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Title: Infrared singularities of scattering amplitudes in perturbative QCD

Abstract

An exact formula is derived for the infrared singularities of dimensionally regularized scattering amplitudes in massless QCD with an arbitrary number of legs, valid at any number of loops. It is based on the conjecture that the anomalous-dimension matrix of n-jet operators in soft-collinear effective theory contains only a single non-trivial color structure, whose coefficient is the cusp anomalous dimension of Wilson loops with light-like segments. Its color-diagonal part is characterized by two anomalous dimensions, which are extracted to three-loop order from known perturbative results for the quark and gluon form factors. This allows us to predict the three-loop coefficients of all 1/epsilon^k poles for an arbitrary n-parton scattering amplitudes, generalizing existing two-loop results.

Authors:
 [1];  [2]
  1. Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)
  2. Johannes Gutenberg-Universitaet Mainz, Mainz (Germany)
Publication Date:
Research Org.:
Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
OSTI Identifier:
1155694
Report Number(s):
MZ-TH-09-01
Journal ID: ISSN 0031-9007; PRLTAO; ArticleNumber: 199905
DOE Contract Number:
AC02-07CH11359
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review Letters; Journal Volume: 111; Journal Issue: 19
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats

Becher, Thomas, and Neubert, Matthias. Infrared singularities of scattering amplitudes in perturbative QCD. United States: N. p., 2013. Web. doi:10.1103/PhysRevLett.111.199905.
Becher, Thomas, & Neubert, Matthias. Infrared singularities of scattering amplitudes in perturbative QCD. United States. doi:10.1103/PhysRevLett.111.199905.
Becher, Thomas, and Neubert, Matthias. Fri . "Infrared singularities of scattering amplitudes in perturbative QCD". United States. doi:10.1103/PhysRevLett.111.199905. https://www.osti.gov/servlets/purl/1155694.
@article{osti_1155694,
title = {Infrared singularities of scattering amplitudes in perturbative QCD},
author = {Becher, Thomas and Neubert, Matthias},
abstractNote = {An exact formula is derived for the infrared singularities of dimensionally regularized scattering amplitudes in massless QCD with an arbitrary number of legs, valid at any number of loops. It is based on the conjecture that the anomalous-dimension matrix of n-jet operators in soft-collinear effective theory contains only a single non-trivial color structure, whose coefficient is the cusp anomalous dimension of Wilson loops with light-like segments. Its color-diagonal part is characterized by two anomalous dimensions, which are extracted to three-loop order from known perturbative results for the quark and gluon form factors. This allows us to predict the three-loop coefficients of all 1/epsilon^k poles for an arbitrary n-parton scattering amplitudes, generalizing existing two-loop results.},
doi = {10.1103/PhysRevLett.111.199905},
journal = {Physical Review Letters},
number = 19,
volume = 111,
place = {United States},
year = {Fri Nov 01 00:00:00 EDT 2013},
month = {Fri Nov 01 00:00:00 EDT 2013}
}
  • An exact formula is derived for the infrared singularities of dimensionally regularized scattering amplitudes in massless QCD with an arbitrary number of loops and legs. It is based on the conjecture that the anomalous-dimension matrix of n-jet operators in soft-collinear effective theory is fully determined by three functions of {alpha}{sub s}, which can be extracted from known perturbative results for the quark and gluon form factors. This allows us to predict the three-loop coefficients of all 1/{epsilon}{sup k} poles for arbitrary n-parton scattering amplitudes, generalizing existing two-loop results.
  • A formula for the two-loop infrared singularities of dimensionally regularized QCD scattering amplitudes with an arbitrary number of massive and massless legs is derived. The singularities are obtained from the solution of a renormalization-group equation, and factorization constraints on the relevant anomalous-dimension matrix are analyzed. The simplicity of the structure of the matrix relevant for massless partons does not carry over to the case with massive legs, where starting at two-loop order new color and momentum structures arise, which are not of the color-dipole form. The resulting two-loop three-parton correlations can be expressed in terms of two functions, for whichmore » some general properties are derived. This explains observations recently made by Mitov et al. in terms of symmetry arguments.« less
  • No abstract prepared.
  • We discuss quark distribution amplitudes for the nucleon obtained from perturbative QCD in connection with QCD sum rules on the light cone. Because of nonperturbative contributions these amplitudes have a complex nonsmooth structure and are dominated by strong correlations at the edges of the phase space. The antisymmetric part of the mixed symmetry amplitudes is found to be enhanced.
  • We compute the helicity density matrix of {rho} vector mesons produced in the two-body decays of polarized {chi}{sub {ital c}2}{close_quote}s in the framework of massless perturbative QCD. The {chi}{sub {ital c}2}{close_quote}s are either exclusively or inclusively produced in {ital p{bar p}} or {ital pp} interactions, via quark-antiquark annihilation or gluon fusion. Our results show unambiguous significant differences depending on the choice of the {rho} distribution amplitudes and allow us to discriminate between different proposed models. {copyright} {ital 1996 The American Physical Society.}