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

Abstract

Experimental measurements of decay branching fractions of semitaunic and semimuonic $B_c$ into $J/\psi$ has challenged the lepton flavor universality in standard model with about two standard deviations. In this paper, we first investigate the unitary constraint on form factors of $B_c$ meson into $S$-wave and $P$-wave charmonium. Such constraint leads to the exploration of the $R_{J/\psi }$ and other ratios $R_{{\eta }_c}$, $R_{h_c}$, and $R_{{\chi }_{cJ}}$ in a model-independent way. These results together with future experimental measurements can be used to explore the lepton flavor universality in a more systematic way. In addition, we point out that the helicity-dependent ratios $R_{J/\psi }^L$ and $R_{J/\psi }^{\perp }$ can also provide complementary information.

18pages, 7 figures, and 3 tables; update new contents

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• Semileptonic $B_c$ decays to $P-$wave charmonium and the nature of ${\chi }_{c1}(3872)$
• New physics in the angular distribution of $B_c^{-}\to J/\psi (\to {\mu }^{+}{\mu }^{-}){\tau }^{-}(\to {\pi }^{-}{\nu }_{\tau }){\bar{\nu }}_{\tau }$ decay
• Relations between $b\to c\tau \nu$ Decay Modes in Scalar Models
• Visible energy and angular distributions of the charged particle from the $\tau -$decay in $b\to c\tau (\mu {\bar{\nu }}_{\mu }{\nu }_{\tau },\pi {\nu }_{\tau },\rho {\nu }_{\tau }){\bar{\nu }}_{\tau }$ reactions
• Nonleptonic $B_c$ decay rates from model independent relations
• Inclusive quasielastic (anti-)neutrino nucleus scattering within the Standard Model and beyond
• Probing New Physics and CP Violation in ${\nu }_{\tau }n\to {\Lambda }_c{\tau }^{-}({\pi }^{-}{\nu }_{\tau })$ and ${\bar{\nu }}_{\tau }p\to \Lambda {\tau }^{+}({\pi }^{+}{\bar{\nu }}_{\tau })$