Resummation and renormalization of kinematical effects in inclusive $P$-wave quarkonium production

Abstract

We investigate the renormalization properties of the shape function formalism for inclusive production of $P$-wave heavy quarkonia, which arises from resumming a class of corrections coming from kinematical effects associated with the motion of the heavy quark and antiquark pair relative to the quarkonium. Such kinematical effects are encoded in the nonperturbative shape functions, which are normalized to the corresponding nonrelativistic QCD long-distance matrix elements. By using the known ultraviolet divergences in the matrix elements, we derive the large-momentum asymptotic behavior of the shape functions. This strongly constrains the form of the shape functions and significantly reduces the dependence on the nonperturbative model. Based on these results we show that the shape function formalism at loop level can be useful in taming the threshold logarithms at large transverse momentum, and at small transverse momentum the kinematical corrections reduce the sizes of ${\chi }_c$ and ${\chi }_b$ cross sections which may improve agreement with measurements.

51 pages, 11 figures, minor revisions, version published in JHEP

References in corpus (14)

• Reconciling J/psi production at HERA, RHIC, Tevatron, and LHC with NRQCD factorization at next-to-leading order
• Polarization for Prompt J/psi, psi(2s) production at the Tevatron and LHC
• QCD radiative corrections to ${\chi }_{cJ}$ production at hadron colliders
• Next-to-leading-order tests of nonrelativistic-QCD factorization with $J/\psi$ yield and polarization
• NRQCD Factorization and Velocity-dependence of NNLO Poles in Heavy Quarkonium Production
• Inclusive production of $J/\psi$, $\psi (2S)$, and ${\rm Y}$ states in pNRQCD
• Inclusive Production of Heavy Quarkonia in pNRQCD
• Breakdown of QCD Factorization for P-Wave Quarkonium Production at Low Transverse Momentum
• Quark fragmentation into spin-triplet $S$-wave quarkonium
• Heavy Pair Production Currents with General Quantum Numbers in Dimensionally Regularized NRQCD
• Production and polarization of $S$-wave quarkonia in potential nonrelativistic QCD
• FDCHQHP:A Fortran Package for Heavy Quarkonium HadroProduction
• Global analysis of $\psi (2S)$ inclusive hadroproduction at next-to-leading order in nonrelativistic-QCD factorization
• $P$-wave quarkonium wavefunctions at the origin in the $\overline{\mathrm{MS}}$ scheme

Cited by in corpus (2)

• Resummation of threshold double logarithms in hadroproduction of heavy quarkonium
• Resummation of threshold double logarithms in quarkonium fragmentation functions