A forest formula to subtract infrared singularities in amplitudes for wideangle scattering
Abstract
For any hard QCD amplitude with massless partons, infrared (IR) singularities arise from pinches in the complex planes of loop momenta, called pinch surfaces. To organize and study their leading behaviors in the neighborhoods of these surfaces, we can construct approximation operators for collinear and soft singularities. A BPHZlike forest formula can be developed to subtract them systematically.In this paper, we utilize the positionspace analysis of Erdoğan and Sterman for Green functions, and develop the formalism for momentum space. A related analysis has been carried out by Collins for the Sudakov form factors, and is generalized here to any wideangle kinematics with an arbitrary number of external momenta. We will first see that the approximations yield much richer IR structures than those of an original amplitude, then construct the forest formula and prove that all the singularities appearing in its subtraction terms cancel pairwise. With the help of the forest formula, the full amplitude can also be reorganized into a factorized expression, which helps to generalize the Sudakov form factor result to arbitrary numbers of external momenta. All our analysis will be on the amplitude level.
 Publication:

Journal of High Energy Physics
 Pub Date:
 May 2020
 DOI:
 10.1007/JHEP05(2020)012
 arXiv:
 arXiv:1910.11304
 Bibcode:
 2020JHEP...05..012M
 Keywords:

 Perturbative QCD;
 Scattering Amplitudes;
 High Energy Physics  Phenomenology;
 High Energy Physics  Theory
 EPrint:
 108 pages, 47 figures