Higher order QCD corrections to the transverse and longitudinal fragmentation functions in electron-positron annihilation

We present the calculation of the order alpha(s)(2) corrections to the coefficient functions contributing to the longitudinal (F-L(x,Q(2))) and traverse fragmentation functions (F-T(x,Q(2))) measured in electron-position annihilation. The effect of these higher order QCD corrections on the behaviour of the fragmentation functions and the corresponding longitudinal (d sigma(L)(x,Q(2))/dx) and transverse cross sections (d sigma(T)(x,Q(2))/dx) are studied. In particular we investigate the dependence of the above quantities on the mass factorization scale (M) and the various parameterizations chosen for the parton fragmentation densities D-p(H)(x,M(2)) (p = q,g; H = pi(+/-),K-+/-,P,(P) over bar). Our analysis reveals that the order alpha(s)(2) contributions to F-L(x,Q(2)) are large whereas these contributions to F-T(x,Q(2)) are small. From the above fragmentation functions one can also compute the integrated cross sections sigma(L) and sigma(T) in an independent way. The sum sigma(tot) = sigma(L) + sigma(T), corrected up to order alpha(s)(2), agrees with the well-known result in the literature providing us with an independent check on our calculations.