Numerical solution of Q2 evolution equation for the transversity distribution ΔTq Original Research Article

We investigate a numerical solution of the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) Q2 evolution equation for the transversity distribution ΔTq or the structure function h1. The leading-order (LO) and next-to-leading-order (NLO) evolution equations are studied. The renormalization scheme is MS or image in the NLO case. Dividing the variables x and Q2 into small steps, we solve the integrodifferential equation by the Euler method in the variable Q2 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 Q2 steps and more than five hundred x steps are taken. We provide a FORTRAN program for the Q2 evolution and devolution of the transversity distribution ΔTq or h1. Using the program, we show the LO and NLO evolution results of the valence-quark distribution ΔTuv + ΔTdv, the singlet distribution image, and the flavor asymmetric distribution image. They are also compared with the longitudinal evolution results.