Relativistic corrections of the fragmentation functions for a heavy quark to B_c and *

Abstract

In this paper, we compute the relativistic corrections of the fragmentation functions (FFs) for a heavy quark to Bc and within the framework of non-relativistic QCD (NRQCD) factorization. The non-singlet and singlet DGLAP evolutions are also presented.

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

“…The relativistic corrections to the heavy quark fragmenting into the S-wave charmonia were addressed in Refs. [10][11][12]. The perturbative corrections for heavy quark fragmentation into Swave charmonia were evaluated in Refs.…”

“…Note in (12) the UV pole is subtracted in accordance with the MS scheme. Finally, the renormalized SDCs at NLO in α s can be parameterized in the following form:…”

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

“…[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].…”

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

“…The relativistic corrections to the heavy quark fragmenting into the S-wave charmonia were addressed in Refs. [12][13][14]. The perturbative corrections for heavy quark fragmentation into S-wave charmonia were evaluated in Refs.…”

“…2 for c to charmonium and b to bottomonium, respectively. We have equated the renormalization scale µ R and factorization scale µ in (14) for simplicity. The central curves are obtained by setting µ = 2m Q , while the uncertainty bands are obtained by varying µ from m Q to 3m Q .…”