On threshold resummation of singlet structure and fragmentation functions

Understand

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.