Relativistic Independent Quark Model Research Articles

Study of angular observables in exclusive semileptonic Bc decays

In this work, we investigate angular observables such as the longitudinal polarization of charged leptons, τ-polarization, and forward-backward asymmetry in semileptonic Bc decays. Additionally, we provide predictions for lepton flavor violating observables, the R ratios in the decay channels Bc→ηc(J/ψ)lνl and Bc→D(D*)lνl across the entire q2 region. Our analysis is conducted within the relativistic independent quark model, focusing on the potential model-dependent aspects of these observables. We compare our model predictions with existing lattice predictions, highlighting the strong applicability of our framework in describing Bc decays. Considering the forthcoming experimental upgrades and the Run 3 data results on Bc meson decays, rapid confirmation of these quantities could indicate significant discoveries of physics beyond the Standard Model. This may open up new avenues for understanding the complex flavor dynamics in heavy meson decays. Published by the American Physical Society 2024

Purely leptonic decays of heavy-flavored charged mesons

We study the purely leptonic decays of heavy-flavored charged pseudoscalar (P) and vector (V) mesons (D(s)(*)+, B(c)(*)+) in the relativistic independent quark (RIQ) model based on an average flavor-independent confining potential in an equally mixed scalar-vector harmonic form. We first compute the mass spectra of the ground-state-mesons and fix the model parameters necessary for the present analysis. Using the meson wave functions derivable in the RIQ model, and model parameters so fixed from hadron spectroscopy, we predict the decay constants: fP(V), ratios of decay constants: fV/fP, fP1/fP2, fV1/fV2, and the branching fractions (BFs): B(P(V)→l+νl), l=e, μ, τ, which agree with the available experimental data and other Standard Model (SM) predictions. For the unmeasured decay constants, especially in the purely leptonic decays of the charged vector mesons, our predictions could be tested in the upcoming Belle-II, SCTF, CEPC, FCC-ee, and LHCb experiments in the near future. Published by the American Physical Society 2024

The nonleptonic decays of b-flavored mesons to S-wave charmonium and charm meson states

The detection of radially excited charmonium and charm meson states, and measurement of heavy meson decays, particularly Bc+→J/ψDs+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_c^+\\rightarrow J/\\psi D_s^+$$\\end{document} and Bc+→J/ψDs∗+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_c^+\\rightarrow J/\\psi D_s^{*+}$$\\end{document}, by the LHCb and ATLAS Collaborations, have aroused a lot of theoretical interest in the nonleptonic decays of b-flavored mesons. In this paper, we study the exclusive two-body nonleptonic B¯0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\bar{B}}^0$$\\end{document}, Bs0¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\bar{B_s^0}$$\\end{document}, B-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B^-$$\\end{document} and Bc-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_c^-$$\\end{document}-meson decays to two vector meson (V1(nS)V2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V_1(nS)V_2$$\\end{document}) states. Assuming the factorization hypothesis, we calculate the weak-decay form factors from the overlapping integrals of meson wave functions, in the framework of the relativistic independent quark (RIQ) model. We find a few dominant decay modes: B-→D∗0ρ-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B^-\\rightarrow D^{*0}\\rho ^-$$\\end{document}, B0¯→D∗+ρ-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\bar{B^0}\\rightarrow D^{*+}\\rho ^-$$\\end{document}, Bs0¯→Ds∗+ρ-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\bar{B_s^0}\\rightarrow D_s^{*+}\\rho ^-$$\\end{document}, B-→J/ψK∗-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B^-\\rightarrow J/\\psi K^{*-}$$\\end{document} and Bc-→J/ψDs∗-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_c^-\\rightarrow J/\\psi D_s^{*-}$$\\end{document} with predicted branching fractions of 1.52, 1.40, 1.16, 0.46 and 0.27 (in %\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\%$$\\end{document}), which are experimentally accessible. The predicted branching fractions for corresponding decay modes to excited (2S) states, obtained in O(10-3-10-4)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathscr {O}} }(10^{-3}-10^{-4})$$\\end{document} lie within the detection accuracy of the current experiments at LHCb and Tevatron. Our predicted CP-odd fractions (R⊥\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R_\\perp $$\\end{document}) for color-favored Bc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_c$$\\end{document}-decays to two charmful states (D∗D(s)∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D^*D^*_{(s)}$$\\end{document}) are found significant as compared to similar decay modes of other b-flavored mesons.

