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We investigate the exclusive rare semileptonic decays: $B(B_c)\to K(D_{(s)})l\bar{l}/\Sigma\nu_l\bar{\nu_l}$ ($l=\mu, \tau$) in the framework of relativistic independent quark (RIQ) model based on an average flavor independent confining potential in equally mixed scalar-vector harmonic form. The invariant weak form factors, parametrising the matrix elements between participating meson states are calculated in the parent meson rest frame. The momentum transfer dependence of the form factors is reliably determined in the whole accessible kinematical range: $q^2_{min}\leq 0\leq q^2_{max}$. Our predicted branching fractions for $B\to K\mu^+\mu^-/\tau^+\tau^-(\Sigma\nu_l\bar{\nu_l})$, $B_c\to D(D_s)\mu^+\mu^-$, $B_c\to D(D_s)\tau^+\tau^-$ and $B_c\to D(D_s)\Sigma\nu_l\bar{\nu_l}$, obtained in order of $10^{-7}(10^{-6})$, $10^{-9}(10^{-7})$, $10^{-9}(10^{-8})$ and $10^{-8}(10^{-7})$, respectively are in reasonable agreement with other Standard Model predictions and Lattice QCD results. The averaged values of the lepton polarization asymmetries for decay modes are obtained as $\langle P_L(B\to K\mu^+\mu^-)\rangle$=-0.97, $\langle P_L(B_c\to D_{(s)}\mu^+\mu^-)\rangle$=-0.972, $\langle P_L(B\to K\tau^+\tau^-)\rangle$=-0.224, $\langle P_L(B_c\to D\tau^+\tau^-)\rangle$=-0.275 and $\langle P_L(B_c\to D_s\tau^+\tau^-)\rangle$=-0.194., Comment: 34 pages, 16 figures, 8 tables

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 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: $f_{P(V)}$, ratios of decay constants: $f_{V}/f_{P}$, $f_{P_1}/f_{P_2}$, $f_{V_1}/f_{V_2}$, and the branching fractions (BFs): ${\cal B}(P(V)\to l^+\nu_l)$, $l=e, \mu, \tau$, 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 near future., Comment: 28 pages, 8 figures, 9 tables

The detection of radially excited heavy meson \\states in recent years and measurement of heavy meson decays, particularly $B_c^+\to J/\psi D_s^+$ and $B_c^+\to J/\psi D_s^{*+}$, 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 $\bar{B}^0$, $\bar{B_s^0}$, $B^-$ and $B_c^-$-meson decays to two vector meson ($V_1(nS)V_2$) 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: $B^-\to D^{*0}\rho^-$, $\bar{B^0}\to D^{*+}\rho^-$, $\bar{B_s^0}\to D_s^{*+}\rho^-$, $B^-\to J/\psi K^{*-}$ and $B_c^-\to J/\psi D_s^{*-}$ with predicted branching fractions of 1.54, 1.42, 1.17, 0.53 and 0.52 (in $\%$), which are experimentally accessible. The predicted branching fractions for corresponding decay modes to excited ($2S$) states, obtained in the order ${\cal O }(10^{-3}-10^{-4})$ lie within the detection accuracy of the current experiments at LHCb and Tevatron. The sizeable $CP$-odd fractions predicted for $B_c^-$-meson decay to two charmful states: $D^{*0}D^{*-}_{(s)}$ and $\bar{D}^{*0}D^{*-}_{(s)}$ indicate significant $CP$-violation hinting at the so-called new physics beyond the standard model., Comment: arXiv admin note: text overlap with arXiv:2202.01167

In the wake of recent measurements of ratios of semileptonic branching fractions: ${\cal R}_{J/\psi}, {\cal R}_D$ and ${\cal R}_{D^*}$ 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 $b\to c,u$ transition at the quark level. Our predictions on branching fractions for $B_c\to \eta_c/\psi(nS)$ are found $\sim10^{-2}-10^{-4}$ and that for $B_c\to D^*(nS)$ 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 ${\cal R}$ in this sector are found comparable to other standard model (SM) predictions that violate the lepton flavor universality hinting at new physics beyond SM., Comment: 40 pages and 23 figure files. arXiv admin note: substantial text overlap with arXiv:2106.09463

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.

In this work, we discuss exclusive semileptonic $B_c$-meson decays: $B_c\to \eta_c(J/\psi)l\nu$ and $B_c\to D(D^*)l\nu$ in the framework of the relativistic independent quark(RIQ) model based on an average flavor independent confining potential in equally mixed scalar-vector harmonic form. We calculate the invariant form factors representing decay amplitudes from the overlapping integrals of meson wave functions derivable in the RIQ model. To evaluate the lepton mass effects in the semileptonic decays, we first study the $q^2$-dependence of the form factors in the accessible kinematic range of $q^2$ involved in the decay process in its $e^-$ and $\tau^-$ mode separately. Similar studies on helicity amplitudes, $q^2-$spectra for different helicity contributions, and total $q^2$-spectra for each decay process are carried out separately in their $e^-$ and $\tau^-$ modes. We predict the decay rates/ branching fractions, forward-backward asymmetry, and the asymmetry parameter in reasonable agreement with other model predictions, which can hopefully be tested in future experiments at the Tevatron and LHC. We also predict the observable $'R'$ which corresponds to the ratio of branching fractions for the decay process in its $e^-$ mode to its corresponding value in the $\tau^-$ mode. Our results are comparable to another standard model(SM) predictions which highlight the failure of the lepton flavor universality hinting at new physics beyond SM for the explanation of the observed deviation of observable $'R'$ value from the corresponding SM predictions.

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 $B_c^+\to \eta_c /\psi e^+\nu_e$ 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 mpdel predictions, our predicted BR are obtained in the hierarchy: BR($B_c^+\to \eta_c /\psi (3S)$) $<$ BR($B_c^+\to \eta_c/ \psi (2S)$) $<$ BR($B_c^+\to \eta_c /\psi (1S)$). The longitudinal ($\Gamma_L$) and transverse polarization ($\Gamma_T$) for $B_c \to \psi(ns)$ decay modes are predicted in the small and large $q^2$ - region as well as in the whole physical region. The ratios for such transitions are obtained $\frac {\Gamma_L}{\Gamma_T} < 1$ throughout the kinematic range which means the $B_c^+$ meson transitions to vector meson charmonium states take place predominantly in transverse polarization mode. The theoretical predictions on these transitions could be tested in the on-going and forthcoming experiments at LHCb.

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., Comment: arXiv admin note: text overlap with arXiv:1710.08242

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.