Next-to-leading-order QCD corrections to gluon fragmentation into ${}^1S_0^{(1,8)}$ quarkonia

Abstract

Within the NRQCD factorization framework, we compute the next-to-leading-order QCD corrections to the gluon fragmentation into the ${}^1S_0^{(1,8)}$ Fock components of a quarkonium, at the lowest order in velocity expansion. We follow the operator definition of the fragmentation function advanced by Collins and Soper. The key technique underpinning our calculation is the sector decomposition method widely used in the area of multi-loop computation. It is found that the NLO QCD corrections have significant effects, and qualitatively modify the profiles of the corresponding leading-order fragmentation functions.

Figures (2)

• Figure 1: Representative cut diagrams for the gluon fragmentation function $d_{g\to c\bar{c}(^1S_0^{(1,8)})}(z)$. The cap represents the gluonic field strength operator $G_a^{+\nu}$, and double line signifies the eikonal line.
• Figure 2: The SDCs $d_{1,8}(z)$ associated with gluon fragmentation into quarkonium, including the NLO QCD corrections. The two figures in the top row correspond to $d_1(z)$ for gluon fragmentation into the color-singlet charmonium and bottomonium, while the two figures in the lower panel correspond to $d_8(z)$ for gluon into the color-octet charmonium and bottomonium.