A Light Shed on Lepton Flavor Universality in B Decays

Behind succeeding measurements of anomalies in semileptonic decays at LHCb and several collider experiments hinting at the possible violation of lepton flavor universality, we undertake a concise review of theoretical foundations of the tree- and loop-level b-hadron decays, b→clνl and b→sl+l− along with experimental environments. We revisit the world averages for RD(D*), RK(K*), RJ/ψ, and Rηc, for the semileptonic transitions and provide results within the framework of the relativistic independent quark model in addition to the results from model-independent studies. If the ongoing evaluation of the data of LHC Run 2 confirms the measurements of Run 1, then the statistical significance of the effect in each decay channel is likely to reach 5 σ. A confirmation of these measurements would soon turn out to be the first remarkable observation of physics beyond the Standard Model, providing a wider outlook on the understanding of new physics.

Exclusive semileptonic B_c-meson decays to radially excited charmonium and charm meson states

In the wake of recent measurements of ratios of semileptonic branching fractions: {mathscr {R}}_{J/psi }, {mathscr {R}}_D and {mathscr {R}}_{D^{*}} reported by the LHCb, BELLE and HFLAV Collaborations, we calculate invariant form factors for the exclusive semileptonic B_c-meson decays to radially excited charmonium and charm meson states in the full kinematical region within the framework of relativistic independent quark (RIQ) model. We evaluate the lepton mass effect in the decay processes induced by brightarrow c,u transition at the quark level. Our predictions on branching fractions for B_crightarrow eta _c/psi (nS) are found sim 10^{-2}-10^{-4} and that for B_crightarrow D^{*}(nS) are sim 10^{-4} in their e^{-} decay modes, which lie within the detection accuracy of current experiment. Our predictions on branching fractions, forward backward asymmetry and asymmetry parameter are found in reasonable agreement with other model predictions; which can hopefully be tested in future experiments at LHC and Tevatron. Our predicted observable {mathscr {R}} in this sector are found comparable to other standard model (SM) predictions that violate the lepton flavor universality hinting at new physics beyond SM.

Retraction Note to: Study of Mass Spectra and Decay Properties of D Meson in a Relativistic Independent Quark Model

Retraction Note to: Study of Mass Spectra and Decay Properties of D Meson in a Relativistic Independent Quark Model

Exclusive nonleptonic Bc -meson decays to S -wave charmonium states

We study the exclusive two-body nonleptonic $B_c\to X_{c\bar{c}}M$ decays, where $X_{c\bar{c}}$ is either a ground(1S) or a radially excited (2S or 3S) charmonium and $M$ is a pseudoscalar $(P)$ or a vector $(V)$ meson. We consider here three categories of decays: $B_c \to PP, PV, VP$ decays within the framework of relativistic independent quark(RIQ) model based on a flavor-independent interaction potential in scalar-vector harmonic form. Using the factorization approximation, we calculate the weak form factors from the overlapping integrals of meson wave functions obtained in the RIQ model and predict the branching fractions for a set of exclusive nonleptonic $B_c$-decays in reasonable agreement with other model predictions. Some of the decays of interest are found to have branching fractions $\sim (10^{-3}-10^{-4})$ within the detection ability of the current experiments and can be precisely measured at LHCb in near future. In the wake of the recent measurement of $B_c\to J/\psi\pi(K)$, $B_c\to J/\psi\pi(D_s)$, $B_c\to \pi(J/\psi,\psi(2S))$ and $B_c\to J/\psi(\pi,\mu \nu)$ reported by the LHCb Collaborations, we predict the ratios: ${\cal R}_{K/\pi}$, ${\cal R}_{D_s/\pi}$ and ${\cal R}_{\psi(2S)/{J/\psi}}$ in broad agreement with the LHCb data though our predicted ratio ${\cal R}_{\pi /{\mu\nu}}$ is found to be underestimated. The results indicate that the present approach works well in the description of exclusive nonleptonic $B_c$-decays within the framework of the RIQ model.

