Quark fragmentation into spin-triplet $S$-wave quarkonium

Abstract

We compute fragmentation functions for a quark to fragment to a quarkonium through an $S$-wave spin-triplet heavy quark-antiquark pair. We consider both color-singlet and color-octet heavy quark-antiquark ($Q\bar{Q}$) pairs. We give results for the case in which the fragmenting quark and the quark that is a constituent of the quarkonium have different flavors and for the case in which these quarks have the same flavors. Our results for the sum over all spin polarizations of the $Q\bar{Q}$ pairs confirm previous results. Our results for longitudinally polarized $Q\bar{Q}$ pairs agree with previous calculations for the same flavor cases and correct an error in a previous calculation for the different-flavor case.

arXiv comment22 pages, 3 figures, minor revisions, version published in Phys. Rev. D

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• Next-to-leading-order QCD corrections to gluon fragmentation into ${}^1{S}_0^{(1,8)}$ quarkonia
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• Fragmentation function of gluon into spin-singlet $P$-wave quarkonium
• Next-to-leading-order QCD corrections to heavy quark fragmentation into ${}^1{S}_0^{(1,8)}$ quarkonia
• Fragmentation of charm to charmonium in $e^{+}{e}^{-}$ and $pp$ collisions
• Gluon fragmentation into ${}^3{P}_J^{[1,8]}$ quark pair and test of NRQCD factorization at two-loop level
• Resummation and renormalization of kinematical effects in inclusive $P$-wave quarkonium production
• Resolving negative cross section of quarkonium hadroproduction using soft gluon factorization
• Relativistic effect of $J/\psi$ hadroproduction in large $p_T$ region