Abstract
Analyzing the single inclusive annihilation spectrum of charged hadrons in e+e− collisions, I confront the hadronization hypothesis of local parton-hadron duality with a systematic resummation of the dependence on the small energy fraction. This resummation is based on the reciprocity between time-like and space-like splitting processes in 4 − 2ϵ-dimensions, which I extend to resum all the soft terms of the cross-section for inclusive jet production. Under the local-parton-hadron duality hypothesis, the resulting distribution of jets essentially determines the spectrum of hadrons as the jet radius goes to zero. Thus I take the resummed perturbative jet function as the non-perturbative fragmentation function with an effective infra-red coupling. I find excellent agreement with data, and comment on the mixed leading log approximation previously used to justify local parton-hadron duality.
Highlights
Within factorization, one constructs the fragmentation spectrum as the convolution of a non-perturbative boundary condition, the fragmentation function, with a perturbatively calculable renormalization group evolution, and a perturbatively calculable coefficient function
While it is clear that the leading order DGLAP kernel acts as the leading order kernel for the mixed leading log” approximation (MLLA) equations, none-the-less, the MLLA derived anomalous dimension differs from the next-to-leading logarithmic MS anomalous dimension from small-zh resummed perturbation theory of refs. [10, 11]
I need for the non-perturbative fragmentation function: the jet function evaluated with a frozen coupling scale in the infra-red
Summary
I will explain how to resum the fragmentation function. I note the conventions for moment transforms as: f(n) = 1 dx xn (xf (x)) , 0x c+i∞. The constant c is chosen to place all singularities of fto the left of the contour. The soft region of zh → 0 corresponds to n → 0. The log counting I adopt is αs ∼ n2, and the order. Of the pole in n at 0 corresponds to the number of logarithms in momentum space:. I start with the basic angular-ordered factorization posited in ref. [12], outline its connection to the standard formulation of the fragmentation spectrum in the factorization approach of perturbative QCD, focusing on the case of pure Yang-Mills theory. QCD in the following, as required to compare to data
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