RETRACTED ARTICLE: Study of Mass Spectra and Decay Properties of D Meson in a Relativistic Independent Quark Model

RETRACTED ARTICLE: Study of Mass Spectra and Decay Properties of D Meson in a Relativistic Independent Quark Model

Semileptonic $$B_c$$ meson decays to S-wave charmonium states

We study the semileptonic decays of $$B_c$$ meson to S-wave charmonium states in the framework of relativistic independent quark model based on an average flavor-independent confining potential U(r) in the scalar–vector harmonic form $$U(r)=\frac{1}{2}(1+\gamma ^0)(ar^2+V_0)$$ , where (a, $$V_0$$ ) are the potential parameters. The form factors for $$B_c^+\rightarrow \eta _c /\psi e^+\nu _e$$ transitions are studied in the physical kinematic range. Our predicted branching ratios (BR) for transitions to ground-state charmonia are found comparatively large $$\sim $$ $$10^{-2}$$ , compared to those for transitions to radially excited 2S and 3S states. Like all other model predictions, our predicted BR are obtained in the hierarchy: BR( $$B_c^+\rightarrow \eta _c /\psi (3S)$$ ) < BR( $$B_c^+\rightarrow \eta _c/ \psi (2S)$$ ) < BR( $$B_c^+\rightarrow \eta _c /\psi (1S)$$ ). The longitudinal ( $$\varGamma _L$$ ) and transverse ( $$\varGamma _T$$ ) polarization for $$B_c \rightarrow \psi (ns)$$ decay modes is predicted in the small and large $$q^2$$ -region as well as in the whole physical region. Our predicted polarization ratios: $$\frac{\varGamma _L}{\varGamma _T} < 1$$ for $$B_c^+\rightarrow J/\psi e^+\nu _e$$ and $$B_c^+\rightarrow \psi (2S)e^+\nu _e$$ which means these transitions take place predominantly in transverse mode, whereas for $$B_c\rightarrow \psi (3S)e\nu _e$$ , $$\varGamma _L$$ is comparable with $$\varGamma _T$$ in the whole physical region. These theoretical predictions could be tested in the LHCb and the forthcoming Super-B experiments.

Erratum: Magnetic dipole transitions of Bc and Bc* mesons in the relativistic independent quark model [Phys. Rev. D 96 , 116010 (2017)

Received 19 December 2018DOI:https://doi.org/10.1103/PhysRevD.99.019901© 2019 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasParticle decaysParticles & Fields

Electromagnetic transitions of (bc¯) bound system

We study electromagnetic transitions: $B_c^*(ns)\to B_c(ns) e^+ e^-$, $B_c^*(ns)\to B_c(n^{\prime}s) e^+ e^-$ and $B_c(ns)\to B^*_c(n^{\prime}s) e^+ e^-$ in the relativistic independent quark (RIQ) model based on a flavor-independent potential in the scalar-vector harmonic form. The transition form factors for energetically possible transitions involving $B_c$ - and $B_c^*$- mesons in ground as well as orbitally excited states are predicted in their respective kinematic range. Our predictions on decay width for the allowed and hindered transitions are found compatible with those of the model calculations based on Bethe-Salpeter approach. Predictions in this sector would not only provide more information about members of the $B_c$-family including mass splitting between vector mesons and corresponding pseudoscalar counterparts but give hints for experimental determination of unknown masses of other excited $B_c$ - and ground state of $B_c^*$-meson, which is expected at LHCb and $Z^0$ factory in near future.

Magnetic dipole transitions of Bc and Bc* mesons in the relativistic independent quark model

We study M1-transitions involving mesons: $B_c(1s)$, $B_c^*(1s)$, $B_c(2s)$, $B_c^*(2s)$, $B_c(3s)$ and $B_c^*(3s)$ in the relativistic independent quark (RIQ) model based on a flavor independent average potential in the scalar-vector harmonic form. The transition form factor for $B_c^*\to B_c\gamma$ is found to have analytical continuation from spacelike to physical timelike region. Our predicted coupling constant $g_{B_c^* B_c}$ = 0.34 Ge$V^{-1}$ and decay width $\Gamma(B_c^*\to B_c\gamma)$ = 23 eV agree with other model predictions. In view of possible observation of $B_c$ and $B_c^*$ s-wave states at LHC and Z-factory and potential use of theoretical estimate on M1-transitions, we investigate the allowed as well as hindered transitions of orbitally excited $B_c$-meson states and predict their decay widths in overall agreement with other model predictions. We consider the typical case of $B_c^*(1s)\to B_c(1s)\gamma$, where our predicted decay width which is found quite sensitive to the mass difference between $B_c^*$ and $B_c$ mesons may help in determining the mass of $B_c^*$ experimentally.

