Soft parton-to-hadron FFs at NNLO*+NNLL

The evolution of the parton-to-hadron fragmentation functions (FF) at lowfractional hadron momenta z is theoretically studied in a framework combiningnext-to-next-to-leading-order (NNLO) α s corrections with next-to-modified-leading logarithmic resummations of soft and collinear parton radiation. Theenergy evolution of the moments of the low-z FFs are thereby computed, andcompared to the existing experimental e + e − and DIS e ± p jet data. The impactof hadron-mass effects and higher-order corrections is presented. Thedata–theory comparison of the four FF moments (total hadron multiplicity, peak,width, and skewness) allow us to extract the QCD coupling α s at approximateNNLO accuracy, α s (m 2 Z) = 0.1205±0.0010 +0.0022 −0.0000 , in excellentnumerical agreement with the current world average.