Bridging light-cone and NRQCD approaches: asymptotic behavior of $B_c$ electromagnetic form factor

Abstract

This work aims at illustrating that, for a class of leading-twist hard exclusive reactions involving two heavy quarkonia, the light-cone approach, when equipped with the strategy of refactorization of the light-cone distribution amplitude of quarkonium, can be employed to elegantly reproduce the corresponding predictions made in the nonrelativistic QCD (NRQCD) factorization approach, order by order in perturbative expansion. Taking the electromagnetic form factor of the $B_c$ meson at large momentum transfer, $Q^2$, as a concrete example, we compare the results obtained from both NRQCD-based and light-cone-based calculations through the next-to-leading order (NLO) in ${\alpha }_s$, while at the leading order (LO) in both velocity and $1/Q^2$ expansion, and explicitly confirm their mutual agreement. As a byproduct, we apply our NLO result to explore certain features about the asymptotic behavior of the heavy-light meson form factor. We also address the major theoretical obstacles that prevent us from establishing an analogous equivalence between these two approaches for the double charmonium production process of phenomenological interest, $e^{+}{e}^{-}\to J/\psi +{\eta }_c$.

v3, 39 pages, 5 figures. A minor error in equation (37) corrected, Fig. 4 redrawn. A new paragraph added to discuss the numerical significance of double logarithm term in O(alpha_s) short-distane coefficient for gamma*->J/psi+eta_c process, and one reference added

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Cited by in corpus (21)

• $Apart: A Generalized Mathematica Apart Function
• S-wave ground state charmonium decays of $B_c$ mesons in the perturbative QCD approach
• Can NRQCD explain the $\gamma {\gamma }^{\ast }\to {\eta }_c$ transition form factor data?
• The leading twist light-cone distribution amplitudes for the S-wave and P-wave quarkonia and their applications in single quarkonium exclusive productions
• $O({\alpha }_s{v}^2)$ correction to $e^{+}{e}^{-}\to J/\psi +{\eta }_c$ at $B$ factories
• Relativistic corrections to light-cone distribution amplitudes of S-wave $B_c$ mesons and heavy quarkonia
• Quasi Distribution Amplitude of Heavy Quarkonia
• Renormalization of the radiative jet function
• Pseudoscalar Quarkonium+gamma Production at NLL+NLO accuracy
• Exclusive decay of ${\rm Y}$ into $J/\psi +{\chi }_{c0,1,2}$
• Study of $B_c\to DS$ Decays in PQCD Approach
• Analyticity, renormalization, and evolution of the soft-quark function
• A factorization theorem connecting the light-cone distribution amplitudes of heavy-flavor mesons in QCD and HQET
• Double Logarithms in $e^{+}{e}^{-}\to J/\psi +{\eta }_c$
• The leading twist light-cone distribution amplitudes for the S-wave and P-wave Bc mesons
• $W$ radiative decay to heavy-light mesons in HQET factorization through $\mathcal{O}({\alpha }_s)$
• Endpoint Logarithms in e+e- -> J/psi + eta_c
• Two loop QCD corrections to $e^{+}{e}^{-}\to J/\psi +{\eta }_c$ in asymptotic expansion
• Semileptonic $W$ Decay to the $B$ Meson with Lepton Pairs in Heavy Quark Effective Theory Factorization upto $\mathcal{O}$$({\alpha }_s)$
• $\mathcal{O}({\alpha }_s)$ corrections to $e^{+}{e}^{-}\to J/\psi +{\eta }_{c2}({\chi }_{c1}^{\prime })$ at $B$ factories
• Some recent progress in understanding exclusive double charmonium production at $B$ factories