Spectroscopy and flavor changing decays ofB,Bsmesons in a Dirac formalism

In the framework of the relativistic independent quark model, the mass spectra and decay properties of $B$ and ${B}_{s}$ mesons are obtained using a Martin-like potential for the quark confinement. The predicted excited states are in good agreement with the experimental results as well as with the lattice QCD and other theoretical predictions. For instance, the ${B}_{2}(5747)$ as $1{^{3}P}_{2}$, ${B}_{1}(5721)$ as $1{^{3}P}_{1}$, and ${B}_{0}(5732)$ as $1{^{3}P}_{0}$ are identified. The spectroscopic parameters are used to calculate the electromagnetic transitions, pseudoscalar decay constants, hadronic decay widths, and leptonic decay widths. The present result for the decay constant, ${f}_{B}(1S)=188.56\text{ }\text{ }\mathrm{MeV}$, is in good agreement with recent lattice results (UKQCD Collaboration, Fermilab) and comparable with the experimental value of $(206.7\ifmmode\pm\else\textpm\fi{}8.9)$. The pseudoscalar decay constant for the ${B}_{s}$ meson obtained here, ${f}_{{B}_{s}}(1S)=240.21\text{ }\text{ }\mathrm{MeV}$, is in very good agreement with recent lattice QCD and QCD sum rule predictions. The predicted branching ratio for ${B}^{+}\ensuremath{\rightarrow}{\ensuremath{\tau}}^{+}{\ensuremath{\nu}}_{\ensuremath{\tau}}$ ($1.354\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$) is in accordance with the value, $(1.65\ifmmode\pm\else\textpm\fi{}0.34)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ reported by the Particle Data Group (PDG). The branching ratios of the rare decays ${B}_{s}^{0}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ ($(3.1\ifmmode\pm\else\textpm\fi{}0.7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$) and ${B}^{0}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ ($l6.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$) as observed by the CMS and LHCb Collaborations very recently are in accordance with our predictions of $3.602\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ and $1.018\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, respectively. The Cabibbo-favored hadronic branching ratios of ${B}^{0}\ensuremath{\rightarrow}{D}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$ ($3.724\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$), ${B}^{0}\ensuremath{\rightarrow}{D}^{*\ensuremath{-}}{\ensuremath{\pi}}^{+}$ ($3.475\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$), and ${B}_{s}\ensuremath{\rightarrow}{D}_{s}^{\ensuremath{-}}{\ensuremath{\rho}}^{+}$ ($3.800\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$) are in good agreement with the respective PDG values. The mixing parameters ${x}_{q}$, ${\ensuremath{\chi}}_{q}$ for ${B}^{0}\ensuremath{-}{\overline{B}}^{0}$ (${x}_{d}=0.769$, ${\ensuremath{\chi}}_{d}=0.1859$) and ${B}_{s}\ensuremath{-}{\overline{B}}_{s}$ (${x}_{s}=26.41$, ${\ensuremath{\chi}}_{s}=0.49929$) are also found to be in excellent agreement with the PDG values of ($0.770\ifmmode\pm\else\textpm\fi{}0.008$, $0.1862\ifmmode\pm\else\textpm\fi{}0.0023$) and ($26.49\ifmmode\pm\else\textpm\fi{}0.29$, $0.499292\ifmmode\pm\else\textpm\fi{}0.000016$), respectively.

D meson spectroscopy and their decay properties using Martin potential in a relativistic Dirac formalism

The mass spectra of $D$ meson states are calculated in the framework of a relativistic independent quark model. For the present study, we have used the martin like potential for the quark confinement. Our predicted states in S-wave, $2\ ^3S_1$ (2605.86 MeV) and $2\ ^1S_0$ (2521.72 MeV) are in very good agreement with experimental result of $2608\pm{2.4}\pm{2.5}$ MeV and $2539.4\pm{4.5}\pm{6.8}$ MeV respectively reported by BABAR Collaboration. The calculated P-wave $D$ meson states, $1^3P_2$ (2468.22 MeV), $1^3P_1$ (2404.94 MeV), $1^3P_0$ (2315.24 MeV) and $1^1P_1$ (2367.94 MeV) are in close agreement with experimental average (Particle Data Group) values of $2462.6 \pm 0.7 $ MeV, $2427 \pm 26 \pm 25$ MeV, $2318 \pm 29 $ MeV and $2421.3 \pm 0.6 $ MeV respectively. The pseudoscalar decay constant ($f_P$= 202.57 MeV) of $D$ meson obtained using this relativistic formalism is in very good agreement with the experiment as well as with the lattice and other available theoretical predictions. The Cabibbo favoured hadronic decay branching ratios, BR$(D^0\rightarrow K^- \pi^+)$ as $3.835 \%$ and BR $(D^0\rightarrow K^+ \pi^-)$ as $1.069 \times 10^{-4} $ are also in very good agreement with the respective experimental values of $ 3.91 \pm 0.08\%$ and $(1.48\pm 0.07) \times 10^{-4}$ reported by CLEO Collaboration. Our predicted results in leptonic decay widths of $D$ meson are also in better accord with experiment as well as other theoretical results. The mixing parameters of $D^0 - \bar{D}^0$ oscillation, $x_q$ (5.14 $\times 10^{-3}$), $y_q$ (6.02 $\times 10^{-3}$) and $R_M$ (3.13 $\times 10^{-5}$) are in very good agreement with BaBar and Belle Collaboration results.

