Generalized threshold resummation in inclusive DIS and semi-inclusive electron-positron annihilation

• Published in: The journal of high energy physics Vol. 2016; no. 1; pp. 1 - 22
• Main Authors: Almasy, A. A., Lo Presti, N. A., Vogt, A.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-01-2016; Springer Nature B.V
• Subjects: Classical and Quantum Gravitation; Coefficients; Elementary Particles; High energy physics; Logarithms; Mathematical analysis; Mathematical models; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Regularization; Relativity Theory; Scattering; Splitting; String Theory; Thresholds; Resummation; Perturbative QCD
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP01(2016)028

A
bstract
We present analytic all-order results for the highest three threshold logarithms of the space-like and time-like off-diagonal splitting functions and the corresponding coefficient functions for inclusive deep-inelastic scattering (DIS) and semi-inclusive
e
+
e
−
annihilation. All these results, obtained through an order-by-order analysis of the structure of the corresponding unfactorized quantities in dimensional regularization, can be expressed in terms of the Bernoulli functions introduced by one of us and leading-logarithmic soft-gluon exponentials. The resulting numerical corrections are small for the splitting functions but large for the coefficient functions. In both cases more terms in the threshold expansion need to be determined in order to arrive at quantitatively reliable results.