Next-to-leading-logarithm $k_T$ resummation for $B_c\to J/\psi$ decays

Abstract

We derive the $k_T$ resummation for a transverse-momentum-dependent charmonium wave function, which involves the bottom quark mass $m_b$, the charm quark mass $m_c$, and the charm quark transverse momentum $k_T$, up to the next-to-leading-logarithm (NLL) accuracy under the hierarchy $m_b\gg m_c\gg k_T$. The resultant Sudakov factor is employed in the perutrbative QCD (PQCD) approach to the $B_c\to J/\psi$ transition form factor $A_0^{B_c\to J/\psi }(0)$ and the $B_c^{+}\to J/\psi {\pi }^{+}$ decay. We compare the NLL resummation effect on these processes with the leading-logarithm one in the literature, and find a $(5-10)\%$ enhancement to the form factor $A_0^{B_c\to J/\psi }(0)$ and a $(10-20)\%$ enhancement to the decay rate $\mathrm{BR}(B_c^{+}\to J/\psi {\pi }^{+})$. The improved $k_T$ resummation formalism is applicable to the PQCD analysis of heavy meson decays to other charmonia.

8 pages, 3 figures, and 1 table; more references and clarifications added, results and conclusions remain unchanged; final version to appear in Physics Letters B

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Cited by in corpus (9)

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• Systematic analysis of the form factors of $B_c\to {\eta }_c$, $J/\psi$ and corresponding weak decays
• Next-to-leading order QCD calculation of $B_c$ to charmonium tensor form factors
• Perturbative QCD analysis of neutral $B$-meson decays into $\sigma \sigma ,\sigma f_0$ and $f_0{f}_0$
• $S$-wave contributions to the $B_{(s)}\to {\chi }_{c1}(\pi \pi ,K\pi ,KK)$ decays
• Semileptonic baryon decays ${\Xi }_b\to {\Xi }_c{\ell }^{-}{\bar{\nu }}_{\ell }$ in perturbative QCD
• Systematic analysis of the form factors of $B_c$ to $P$-wave charmonia and corresponding weak decays
• Study of Form Factors and Observables in $B_c^{-}\to {\bar{D}}^{(\ast )0}{\ell }^{-}{\bar{\nu }}_{\ell }$ and $B_c^{-}\to D^{(\ast )-}{\ell }^{+}{\ell }^{-}$ decays