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Two-loop mixed QCD-EW corrections to neutral current Drell-Yan

Tommaso Armadillo, Roberto Bonciani, Simone Devoto, Narayan Rana, Alessandro Vicini

TL;DR

This work delivers the exact two-loop mixed QCD-EW virtual corrections to neutral current Drell-Yan, computing the UV-renormalised, IR-subtracted amplitude at ${\cal O}(\alpha\alpha_s)$ for $q\bar{q}\to\ell^+\ell^-$. It reduces the relevant Feynman integrals to a large master-integral basis (204 MIs) and handles two-mass cases with a combination of analytic and semi-analytic methods, including a semi-analytical solution for five two-mass MIs in the presence of complex gauge-boson masses. The finite remainder, together with a UV-renormalised hard function $H^{(1,1)}$, is provided in ancillary files, accompanied by a numerical grid suitable for phenomenological use across the NC DY phase space. The results are obtained within the $q_T$-subtraction framework and rely on a careful treatment of infrared singularities, the complex-mass scheme, and a consistent treatment of $\gamma_5$ in dimensional regularization. The study advances the precision frontier for Drell-Yan predictions at colliders and lays groundwork for automation and extension of two-loop mixed radiative corrections in collider phenomenology.

Abstract

We present the two-loop mixed strong-electroweak virtual corrections to the neutral current Drell-Yan process and we provide, in ancillary files, the explicit formulae of the infrared-subtracted finite remainder. The final state collinear singularities are regularised by the lepton mass. The evaluation of all the relevant Feynman integrals, including those with up to two internal massive lines, has been worked out relying on analytical and semi-analytical techniques, in the case of complex-valued masses.

Two-loop mixed QCD-EW corrections to neutral current Drell-Yan

TL;DR

This work delivers the exact two-loop mixed QCD-EW virtual corrections to neutral current Drell-Yan, computing the UV-renormalised, IR-subtracted amplitude at for . It reduces the relevant Feynman integrals to a large master-integral basis (204 MIs) and handles two-mass cases with a combination of analytic and semi-analytic methods, including a semi-analytical solution for five two-mass MIs in the presence of complex gauge-boson masses. The finite remainder, together with a UV-renormalised hard function , is provided in ancillary files, accompanied by a numerical grid suitable for phenomenological use across the NC DY phase space. The results are obtained within the -subtraction framework and rely on a careful treatment of infrared singularities, the complex-mass scheme, and a consistent treatment of in dimensional regularization. The study advances the precision frontier for Drell-Yan predictions at colliders and lays groundwork for automation and extension of two-loop mixed radiative corrections in collider phenomenology.

Abstract

We present the two-loop mixed strong-electroweak virtual corrections to the neutral current Drell-Yan process and we provide, in ancillary files, the explicit formulae of the infrared-subtracted finite remainder. The final state collinear singularities are regularised by the lepton mass. The evaluation of all the relevant Feynman integrals, including those with up to two internal massive lines, has been worked out relying on analytical and semi-analytical techniques, in the case of complex-valued masses.
Paper Structure (18 sections, 54 equations, 5 figures)

This paper contains 18 sections, 54 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Framework of the Calculation
  3. The process
  4. Treatment of g5 in Dimensional Regularisation
  5. Ultraviolet renormalisation
  6. Charge renormalisation
  7. Renormalisation of the gauge boson propagators
  8. Checks
  9. The UV-renormalised unsubtracted amplitude
  10. Generation of the full amplitude and evaluation of the interference terms
  11. Integral families and the representation of the result in terms of MIs
  12. Infrared Singularities and Universal Pole Structure
  13. Results
  14. The UV-renormalised IR-subtracted hard function
  15. Semi-analytical solution of MIs via series expansion
  16. ...and 3 more sections

Figures (5)

  • Figure 1: Sample Feynman diagrams of two-loop corrections and associated two-loop counterterms.
  • Figure 2: Sample Feynman diagrams of factorisable corrections, including one-loop counterterm corrections.
  • Figure 3: Sample Feynman diagrams contributing to the $\gamma Z$ and to the $WW$ subsets.
  • Figure 4: Real (left column) and imaginary (right column) parts of the $\epsilon^0$ coefficient of the two-mass MIs labeled 32 to 36 in ref. Bonciani:2016ypc.
  • Figure 5: The contributions from all the vertex and box Feynman diagrams to the ${\cal O}(\alpha\alpha_s)~$ correction to the finite hard function, in two different invariant mass ranges, as a function of $\sqrt{s}$ and $\cos\theta$.