NLO fragmentation functions for a quark into a spin-singlet quarkonium: same flavor case
Xu-Chang Zheng, Xing-Gang Wu, Xu-Dong Huang
Abstract
A bstract In the paper, we calculate the fragmentation functions for c → η c and b → η b up to next-to-leading-order (NLO) QCD accuracy. The ultraviolet divergences in the real corrections are removed through operator renormalization under the modified min- imal subtraction scheme. We then obtain the fragmentation functions $$ {D}_{c\to {\eta}_c} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>D</mml:mi> <mml:mrow> <mml:mi>c</mml:mi> <mml:mo>→</mml:mo> <mml:msub> <mml:mi>η</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:mrow> </mml:msub> </mml:math> ( z, μ F ) and $$ {D}_{b\to {\eta}_b} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>D</mml:mi> <mml:mrow> <mml:mi>b</mml:mi> <mml:mo>→</mml:mo> <mml:msub> <mml:mi>η</mml:mi> <mml:mi>b</mml:mi> </mml:msub> </mml:mrow> </mml:msub> </mml:math> ( z, μ F ) up to NLO QCD accuracy, which are presented as figures and fitting functions. The numerical results show that the NLO corrections are significant. The sensitives of the fragmentation functions to the renormalization scale and the factorization scale are analyzed explicitly.