Next-to-leading-order QCD corrections to heavy quark fragmentation into $${}^1S^{(1,8)}_0$$ quarkonia

Abstract

Within NRQCD factorization framework, in this work we compute, at the lowest order in velocity expansion, the next-to-leading-order (NLO) perturbative corrections to the short-distance coefficients associated with heavy quark fragmentation into the $${}^1S_0^{(1,8)}$$ 1 S 0 ( 1 , 8 ) components of a heavy quarkonium. Starting from the Collins and Soper’s operator definition of the quark fragmentation function, we apply the sector decomposition method to facilitate the numerical manipulation. It is found that the NLO QCD corrections have a significant impact.

Fragmentation functions for a quark into a spin-singlet quarkonium: Different flavor case

“…The SDCs can be calculated perturbatively, while the LDMEs are nonperturbative in nature but can be extracted via global fitting of experimental data or estimated using the Lattice QCD or the QCD potential models. Most of the fragmentation functions for quarkonia have been calculated up to order α 2 s , and a few fragmentation functions for quarkonia have been calculated up to order α 3 s [36][37][38][39][40][41][42][43][44][45]. Among these studies, the fragmentation functions for q → η Q (q = Q), which are of order α 3 s , have been calculated in our recent paper [45].…”

A Short Theoretical Review of Charmonium Production

“…J Þ are calculated in Refs. [38,44,[53][54][55][56][57][58][59][60]. Recently, the heavy quark FFs to 1 S ½1,8 0 state are obtained in Refs.…”

Gluon fragmentation into $B_c^{(*)}$ in NRQCD factorization

“…Nevertheless, it turns out to be a quite subtle issue to use these techniques to deal with our case. In this work, similar to [27,29], we choose to apply the sector decomposition method [36,37] to evaluate the phase space integration as given in (9). Consequently, we will present our final results in an entirely numerical manner.…”

“…During the past three decades, a number of fragmentation functions for S-wave/P -wave charmonia/bottomonia have been investigated in the context of NRQCD factorization approach, typically at lowest order in α s (for a very incomplete list, see [2,3,. With the advance of higher-order calculational technique, the SDCs associated with some S-wave quarkonium FFs have recently been calculated through the next-to-leading order (NLO) in α s [14,19,[26][27][28][29].…”