QCD evolution of naive-time-reversal-odd fragmentation functions

TL;DR

This work derives the QCD evolution equations for the first transverse-momentum moments of naive-time-reversal-odd fragmentation functions: the Collins function H1_perp and the polarizing fragmentation function D1T_perp. The authors show that the diagonal parts of the evolution kernels match those of the transversity and unpolarized fragmentation functions, respectively, while the off-diagonal mixing involves two-variable F-type fragmentation correlators that vanish at z1=z, potentially reducing their impact. The results have important implications for the energy-scale dependence of spin observables and for global analyses of spin asymmetries, with the caveat of no gluon Collins contribution at this order and possible gluon polarizing fragmentation effects not explored here. Overall, the paper advances the theoretical understanding of the scale evolution of spin-dependent fragmentation and informs phenomenological fits in SIDIS and e+e- processes.

Abstract

We study QCD evolution equations of the first transverse-momentum-moment of the naive-time-reversal-odd fragmentation functions - the Collins function and the polarizing fragmentation function. We find for the Collins function case that the evolution kernel has a diagonal piece same as that for the transversity fragmentation function, while for the polarizing fragmentation function case this piece is the same as that for the unpolarized fragmentation function. Our results might have important implications in the current global analysis of spin asymmetries.

Figures (4)

• Figure 1: Feynman diagram representation: (a) the first transverse-momentum-moment of TMD fragmentation functions, (b) evolution contribution from itself: $\ell_q\approx P/z+\ell_{q_\perp}$, (c) evolution contribution from the two-variable$F$-type fragmentation correlations: $\ell_q=P/z$, $\ell_{q_1}=P/z_1$, and $\ell_g=\ell_q-\ell_{q_1}$.
• Figure 2: Contribution from the first transverse-momentum-moment of the TMD fragmentation functions themselves: (a) real contribution, (b) and (c) virtual contributions.
• Figure 3: Contribution from the $F$-type fragmentation correlation functions: real diagrams. The "mirror" diagrams for which the additional gluon attaches on the left of the cut are not shown, but are included in the calculations.
• Figure 4: Contribution from the $F$-type fragmentation correlation functions: virtual diagrams. The "mirror" diagrams for which the additional gluon attaches on the left of the cut are not shown, but are included in the calculations.