On threshold resummation of singlet structure and fragmentation functions

Abstract

The large-x behavior of the physical evolution kernels appearing in the second order evolution equations of the singlet F_2 structure function and of the F_{phi} structure function in phi-exchange DIS is investigated. The validity of a leading logarithmic threshold resummation, analogous to the one prevailing for the non-singlet physical kernels, is established, allowing to recover the predictions of Soar et al. for the double-logarithmic contributions (ln^i(1-x), i=4,5,6) to the four loop splitting function P^{(3)}_{qg}(x) and P^{(3)}_{gq}(x). Threshold resummation at the next-to-leading logarithmic level is found however to break down in the three loop kernels, except in the "supersymmetric" case C_A=C_F. Assuming a full threshold resummation does hold in this case also beyond three loop gives some information on the leading and next-to-leading single-logarithmic contributions (ln^i(1-x), i=2,3) to P^{(3)}_{qg}(x) and P^{(3)}_{gq}(x). Similar results are obtained for singlet fragmentation functions in e^+e^- annihilation up to two loop, where a large-x Gribov-Lipatov relation in the physical kernels is pointed out. Assuming this relation also holds at three loop, one gets predictions for all large-x logarithmic contributions to the three loop timelike splitting function P^{(2)T}_{gq}(x), which are related to similar terms in P^{(2)}_{qg}(x).

29 pages, no figure, v2: inappropriate statements on the normalization of the timelike gluon coefficient function removed; new section added to deal with the large-x behavior of the P_{gq}(x) splitting function, v3: a few stylistic changes; to be published in Nuclear Physics B

References in corpus (15)

• Anomalous dimensions of high-spin operators beyond the leading order
• Next-to-Next-to-Leading Order Evolution of Non-Singlet Fragmentation Functions
• On Third-Order Timelike Splitting Functions and Top-Mediated Higgs Decay into Hadrons
• On Higgs-exchange DIS, physical evolution kernels and fourth-order splitting functions at large x
• On non-singlet physical evolution kernels and large-x coefficient functions in perturbative QCD
• Generalized double-logarithmic large-x resummation in inclusive deep-inelastic scattering
• On threshold resummation beyond leading 1-x order
• Higher-order threshold resummation for semi-inclusive e^+e^- annihilation
• Large-x structure of physical evolution kernels in Deep Inelastic Scattering
• Leading logarithmic large-x resummation of off-diagonal splitting functions and coefficient functions
• A dispersive approach to Sudakov resummation
• Threshold resummation to any order in (1-x)
• The Large-x Factorization of the Longitudinal Structure Function
• Threshold resummation beyond leading eikonal level
• On threshold resummation of the longitudinal structure function

Cited by in corpus (4)

• On the Next-to-Next-to-Leading Order Evolution of Flavour-Singlet Fragmentation Functions
• Generalized threshold resummation in inclusive DIS and semi-inclusive electron-positron annihilation
• Timelike structure functions and hadron multiplicities
• Generalized threshold resummation for semi-inclusive e+e- annihilation