Fragmentation functions beyond fixed order accuracy

We give a detailed account of the phenomenology of all-order resummations of logarithmically enhanced contributions at small momentum fraction of the observed hadron in semi-inclusive electron-positron annihilation and the timelike scale evolution of parton-to-hadron fragmentation functions. The for...

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Bibliographic Details
Published in:Physical review. D 2017-03, Vol.95 (5), p.054003, Article 054003
Main Authors: Anderle, Daniele P., Kaufmann, Tom, Stratmann, Marco, Ringer, Felix
Format: Article
Language:English
Subjects:
ATOMIC AND MOLECULAR PHYSICS
Atomic and Nuclear Physics
Contour matching
Dependence
Evolution
Factorization
Fragmentation
Iterative methods
Iterative solution
Phenomenology
Positron annihilation
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Summary:We give a detailed account of the phenomenology of all-order resummations of logarithmically enhanced contributions at small momentum fraction of the observed hadron in semi-inclusive electron-positron annihilation and the timelike scale evolution of parton-to-hadron fragmentation functions. The formalism to perform resummations in Mellin moment space is briefly reviewed, and all relevant expressions up to next-to-next-to-leading logarithmic order are derived, including their explicit dependence on the factorization and renormalization scales. We discuss the details pertinent to a proper numerical implementation of the resummed results comprising an iterative solution to the timelike evolution equations, the matching to known fixed-order expressions, and the choice of the contour in the Mellin inverse transformation. First extractions of parton-to-pion fragmentation functions from semi-inclusive annihilation data are performed at different logarithmic orders of the resummations in order to estimate their phenomenological relevance. To this end, we compare our results to corresponding fits up to fixed, next-to-next-to-leading order accuracy and study the residual dependence on the factorization scale in each case.
ISSN:2470-0010
2470-0029
DOI:10.1103/PhysRevD.95.054003