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Register a new userSemileptonic Decay of $B_c$ to $eta_c$ and $J/psi$ on the Light Front
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We study the semileptonic decay of the $B_c (0^-)$ to charmonia through the bottom-to-charm-quark electroweak current in the framework of basis light-front quantization. Explicitly, we calculate the weak transition form factors for processes of $B_c$ decaying into $eta_c$ or $J/psi$ based on the corresponding initial and final valence light-front wave functions both obtained from the basis light-front quantization. We also present the corresponding differential decay width and branching ratios, as well as the branching ratios for decays into the $eta_c$ and the $psi$. We observe unphysical frame dependence of the calculated form factors, which is attributed to only including the valence light-front wave functions. Based on the analysis of current component, we propose a preferred set of frames to calculate these form factors.
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We evaluate the form factors describing the semileptonic decays $bar{B^0}to J/psi (eta_c) D^+ ell^- bar u_ell$, within the framework of a QCD relativistic potential model. This decay is complementary to $bar{B^0}to J/psi (eta_c) D^+ pi^-$ in a phase space region where a pion factors out.We estimate the branching ratio for these semileptonic and nonleptonic channels, finding $mathcal{BR}(bar{B^0} to J/psi (eta_c) D^+ ell u_ell) simeq 10^{-13}$, $mathcal{BR}(bar{B^0} to J/psi D^+ pi^-) = 3.1 times 10^{-8}$ and $mathcal{BR}(bar{B^0} to eta_c D^+ pi^-) = 3.5 times 10^{-8}$.
Measurements of $B_c^+$ production and mass are performed with the decay mode $B_c^+ to J/psi pi^+$ using 0.37 fb$^{-1}$ of data collected in $pp$ collisions at $sqrt{s}=7$ TeV by the LHCb experiment. The ratio of the production cross-section times branching fraction between the $B_c^+ to J/psi pi^+$ and the $B^+ to J/psi K^+$ decays is measured to be $(0.68 pm 0.10,({rm stat.}) pm 0.03,({rm syst.}) pm 0.05,({rm lifetime}))$% for $B_c^+$ and $B^+$ mesons with transverse momenta $p_{rm T}>4 $GeV/$c$ and pseudorapidities $2.5<eta<4.5$. The $B_c^+$ mass is directly measured to be $6273.7 pm 1.3,({rm stat.}) pm 1.6 ,({rm syst.})$ MeV/$c^2$, and the measured mass difference with respect to the $B^+$ meson is $M(B_c^+)-M(B^+) = 994.6 pm 1.3,({rm stat.}) pm 0.6,({rm syst.})$ MeV/$c^2$.
In this paper, we calculate the $B_cto J/psi$ helicity form factors (HFFs) up to twist-4 accuracy by using the light-cone sum rules approach. After extrapolating those HFFs to the physically allowable $q^2$ region, we investigate the $B^+_c$-meson two-body decays and semi-leptonic decays $B_c^+ to J/psi+(P, V, ell^+ u_ell)$, where $P$ and $V$ stand for a light pseudo-scalar meson and a vector meson, respectively. The branching fractions can be derived by using the CKM matrix element and the $B_c$ lifetime from the Particle Data Group, and we obtain ${cal B}(B_c^+ to J/psi pi^+)=(0.132^{+0.002}_{-0.002})%$, ${cal B}(B_c^+ to J/psi K^+)=(0.010^{+0.000}_{-0.000})%$, ${cal B}(B_c^+ to J/psi rho^+) =(0.755^{+0.030}_{-0.034})%$, ${cal B}(B_c^+ to J/psi K^{ast +})=(0.043^{+0.001}_{-0.001})%$, ${cal B}(B_c^+ to J/psi mu^+ u_mu)=(2.808^{+0.547}_{-0.704})%$ and ${cal B}(B_c^+ to J/psi tau^+ u_tau)=(0.563^{+0.137}_{-0.178})%$. We then obtain ${cal R}_{pi^+/mu^+ u_mu} = 0.047^{+ 0.009}_{-0.012}$ and ${cal R}_{K^+ / pi^+} = 0.075^{+0.005}_{-0.005}$, which agree with the LHCb measured value within $1sigma$-error. We also obtain ${cal R}_{J/psi}=0.200^{+ 0.062}_{-0.081}$, which like other theoretical predictions, are consistent with the LHCb measured value within $2sigma$-error.
Predictions for $e^+e^-to J/psi eta_c$ from previous studies are made by taking charmonia as a nonrelativistic bound state and by using nonrelativistic QCD(NRQCD) approach. The predicted cross-section is smaller by an order of magnitude than the experimentally observed. We study the process by taking charm quark as a light quark and use light-cone wave-functions to parameterize nonperturbative effects related to charmonia. The total cross section of $e^+e^-to J/psi eta_c$ can be predicted, if these wave-functions are known. Motivated by studies of light-cone wave-functions of light hadrons, we make a reasonable assumption of the forms of light-cone wave-functions. With these light-cone wave-functions we can obtain the cross section which is more closer to the experimentally observed than that from NRQCD approach. We also discuss in detail the difference between two approaches.
Evidence is presented for the decay $B_c+rightarrow J/psi 3pi^+2pi^-$ using proton-proton collision data, corresponding to an integrated luminosity of 3fb$^{-1}$, collected with the LHCb detector. A signal yield of $32pm8$ decays is found with a significance of 4.5 standard deviations. The ratio of the branching fraction of the $B_c^+rightarrow J/psi 3pi^+ 2pi^-$ decay to that of the $B_c^+ rightarrow J/psi pi^+$ decay is measured to be $$ frac{Br (B_c^+ rightarrow J/psi 3pi^+2pi^)}{Br (B_c^+ rightarrow J/psi pi^+)} = 1.74pm0.44pm0.24, $$ where the first uncertainty is statistical and the second is systematic.
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