Numerical solution of Q^2 evolution equation for the transversity distribution Delta_T q

Abstract

We investigate numerical solution of the Dokshitzer-Gribov-Lipatov-Altarelli- Parisi (DGLAP) Q^2 evolution equation for the transversity distribution Delta_T q or the structure function h_1. The leading-order (LO) and next-to- leading-order (NLO) evolution equations are studied. The renormalization scheme is MS or overline{MS} in the NLO case. Dividing the variables x and Q^2 into small steps, we solve the integrodifferential equations by the Euler method in the variable Q^2 and by the Simpson method in the variable x. Numerical results indicate that accuracy is better than 1% in the region 10^{-5}<x<0.8 if more than fifty Q^2 steps and more than five hundred x steps are taken. We provide a FORTRAN program for the Q^2 evolution and devolution of the transversity distribution Delta_T q or h_1. Using the program, we show the LO and NLO evolution results of the valence-quark distribution Delta_T u_v + Delta_T d_v, the singlet distribution sum_i (Delta_T q_i + Delta_T qbar_i), and the flavor asymmetric distribution Delta_T ubar - Delta_T dbar.They are also compared with the longitudinal evolution results.