Abstract
We analyze the iterative structure of unfactorized partonic structure functions in the large-x limit, and derive all-order expressions for the leading-logarithmic off-diagonal splitting functions Pgq and Pqg and the corresponding coefficient functions Cϕ,q and C2,g in Higgs- and gauge-boson exchange deep-inelastic scattering. The splitting functions are given in terms of a new function not encountered in perturbative QCD so far, and vanish maximally in the supersymmetric limit CA−CF→0. The coefficient functions do not vanish in this limit, and are given by simple expressions in terms of the above new function and the well-known leading-logarithmic threshold exponential. Our results also apply to the evolution of parton fragmentation functions and semi-inclusive e+e− annihilation.
Highlights
We analyze the iterative structure of unfactorized partonic structure functions in the large-x limit, and derive all-order expressions for the leading-logarithmic off-diagonal splitting functions Pgq and Pqg and the corresponding coefficient functions Cφ,q and C2,g in Higgs- and gauge-boson exchange deep-inelastic scattering
Only Pgg is known at next-to-leading logarithmic (NLL) small-x accuracy at this point
It is useful to switch to Mellin moments, f (N) =
Summary
In conjunction with the three-loop coefficient functions computed in Refs. [13, 16]. In particular it turned out that the fourth-order coefficient D0(3) vanishes, a fact that was attributed to an accidental cancellation of contributions. The single-log enhancement of the physical kernels provides relations between double-logarithmic contributions to the singlet splitting functions and coefficient functions beyond this order but, unlike in corresponding non-singlet cases [17] which include Eq (4) but not Eq (5), no definite higher-order predictions of any expansion coefficients. We obtain the corresponding αsn ln2n−1(1 − x) contributions to the off-diagonal coefficient functions C2,g and Cφ,q in Eq (7) as well. (6) and (7) above, all functional dependences on N, αs and the dimensional offset ε with D = 4 − 2ε, these quantities can be factorized as Ta,k = Ca,i Zik. Here the (process-dependent) D-dimensional coefficient functions Ca,i consists of contributions with all non-negative powers of ε.
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