleon interactions are constructed within a mean-field approximation. Our methodology systematically explores key characteristics of nuclear matter, including equations of state, compressibility, binding energy, and pressure. Furthermore, we compute essential parameters such as the nucleon charge radius, axial-vector coupling constant, pion coupling constant, nuclear sigma term, sensitivity, and potential strengths. And also, we calculate symmetry energy, density slop (L) and incompressibility ( K0 ). In addition, we compute the mass and radius of a neutron star and provide a graphical representation illustrating the relationship between mass and radius. To validate our results, we comprehensively compare them with other theoretical models and quark-meson coupling approaches, confirming the precision and reliability of our theoretical paradigm. Overall, our study enhances our understanding of the fundamental properties of nuclear matter and underscores their relevance in elucidating complex astrophysical phenomena.

We investigate the weak leptonic and semileptonic decay widths of pseudoscalar light and heavy mesons in a Dirac formalism. We take relativistic-independent quark model of the form [Formula: see text], where [Formula: see text]. This is computed using the binding quark eigenfunction and taking the assumptions of a significant relationship between the quark and antiquark momenta inside the decaying meson in the rest frame. To calculate the decay constant [Formula: see text], decay width and branching fractions of pseudoscalar mesons, we employ the model parameters that we used earlier. The experimental findings and various similar models are in good agreement with our predictions such as [Formula: see text] and [Formula: see text]”. Finally, we calculate the form factors and branching fractions for the semileptonic [Formula: see text] decays [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]” and find reasonable agreement with the experimental results.

In an approach predicted by the independent quark model with scalar-vector linear potential, we compute the leptonic decay widths and electromagnetic decay constants of vector mesons.We derive the quark-antiquark momentum distribution wave function from bound Quark eigenmode, Supposing a strong association between quark-antiquark momenta within the meson, so that the total momentum identically zero in the mesons center of mass frame.We obtain the leptonic decay width of ρ, ω, ϕ, ψ and Υ as 6.61 keV, 0.71 keV, 1.26 keV, 5.49 keV, and 1.31 keV and decay constants of ρ, ω, ϕ, ψ, and Υ as 0.19 GeV, 0.064 GeV, 0.074 GeV, 0.089 GeV and 0.021 GeV using our model parameter.These values are consistent with the said relevant experimental observations.

In this paper, we investigate the mass spectra and decay properties of [Formula: see text], [Formula: see text] and [Formula: see text] mesons using the relativistic potential model with confining potential [Formula: see text]. The calculated mass spectra of [Formula: see text], [Formula: see text] and [Formula: see text] accord to the findings of the experiments and other theoretical forecasts. Using the same parameters, we calculate possible radiative decay widths of [Formula: see text] and [Formula: see text], [Formula: see text] and weak leptonic decay constants of [Formula: see text], [Formula: see text] and [Formula: see text] mesons. Our results, in most cases, generally agree with experimental and other theoretical predictions. Finally, we also investigate mixing parameters [Formula: see text], [Formula: see text] and [Formula: see text] for [Formula: see text] [Formula: see text] mesons, where our calculated values reasonably agree with the experiment.

A Deeper interweaving of different scientific areas has always proven to be a powerful tool for improving our understanding of several fascinating physical aspects of the world. For example, researchers worldwide have investigated the intriguing existence of the interaction between gravity and superconductivity in recent decades, owing to its enormous conceptual implications and various potential applications. Different theories using various approaches and techniques have been proposed to predict these interactions. To study the anomalous couplings between the super condensate and local gravitational field, we provide a detailed calculation of the thermodynamic properties and coherence length on behalf of the gravitational wave vector. In addition, this study provides a framework for calculating the gravitational penetration depth compared with the electromagnetic (E.M.) penetration depth. Furthermore, we demonstrate macroscopic quantum interference events by applying the Josephson effect using a superconducting quantum interface device (SQUID) link. Finally, similar to other calculations, we demonstrate how the quantum of the gravity flux is used to manage a sinusoidally oscillating current. This phenomenon will help future researchers study the effects of gravitational perturbation on supercurrents and super-condensates, and the latter could be used as 'gravitational antennas' for gravitational wave detection.

