Abstract
We present the first results for the ${\cal O}(\alpha\alpha_s)$ corrections to the total partonic cross section of the process $q\bar q\to Z+X$, with the complete set of contributions, that include photonic and massive weak gauge boson effects. The results are relevant for the precise determination of the hadronic $Z$ boson production cross section. Virtual and real corrections are calculated analytically using the reduction to the master integrals and their evaluation through differential equations. Real corrections are dealt with using the reverse-unitarity method. They require the evaluation of a new set of two-loop master integrals, with up to three internal massive lines. In particular, three of them are expressed in terms of elliptic integrals. We verify the absence, at this perturbative order, of initial state mass singularities proportional to a weak massive virtual correction to the quark-gluon splitting.
Highlights
The production of an electrically neutral gauge boson at hadron colliders is one of the historical processes for our understanding of QCD
We present the first results for the OðααsÞ corrections to the total partonic cross section of the process qq → Z þ X, with the complete set of contributions, that include photonic and massive weak gauge boson effects
The case of the decay of the Z boson into a pair of high transverse momentum leptons is known as the Drell-Yan (DY) process, and it is important for the setting of several high-precision tests of the electroweak (EW) sector of the Standard Model (SM)
Summary
[20,21,22] for a discussion on specific examples), the evaluation of the mixed QCD-EW corrections has emerged as necessary for both the study of the gauge boson resonances and of the high-mass/-momentum tails of the kinematic distributions [23,24]. A realistic estimate of the theoretical uncertainties must account for several sources of ambiguity related to the recipes used in the matching of separate results for the QCD and EW contributions to the scattering amplitude For these reasons, an exact calculation of the full set of OðααsÞ corrections to the DY processes is desirable. We present the first results for the total inclusive cross section of production of an on-shell Z boson in the quark-antiquark partonic channel, including the complete set of QCD-EW corrections of OðααsÞ. The calculation we are presenting in this article is an important step toward the evaluation of the full set of QCDEW corrections to the hadronic cross section
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