NLO fragmentation functions of heavy quarks into heavy quarkonia

Abstract

In the paper, we derive the next-to-leading order (NLO) fragmentation function for a heavy quark, either charm or bottom, into a heavy quarkonium J/Ψ or Υ. The ultra-violet divergences in the real corrections are removed through the operator renormalization, which is performed under the modified minimal subtraction scheme. We then obtain the NLO fragmentation function at an initial factorization scale, e.g. µF = 3mc for c → J/Ψ and µF = 3m b for b → Υ, which can be evolved to any scale via the use of Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equation. As an initial application of those fragmentation functions, we study the J/Ψ (Υ) production at a high luminosity e + e − collider which runs at the energy around the Z pole and could be a suitable platform for testing the fragmentation function.

Fragmentation functions for gluon into $B_c$ or $B_c^*$ meson

“…(2.8) in d dimensions directly due to the fact that A (1−49) is complicated. To carry out the integral, we adopt the subtraction method which was recently used to calculate the real corrections to fragmentation functions for quarkonia [10,12,15,16,21,22]. Under the subtraction method, the contribution of the 49 cut diagrams can be calculated through…”

“…[6][7][8]. In recent years, with the development of the loop-diagram calculation techniques, some fragmentation functions for the heavy quarkonia have been calculated to the higher order of α s and v [9][10][11][12][13][14][15][16][17][18][19][20][21][22], where v is the relative velocity of the constituent quarks in the quarkonia rest frame. Among those studies, the NLO corrections to the fragmentation functions D Q→Bc(B * c ) (z, µ F ), where Q = b or c, have been obtained in our previous work [15].…”

NLO fragmentation functions for a quark into a spin-singlet quarkonium: same flavor case

“…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].…”

Next-to-leading order QCD corrections to the production of Bc and Bc* through W+Zheng1, Chang2, Wu3 et al. 2020Phys. Rev. DSelf Cite9040View full textAdd to dashboardCite

“…More details about those strategies can be found in Refs. [23,58]. For convenience, we 1 Due to the coefficient function dΓ W þ →iþX ðy; μ F Þ is IR safe, the heavy-quark mass m Q in the coefficient function can be approximately set to 0, and this approximation brings only a small error of Oðm 2 Q =m 2 W Þ.…”