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Power corrections to the production of a prompt photon in association with a jet in the $N$-jettiness slicing scheme at NLO QCD

Prem Agarwal, Kirill Melnikov, Ivan Pedron

TL;DR

This work derives the first subleading power corrections in the one-jettiness variable $\mathcal{T}_1$ for prompt-photon plus jet production at NLO QCD in the $q\bar q$ channel, using a realistic $k_\perp$ jet algorithm. The authors extend a previously developed framework to final-state jets, performing a detailed soft and collinear expansion and carefully treating clustered vs non-clustered emissions, with explicit momentum mappings for the collinear $\mathfrak{m}||\mathfrak{n}$ case. The final result expresses the NLP cross section as a sum of clustered, non-clustered, and soft-recoil contributions, with $1/\epsilon$ poles canceled among sectors and logarithmic plus observable-derivative structures surviving, which are numerically validated against exact matrix elements. The findings improve the precision of slicing approaches at NLO for processes with jets and pave the way for extensions to more complex final states and higher orders, enhancing the accuracy of collider predictions in the presence of jet-based resolution variables.

Abstract

We compute the next-to-leading-power corrections in the $N$-jettiness variable to the production of a prompt photon and a jet at next-to-leading order in perturbative QCD in the $q \bar q$ annihilation channel. We employ the $k_\perp$ jet algorithm and assume that the $N$-jettiness value divided by the jet transverse momentum is the smallest parameter in the problem; in particular it should be small compared to the jet radius $R$.

Power corrections to the production of a prompt photon in association with a jet in the $N$-jettiness slicing scheme at NLO QCD

TL;DR

This work derives the first subleading power corrections in the one-jettiness variable for prompt-photon plus jet production at NLO QCD in the channel, using a realistic jet algorithm. The authors extend a previously developed framework to final-state jets, performing a detailed soft and collinear expansion and carefully treating clustered vs non-clustered emissions, with explicit momentum mappings for the collinear case. The final result expresses the NLP cross section as a sum of clustered, non-clustered, and soft-recoil contributions, with poles canceled among sectors and logarithmic plus observable-derivative structures surviving, which are numerically validated against exact matrix elements. The findings improve the precision of slicing approaches at NLO for processes with jets and pave the way for extensions to more complex final states and higher orders, enhancing the accuracy of collider predictions in the presence of jet-based resolution variables.

Abstract

We compute the next-to-leading-power corrections in the -jettiness variable to the production of a prompt photon and a jet at next-to-leading order in perturbative QCD in the annihilation channel. We employ the jet algorithm and assume that the -jettiness value divided by the jet transverse momentum is the smallest parameter in the problem; in particular it should be small compared to the jet radius .

Paper Structure

This paper contains 22 sections, 158 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. General remarks
  3. The collinear case $\mathfrak{n} || a$
  4. The collinear case $\mathfrak{n} || b$
  5. The collinear case $\mathfrak{m} || \mathfrak{n}$
  6. The soft case $E_\mathfrak{n} \to 0$
  7. Computational strategy
  8. Power corrections to the $\gamma$+jet production in the $q \bar{q} \to g \gamma$ channel
  9. Leading order
  10. The soft contribution
  11. Modification of the angular distance in the jet algorithm
  12. Remaining contributions
  13. The clustered case
  14. The non-clustered case.
  15. The case $\mathfrak{n} || a$
  16. ...and 7 more sections

Figures (1)

  • Figure 1: The comparison of the "exact" cross section $\sigma_{\rm num}$ (c.f. Eq. (\ref{['eq3.110']}) and its various approximations obtained by different truncations of the expansion in small $N$-jettiness. The analytic approximations including the leading-power (LP) contributions, the LP + leading-logarithmic (LL) next-to-leading-power (NLP) correction, and the LP + full NLP corrections. The three curves in the plot become indistinguishable for $\tau < 10^{-3}$.