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

We present the calculation of the order αs2 corrections to the coefficient functions contributing to the longitudinal (FL (x, Q2)) and transverse fragmentation functions (FT (x, Q2)) measured in electron-positron annihilation. The effect of these higher order QCD corrections on the behaviour of the fragmentation functions and the corresponding longitudinal (dσL(x,Q2)/dx) and transverse cross sections (dσT(x,Q2)/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 DpH(x,M2) (p = q, g; H = π±, K±, P, P). Our analysis reveals that the order αs2 contributions to FL(x,Q2) are large whereas these contributions to FT(x, Q2) are small. From the above fragmentation functions one can also compute the integrated cross sections σL and σT in an independent way. The sum σtot = σL + σT, corrected up to order αs2, agrees with the well-known result in the literature providing us with an independent check on our calculations.