Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Integral of the double-emission eikonal function for two massive emitters at an arbitrary angle

Ming-Ming Long, Kirill Melnikov, Andrey Pikelner

TL;DR

This work develops a semi-analytic framework to compute the integrated double-emission eikonal function for two massive emitters at arbitrary angle, a key ingredient for extending nested soft-collinear subtraction to processes with massive partons. The authors systematically subtract soft and collinear singularities, derive analytic expressions for all $1/\varepsilon$ poles, and represent the finite remainders using numerically stable combinations of master integrals and generalized polylogarithms up to weight four. The final result combines analytic pole structures with numerically evaluated finite parts, and is validated against differential-equation solutions, sector decomposition, and known limits, with a public code provided for practical implementation. This advances precision QCD computations for processes involving heavy quarks by enabling robust NNLO subtraction schemes in the massive sector.

Abstract

We present a semi-analytic calculation of the integrated double-emission eikonal function of two massive emitters whose momenta are at an arbitrary angle to each other. This result is needed for extending the nested soft-collinear subtraction scheme arXiv:1702.01352 to processes with massive partons.

Integral of the double-emission eikonal function for two massive emitters at an arbitrary angle

TL;DR

This work develops a semi-analytic framework to compute the integrated double-emission eikonal function for two massive emitters at arbitrary angle, a key ingredient for extending nested soft-collinear subtraction to processes with massive partons. The authors systematically subtract soft and collinear singularities, derive analytic expressions for all poles, and represent the finite remainders using numerically stable combinations of master integrals and generalized polylogarithms up to weight four. The final result combines analytic pole structures with numerically evaluated finite parts, and is validated against differential-equation solutions, sector decomposition, and known limits, with a public code provided for practical implementation. This advances precision QCD computations for processes involving heavy quarks by enabling robust NNLO subtraction schemes in the massive sector.

Abstract

We present a semi-analytic calculation of the integrated double-emission eikonal function of two massive emitters whose momenta are at an arbitrary angle to each other. This result is needed for extending the nested soft-collinear subtraction scheme arXiv:1702.01352 to processes with massive partons.

Paper Structure

This paper contains 16 sections, 126 equations, 4 tables.

Table of Contents

  1. Introduction
  2. Conventions
  3. Single emission and iterations
  4. Non-iterative double-real emission contribution
  5. The integral of the strongly-ordered eikonal function ${\cal S}_{\omega}[G_{ij}]$
  6. The soft-subtracted, double-collinear contirbution
  7. The quantity $\overline{\cal S}_\omega[\Delta G_{ij} ] _{\rm fin,a_1}$
  8. Calculation of $\overline{{\cal S}}_{\omega}[G^{(0)}_{ij}]$
  9. The final results: analysis, implementation and checks
  10. Analytic expressions of the poles
  11. Implementation, checks and numerical results
  12. Conclusion
  13. Massless and single-massive angular integrals
  14. Double-massive angular integrals
  15. Two-loop double-massive integrals
  16. ...and 1 more sections