Mass spectra and decay properties ofDsmeson in a relativistic Dirac formalism

The mass spectra of the ${D}_{s}$ meson is obtained in the framework of the relativistic independent quark model using a Martin-like potential for the quark confinement. The predicted excited states are in good agreement with the experimental results as well as with the lattice and other theoretical predictions. The spectroscopic parameters are employed further to compute the decay constant, electromagnetic transition and leptonic decay widths. The present result for its decay constant, ${f}_{P}$ (252.82 MeV) is in excellent agreement with the value $252.6\ifmmode\pm\else\textpm\fi{}11.1\text{ }\mathrm{MeV}$ reported by CLEO-c. The predicted branching ratios for $({D}_{s}\ensuremath{\rightarrow}\ensuremath{\tau}{\overline{\ensuremath{\nu}}}_{\ensuremath{\tau}},\ensuremath{\mu}{\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}})$ ($5.706\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}2},5.812\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}3}$) are in close agreement with the values [$(5.43\ifmmode\pm\else\textpm\fi{}0.31)\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}2},(5.90\ifmmode\pm\else\textpm\fi{}0.33)\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}3}$] reported in Particle Data Group. The Cabibbo favored semileptonic branching ratio of $[{D}_{s}\ensuremath{\rightarrow}\ensuremath{\phi}{e}^{+}{\ensuremath{\nu}}_{e}(2.01%)]$ and that of the hadronic decay $[{D}_{s}\ensuremath{\rightarrow}\ensuremath{\phi}{\ensuremath{\pi}}^{+}(4.62%)]$ are in very good agreement with the respective Particle Data Group values, and the branching ratio $[{D}_{s}\ensuremath{\rightarrow}{K}^{0}{\ensuremath{\pi}}^{+}(2.16\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}3})]$ is in very good agreement with the branching ratio of $(2.40\ifmmode\pm\else\textpm\fi{}0.18)\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}3}$ reported by Belle collaboration.

NonleptonicBc→VVdecays

We study the exclusive nonleptonic ${B}_{c}\ensuremath{\rightarrow}VV$ decays, within the factorization approximation, in the framework of the relativistic independent quark model, based on a confining potential in the scalar-vector harmonic form. The weak form factors are extracted from the overlap integral of meson wave functions derived in the relativistic independent quark model. The predicted branching ratios for different ${B}_{c}$-meson decays are obtained in a wide range, from a tiny value of $\mathcal{O}({10}^{\ensuremath{-}6})$ for ${B}_{c}\ensuremath{\rightarrow}{D}^{*}{D}_{(s)}^{*}$ to a large value of 24.32% for ${B}_{c}\ensuremath{\rightarrow}{B}_{s}^{*}{\ensuremath{\rho}}^{\ensuremath{-}}$, in general agreement with other dynamical-quark-model predictions. The decay modes ${B}_{c}\ensuremath{\rightarrow}{B}_{s}^{*}{\ensuremath{\rho}}^{\ensuremath{-}}$ and ${B}_{c}\ensuremath{\rightarrow}{B}^{*}{\ensuremath{\rho}}^{\ensuremath{-}}$ with high branching ratios of 24.32% and 1.73%, respectively, obtained in this model should be detectable at the LHC and Tevatron in the near future. The $b\ensuremath{\rightarrow}c$, $u$ induced decays are predicted predominantly in the longitudinal mode, whereas the $\overline{c}\ensuremath{\rightarrow}\overline{s}$, $\overline{d}$ induced decays are obtained in a slightly higher transverse mode. The $CP$-odd fractions $({R}_{\ensuremath{\perp}})$ for different decay modes are predicted and those for color-favored ${B}_{c}\ensuremath{\rightarrow}{D}^{*}{D}^{*}$, ${D}^{*}{D}_{s}^{*}$ decays indicate significant $CP$ violation in this sector.

