QCD corrections to the $B_c$ to charmonia semi-leptonic decays

Abstract

We present a detailed analysis on the $B_c$ meson semi-leptonic decays, $B_c\to {\eta }_c(J/\psi )\ell \nu$, up to next-to-leading order (NLO) QCD correction. We adopt the principle of maximum conformality (PMC) to set the renormalization scales for those decays. After applying the PMC scale setting, we determine the optimal renormalization scale for the $B_c\to {\eta }_c(J/\psi )$ transition form factors (TFFs). Because of the same $\{{\beta }_0\}$-terms, the optimal PMC scales at the NLO level are the same for all those TFFs, i.e. ${\mu }_r^{\mathrm{PMC}}\approx 0.8\mathrm{GeV}$. We adopt a strong coupling model from the massive perturbation theory (MPT) to achieve a reliable pQCD estimation in this low energy region. Furthermore, we adopt a monopole form as an extrapolation for the $B_c\to {\eta }_c(J/\psi )$ TFFs to all their allowable $q^2$ region. Then, we predict ${\Gamma }_{B_c\to {\eta }_c\ell \nu }(\ell =e,\mu )=(71.53_{-8.90}^{+11.27})\times 10^{-15}\mathrm{GeV}$, ${\Gamma }_{B_c\to {\eta }_c\tau \nu }=(27.14_{-4.33}^{+5.93})\times 10^{-15}\mathrm{GeV}$, ${\Gamma }_{B_c\to J/\psi \ell \nu }(\ell =e,\mu )=(106.31_{-14.01}^{+18.59})\times 10^{-15}\mathrm{GeV}$, ${\Gamma }_{B_c\to J/\psi \tau \nu }=(28.25_{-4.35}^{+6.02})\times 10^{-15}\mathrm{GeV}$, where the uncertainties are squared averages of all the mentioned error sources. We show that the present prediction of the production cross section times branching ratio for $B_c^{+}\to J/\psi {\ell }^{+}v$ relative to that for $B^{+}\to J/\psi K^{+}$, i.e. $\Re (J/\psi {\ell }^{+}\nu )$, is in a better agreement with CDF measurements than the previous predictions.

arXiv comment11 pages, 5 figures

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• Semileptonic decays $B_c\to ({\eta }_c,J/\psi )l{\bar{\nu }}_l$ in the "PQCD + Lattice" approach
• Model independent investigation of the $R_{J/\psi ,{\eta }_c}$ and ratios of decay widths of semileptonic $B_c$ decays into a P-wave charmonium
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• Application of the Principle of Maximum Conformality to the Top-Quark Charge Asymmetry at the LHC
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• Relativistic calculations of $R(D^{(\ast )})$, $R(D_s^{(\ast )})$, $R({\eta }_c)$ and $R(J/\psi )$
• Next-to-leading order QCD calculation of $B_c$ to charmonium tensor form factors
• Exclusive semileptonic $B_c$-meson decays to radially excited charmonium and charm meson states
• Weak decays of $B_c$ into two hadrons under flavor SU(3) symmetry
• $B_c\to J/\psi$ helicity form factors and the $B_c^{+}\to J/\psi +(P,V,{\ell }^{+}{\nu }_{\ell })$ decays
• $B_c^{-}\to J/\psi (\to {\mu }^{+}{\mu }^{-}){\tau }^{-}(\to {\pi }^{-}{\nu }_{\tau },{\rho }^{-}{\nu }_{\tau },{\ell }^{-}{\bar{\nu }}_{\ell }{\nu }_{\tau }){\bar{\nu }}_{\tau }$ decays with visible final-state kinematics
• Exclusive production of $B_c$ mesons in $e^{+}{e}^{-}$ colliders
• ${\eta }_c$ leading-twist distribution amplitude and the $B_c\to {\eta }_c\ell {\bar{\nu }}_{\ell }$ semileptonic decays using QCD Sum Rules