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Diffractive deep inelastic scattering in the dipole picture: the $q\bar{q}g$ contribution in exact kinematics

Abhiram Kaushik, Heikki Mäntysaari, Jani Penttala

TL;DR

This work addresses the diffractive DIS problem in the dipole picture by computing the finite $|q\bar{q} g\rangle$ contribution at NLO in exact eikonal kinematics, formulating it within the LCWF framework and Wilson-line scattering. The authors implement a numerical evaluation of the three-parton phase space for coherent diffraction using a simple GBW dipole amplitude and compare the exact NLO-trip result to approximations based on soft gluon and soft quark emissions, as well as to the Munier–Shoshi limit. They find that the traditional soft-gluon (Wüsthoff/GBW) approximation underestimates the full NLO-trip cross section by about a factor of three in kinematics relevant to the EIC/LHeC, while the soft-quark contribution is comparably large and non-negligible. When combined, soft quark and soft gluon contributions provide a reasonable approximation to the full NLO-trip in a mid-range of $\beta$ (roughly $0.3 \lesssim \beta \lesssim 0.6$) at high $Q^2$, but deviations persist, and the emission-after-shockwave piece is essential to reach the Munier–Shoshi limit. The results underscore the importance of including full NLO corrections for diffractive structure functions in future EIC phenomenology and provide groundwork and public code toward complete, nucleus- and proton-level NLO predictions.

Abstract

We compute the $q\bar{q}g$ contribution to the diffractive structure functions in high-energy deep inelastic scattering. The obtained result corresponds to a finite part of the next-to-leading-order contribution to the diffractive cross section. Previous phenomenological applications have included this contribution only in the high-$Q^2$ or high-$M_X^2$ limits in the case of a soft gluon, and we numerically demonstrate that these existing estimates do not provide a good approximation for the full $q\bar{q}g$ contribution. Furthermore, we demonstrate that in addition to the soft gluon contribution, there is an equally important soft quark contribution to the diffractive structure functions at high $Q^2$.

Diffractive deep inelastic scattering in the dipole picture: the $q\bar{q}g$ contribution in exact kinematics

TL;DR

This work addresses the diffractive DIS problem in the dipole picture by computing the finite contribution at NLO in exact eikonal kinematics, formulating it within the LCWF framework and Wilson-line scattering. The authors implement a numerical evaluation of the three-parton phase space for coherent diffraction using a simple GBW dipole amplitude and compare the exact NLO-trip result to approximations based on soft gluon and soft quark emissions, as well as to the Munier–Shoshi limit. They find that the traditional soft-gluon (Wüsthoff/GBW) approximation underestimates the full NLO-trip cross section by about a factor of three in kinematics relevant to the EIC/LHeC, while the soft-quark contribution is comparably large and non-negligible. When combined, soft quark and soft gluon contributions provide a reasonable approximation to the full NLO-trip in a mid-range of (roughly ) at high , but deviations persist, and the emission-after-shockwave piece is essential to reach the Munier–Shoshi limit. The results underscore the importance of including full NLO corrections for diffractive structure functions in future EIC phenomenology and provide groundwork and public code toward complete, nucleus- and proton-level NLO predictions.

Abstract

We compute the contribution to the diffractive structure functions in high-energy deep inelastic scattering. The obtained result corresponds to a finite part of the next-to-leading-order contribution to the diffractive cross section. Previous phenomenological applications have included this contribution only in the high- or high- limits in the case of a soft gluon, and we numerically demonstrate that these existing estimates do not provide a good approximation for the full contribution. Furthermore, we demonstrate that in addition to the soft gluon contribution, there is an equally important soft quark contribution to the diffractive structure functions at high .

Paper Structure

This paper contains 13 sections, 67 equations, 9 figures.

Table of Contents

  1. Introduction
  2. Production of $q\overline{q}g$ in exact kinematics
  3. Production of $q\bar{q}g$ in approximative kinematics
  4. Soft gluon at high $Q^2$
  5. Soft quark at high $Q^2$
  6. Amplitude for $q\bar{q}g$ production with a soft quark
  7. Cross section for diffractive $q\bar{q}g$ production with a soft quark
  8. Soft quark contribution to diffractive SIDIS and the structure function
  9. Large $M_X^2$ limit
  10. Numerical results
  11. Conclusions
  12. Aligned jet limit beyond the leading $\log Q^2$
  13. Recovering the large-$M_X^2$ limit

Figures (9)

  • Figure 1: Contributions to the NLO-trip result for the diffractive cross section.
  • Figure 2: Soft quark contribution to the diffractive cross section in the case where the quark emits the gluon before (left) or after (right) the shockwave. The quark is far away from the $\bar{q} g$ system.
  • Figure 3: Soft quark contribution to the diffractive cross section in the case where the antiquark emits the gluon before (left) or after (right) the shockwave. The quark is far away from the $\bar{q} g$ system.
  • Figure 4: Contribution to the diffractive structure function from the $q\bar{q}g$ production channel.
  • Figure 5: Relative accuracy of estimating the NLO-trip contribution by the soft quark and soft gluon contributions.
  • ...and 4 more figures