Abstract
We derive the $k_T$ resummation for doubly heavy-flavored $B_c$ meson decays by including the charm quark mass effect into the known formula for a heavy-light system. The resultant Sudakov factor is employed in the perutrbative QCD study of the "golden channel" $B_c^+ \to J/\psi \pi^+$. With a reasonable model for the $B_c$ meson distribution amplitude, which maintains approximate on-shell conditions of both the partonic bottom and charm quarks, it is observed that the imaginary piece of the $B_c \to J/\psi$ transition form factor appears to be power suppressed, and the $B_c^+ \to J/\psi \pi^+$ branching ratio is not lower than $10^{-3}$. The above improved perutrbative QCD formalism is applicable to $B_c$ meson decays to other charmonia and charmed mesons.
Highlights
A Bc meson is the ground state of the doubly heavyflavored bc system in the Standard Model [1], different from the heavy-light one represented by a B meson and from the heavy-heavy one represented by quarkonia J=ψ and Υ in many aspects
A framework available in the literature is the perturbative QCD (PQCD) approach, which basically follows the conventional one for B meson decays, with the finite charm quark mass being included in hard decay kernels
Given the bottom quark mass mb ≈ mBc − mc ∼ 4.8 GeV for mBc 1⁄4 6.276 GeV, we find that the Bc meson distribution amplitude takes a substantial value around the momentum fraction x1 ∼ mc=mb ∼ 0.3 within the width of about Λ=mb ∼ 0.1
Summary
We derive the kT resummation for doubly heavy-flavored Bc meson decays by including the charm quark mass effect into the known formula for a heavy-light system. The resultant Sudakov factor is employed in the perutrbative QCD study of the “golden channel” Bþc → J=ψπþ. With a reasonable model for the Bc meson distribution amplitude, which maintains approximate on-shell conditions of both the partonic bottom and charm quarks, it is observed that the imaginary piece of the Bc → J=ψ transition form factor appears to be power suppressed, and the Bþc → J=ψπþ branching ratio is not lower than 10−3. The above improved perturbative QCD formalism is applicable to Bc meson decays to other charmonia and charmed mesons
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