Nuclear equation of state in a relativistic independent quark model with chiral symmetry and dependence on quark masses

We have calculated the properties of nuclear matter in a self-consistent manner with a quark-meson coupling mechanism incorporating the structure of nucleons in vacuum through a relativistic potential model; where the dominant confining interaction for the free independent quarks inside a nucleon is represented by a phenomenologically average potential in equally mixed scalar-vector harmonic form. Corrections due to spurious center of mass motion as well as those due to other residual interactions, such as the one gluon exchange at short distances and quark-pion coupling arising out of chiral symmetry restoration, have been considered in a perturbative manner to obtain the nucleon mass in vacuum. The nucleon-nucleon interaction in nuclear matter is then realized by introducing additional quark couplings to $\ensuremath{\sigma}$ and $\ensuremath{\omega}$ mesons through mean field approximations. The relevant parameters of the interaction are obtained self-consistently while realizing the saturation properties such as the binding energy, pressure, and compressibility of the nuclear matter. We also discuss some implications of chiral symmetry in nuclear matter along with the nucleon and nuclear $\ensuremath{\sigma}$ term and the sensitivity of nuclear matter binding energy with variations in the light quark mass.

Nonleptonic two-bodyBc-meson decays

We study the exclusive nonleptonic two-body ${B}_{c}$ decays within factorization approximation, in the framework of the relativistic independent quark model based on a confining potential in the scalar-vector harmonic form. The relevant weak form factors and branching ratios for different decay modes $({B}_{c}\ensuremath{\rightarrow}PP,PV,VP)$ are predicted in reasonable agreement with other quark model predictions. We find that the dominant contribution to the ${B}_{c}$-meson lifetime comes from the Cabibbo-Kobayashi-Masakawa favored $\overline{c}\ensuremath{\rightarrow}\overline{s}$, $\overline{d}$ decay modes, and the most promising modes are found to be ${B}_{c}^{\ensuremath{-}}\ensuremath{\rightarrow}{\overline{B}}_{s}^{0}{\ensuremath{\pi}}^{\ensuremath{-}}$, ${B}_{c}^{\ensuremath{-}}\ensuremath{\rightarrow}{\overline{B}}_{s}^{0}{\ensuremath{\rho}}^{\ensuremath{-}}$ and ${B}_{c}^{\ensuremath{-}}\ensuremath{\rightarrow}{\overline{B}}_{s}^{\ensuremath{\star}0}{\ensuremath{\pi}}^{\ensuremath{-}}$ with predicted branching ratios of 12.01, 9.96, and 8.61%, respectively, which might be easily detected at the hadron collider in the near future.

Quark–pion coupling strength and ground state baryon spectra in a chiral potential model

Chiral symmetry is incorporated into a relativistic independent-quark model with a square root confining potential and the quark–pion coupling strength, Gqqπ for quarks in a nucleon is estimated. The values of (Gqqπ2/4π) obtained with the approximation of a point pion as well as finite size pion are quite comparable with those estimated earlier by other researchers. Under the assumption that the baryon is an assembly of independent quarks confined in a first approximation by the square root potential that represents the nonperturbative gluon interactions, the model is also adopted to study the ground-state baryon spectrum taking into account perturbatively the contribution of the residual quark–pion coupling and that of the quark–gluon coupling in the baryon over and above the necessary center-of-mass correction. The physical masses of the ground state baryons calculated with the quark–gluon coupling constant αc = 0.227 agree reasonably well with experimental data.

( q q ¯ ) -pion mass and decay constant in a relativistic independent-quark model

The mass and decay constant of the [Formula: see text]-pion together with the masses of ρ and ω mesons are calculated in a chiral symmetric potential model of independent quarks, taking into account the corrections due to the possible residual interactions, such as quark–pion coupling arising out of the requirement of chiral symmetry and quark gluon coupling arising out of one-gluon-exchange, and that due to the spurious center-of-mass motion of the meson core. The effective potential representing phenomenologically the nonperturbative gluon interactions, including gluon self coupling, is chosen with equally mixed scalar and vector parts in a logarithmic form. The result obtained for the physical mass of [Formula: see text]-pion is consistent with that of the PCAC-pion, and the pion-decay constant reasonably agrees with experiment.