We compute the S-wave $$~D(c\bar {s})$$ meson spectra using the independent quark model of scalar plus vector with square root potential model. The calculated states in S-wave, 13S1(2009.14), 11S0(1865.96), 23S1(2607.19), 21S0(2536.73), 33S1(3215.43), 31S0(3189.12), 43S1(3552), 41S0(3492) are closely matching with experimental data of the BABAR collaboration. According to this relativistic Dirac formalism, radiative decay and pseudoscalar decay constant ( $${{f}_{{\text{p}}}} = 204.26{\text{ MeV }}$$ ) of D meson is nearly identical to the theoretical, lattice, and experimental results. We get results for leptonic decay width and branch ratio of D meson more consistent with experimental and theoretical data calculated. The computed Cabibbo-favored mesonic decay width and a branching fraction BF $$({{D}^{0}} \to {{K}^{ - }}{{\pi }^{ + }})$$ , and BF $${{({{D}^{0}} \to {{K}^{ + }}{{\pi }^{ - }})}^{{''}}}i$$ is also in excellent agreement with experimental data obtained by CLEO collaboration in the respective experiments. We compute the necessary mesonic form factors using our developed independent confined quark model over the entire kinematical range of momentum transfer. Further, we calculate branching fractions for semileptonic decays ( $${{D}^{0}} \to {{K}^{ - }}{{e}^{ + }}{{\nu }_{e}}~{\kern 1pt} ,$$ $${{D}^{0}} \to {{K}^{ - }}{{\mu }^{ + }}{{\nu }_{{\mu ~}}},$$ $${{D}^{0}}{{\pi }^{ - }}{{e}^{ + }}{{\nu }_{e}},~\,\,{\text{and}}\,\,~{{D}^{0}} \to {{\pi }^{ - }}{{\mu }^{ + }}{{\nu }_{\mu }})$$ and their ratios, which demonstrate excellent agreement with the available experimental data (BESIII), are provided. BABAR and BELLE collaboration results are matching closely to our computed hybrid parameters $$~~{{x}_{q}}{{\;}}$$ (4.95 × 10–3), $${{y}_{q}}$$ (6.47 ×10–3) and $${{R}_{{\text{M}}}}{{\;}}$$ (3.317 × 10–5) of $$~{{D}^{0}} - {{\bar {D}}^{0}}~$$ Meson oscillations.

This article has been retracted. Please see the Retraction Notice for more detail: https://doi.org/10.1134/S1547477122020133

This article has been retracted. Please see the Retraction Notice for more detail: https://doi.org/10.1134/S1547477122020133

It is realized that the Coulomb interaction plays a vital role in describing the magnetic properties of graphene-on-substrate. We attempt here to study the competition between on-site and inter-site repulsive Coulomb interactions, with impurities at both the sub-lattices in graphene-on-substrate .The Hamiltonian describes the electron hopping up to third-nearest-neighbors within tight-binding approximation. Due to substrate effect, A-sub lattice is raised by energy and B-sub lattice acquired energy , besides impurity effects at both the sub lattices. The model consists of on-site repulsive Coulomb interaction at two sublattices with same on-site Coulomb energy U and nearest-neighbor inter-site Coulomb interactions between A and B sub lattice with inter site Coulomb energy . The Coulomb interaction is considered within Hartree-Fock type mean-field approximation. The Hamiltonian is solved by Zubarev's Green's function technique and an expression for temperature dependent difference in electron occupancies between two sub-lattices is calculated and solved self-consistency. Finally the charge gap and hence modified substrate induced gap is computed numerically by varying different physical parameters of the system like on-site and inter-site Coulomb interactions and substrate induced gap, impurity concentration and electron occupancy. It is observed that inter-site Coulomb interaction is smaller than on-site Coulomb interaction and plays an important role in describing the properties of graphene.