Refactorizing NRQCD short-distance coefficients in exclusive quarkonium production

Abstract

In a typical exclusive quarkonium production process, when the center-of-mass energy, $\sqrt{s}$, is much greater than the heavy quark mass $m$, large kinematic logarithms of $s/m^2$ will unavoidably arise at each order of perturbative expansion in the short-distance coefficients of the nonrelativistic QCD (NRQCD) factorization formalism, which may potentially harm the perturbative expansion. This symptom reflects that the hard regime in NRQCD factorization is too coarse and should be further factorized. We suggest that this regime can be further separated into "hard" and "collinear" degrees of freedom, so that the familiar light-cone approach can be employed to reproduce the NRQCD matching coefficients at the zeroth order of $m^2/s$ and order by order in ${\alpha }_s$. Taking two simple processes, exclusive ${\eta }_b+\gamma$ production in $e^{+}{e}^{-}$ annihilation and Higgs boson radiative decay into ${\rm Y}$, as examples, we illustrate how the leading logarithms of $s/m^2$ in the NRQCD matching coefficients are identified and summed to all orders in ${\alpha }_s$ with the aid of Brodsky-Lepage evolution equation.

v2, 17 pages, 2 figures; presentation improved, one important reference added, and Note added

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• Higher Order Corrections to the Cross Section of e+e- to Quarkonium plus gamma
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• $Z$-boson decays to a vector quarkonium plus a photon
• The dipole picture and the non-relativistic expansion
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• Search for $C=+$ charmonium and bottomonium states in $e^{+}{e}^{-}\to \gamma +X$ at B factories
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• Quasi Distribution Amplitude of Heavy Quarkonia
• Addendum: New approach to the resummation of logarithms in Higgs-boson decays to a vector quarkonium plus a photon [Phys. Rev. D 95, 054018 (2017)]
• $O({\alpha }_s)$ corrections to $J/\psi +{\chi }_{cJ}$ production at $B$ factories
• Pseudoscalar Quarkonium+gamma Production at NLL+NLO accuracy
• Exploring Light-Cone Distribution Amplitudes from Quantum Computing
• A factorization theorem connecting the light-cone distribution amplitudes of heavy-flavor mesons in QCD and HQET
• $Z$ boson radiative decays to a $S$-wave quarkonium at NNLO and NLL accuracy
• $Z$ boson radiative decays to a $P$-wave quarkonium at NNLO and LL accuracy
• The leading twist light-cone distribution amplitudes for the S-wave and P-wave Bc mesons
• Double Logarithms in $e^{+}{e}^{-}\to J/\psi +{\eta }_c$
• $P$-wave quarkonium wavefunctions at the origin in the $\overline{\mathrm{MS}}$ scheme
• Exclusive C=+ charmonium production in $e^{+}{e}^{-}\to H+\gamma$ at B-factories within light cone formalism
• $W$ radiative decay to heavy-light mesons in HQET factorization through $\mathcal{O}({\alpha }_s)$
• Power expansion for heavy quarkonium production at next-to-leading order in ${\mathrm{e}}^{+}{\mathrm{e}}^{-}$ annihilation
• Endpoint Logarithms in e+e- -> J/psi + eta_c
• $\mathcal{O}({\alpha }_s)$ 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