Leading logarithmic large-x resummation of off-diagonal splitting functions and coefficient functions

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 P_gq and P_qg and the corresponding coefficient functions C_phi,q and C_2,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 C_A - C_F to 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 fragmentation functions and semi-inclusive e^+ e^- annihilation.

Figures (2)

• Figure 1: Typical diagrams for the leading-logarithmic large-$x$ terms of the $n$-th order quantities $T_{\phi, \rm q}^{\,(n)}$ (left) and $T_{2,\rm g}^{\,(n)}$ (right) in Eqs. (\ref{['Tdec']}) and (\ref{['TijLL']}). Shown are $C_F^{\,n-k}\, C_A^{\:k}$ and ${n^{}_{\! f}}\, C_A^{\,n-k-1}\, C_F^{\:k}$ contributions to the former and latter expressions, respectively.
• Figure 2: The function ${\cal B}_{\,0}(x)$ in Eq. (\ref{['B0']}), evaluated using its defining Taylor expansion.