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Automation of antenna subtraction in colour space: gluonic processes

Xuan Chen, Thomas Gehrmann, Nigel Glover, Alexander Huss, Matteo Marcoli

TL;DR

This work introduces colourful antenna subtraction, a colour-space reformulation that automates NNLO infrared subtraction by deriving the virtual subtraction term from the pole structure of Colour-space amplitudes and then inferring the real-subtraction terms via a systematic correspondence between integrated and unintegrated antenna functions. The method is demonstrated in full colour for gluons-only three-jet production, with comprehensive tests showing correct pointwise IR cancellation and stable numerical behavior. Key outcomes include a detailed NNLO subtraction architecture (including double virtual, real-virtual, and double real terms) and the successful automation of their generation, paving the way for process-independent NNLO predictions. The study also highlights the necessity of including quarks to obtain realistic scale variation and uncovers the relatively small subleading colour effects in the gluons-only scenario, motivating future quark-inclusive extensions.

Abstract

We present the colourful antenna subtraction method, a reformulation of the antenna subtraction scheme for next-to-next-to-leading order (NNLO) calculations in QCD. The aim of this new approach is to achieve a general and process-independent construction of the subtraction infrastructure at NNLO. We rely on the predictability of the infrared singularity structure of one- and two-loop amplitudes in colour space to generate virtual subtraction terms and, subsequently, we define an automatable procedure to systematically infer the expression of the real subtraction terms, guided by the correspondence between unintegrated and integrated antenna functions. To demonstrate the applicability of the described approach, we compute the full colour NNLO correction to gluonic three-jet production $pp(gg)\to ggg$, in the gluons-only assumption.

Automation of antenna subtraction in colour space: gluonic processes

TL;DR

This work introduces colourful antenna subtraction, a colour-space reformulation that automates NNLO infrared subtraction by deriving the virtual subtraction term from the pole structure of Colour-space amplitudes and then inferring the real-subtraction terms via a systematic correspondence between integrated and unintegrated antenna functions. The method is demonstrated in full colour for gluons-only three-jet production, with comprehensive tests showing correct pointwise IR cancellation and stable numerical behavior. Key outcomes include a detailed NNLO subtraction architecture (including double virtual, real-virtual, and double real terms) and the successful automation of their generation, paving the way for process-independent NNLO predictions. The study also highlights the necessity of including quarks to obtain realistic scale variation and uncovers the relatively small subleading colour effects in the gluons-only scenario, motivating future quark-inclusive extensions.

Abstract

We present the colourful antenna subtraction method, a reformulation of the antenna subtraction scheme for next-to-next-to-leading order (NNLO) calculations in QCD. The aim of this new approach is to achieve a general and process-independent construction of the subtraction infrastructure at NNLO. We rely on the predictability of the infrared singularity structure of one- and two-loop amplitudes in colour space to generate virtual subtraction terms and, subsequently, we define an automatable procedure to systematically infer the expression of the real subtraction terms, guided by the correspondence between unintegrated and integrated antenna functions. To demonstrate the applicability of the described approach, we compute the full colour NNLO correction to gluonic three-jet production , in the gluons-only assumption.
Paper Structure (31 sections, 140 equations, 13 figures, 3 tables)

This paper contains 31 sections, 140 equations, 13 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Colour space
  3. Gluon amplitudes in colour space
  4. Gluon exchange in colour space
  5. Leading and subleading colour
  6. Colourful antenna subtraction at NLO
  7. IR singularity structure at one loop
  8. NLO mass factorization
  9. NLO virtual subtraction term
  10. NLO real subtraction term
  11. Colourful antenna subtraction at NNLO
  12. IR singularity structure at two loops
  13. NNLO mass factorization
  14. Double virtual mass factorization term
  15. Real virtual mass factorization term
  16. ...and 16 more sections

Figures (13)

  • Figure 1: Structure of colourful antenna subtraction at NNLO. Descendant red arrows represent the transition from an integrated quantity to its unintegrated counterpart via single insertion (single arrow), double iterated insertion (two disjoint arrows) or double simultaneous insertion (two connected arrows) of unresolved gluons. The definitions of each component are listed in Table \ref{['tab:equations']}.
  • Figure 2: Test of the real virtual subtraction term in single soft (left) and single collinear (right) limits for the leading colour (upper plots) and subleading colour (lower plots) contributions.
  • Figure 3: Test of the double real subtraction term in double soft (left) and soft and collinear (right) limits for the leading colour (upper plots) and subleading colour (lower plots) contributions.
  • Figure 4: Test of the double real subtraction term in triple collinear (left) and double collinear (right) limits at leading colour. The subleading colour contribution does not exhibit IR divergences in these limits.
  • Figure 5: Test of the double real subtraction term in single soft (left) and single collinear (right) limits for the leading colour (upper plots) and subleading colour (lower plots) contributions.
  • ...and 8 more figures