Master integrals for the mixed QCD-QED corrections to the Drell-Yan production of a massive lepton pair
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Springer
Received: May 12, Revised: September 10, Accepted: October 8, Published: November 20,
2020 2020 2020 2020
Syed Mehedi Hasana and Ulrich Schubertb a
INFN — Sezione di Pavia, Via Agostino Bassi 6, 27100 Pavia, Italy b Department of Physics, University at Buffalo, The State University of New York, Buffalo 14260, U.S.A.
E-mail: [email protected], [email protected] Abstract: We showcase the calculation of the master integrals needed for the two loop mixed QCD-QED virtual corrections to the neutral current Drell-Yan process (q q¯ → l+ l− ). After establishing a basis of 51 master integrals, we cast the latter into canonical form by using the Magnus algorithm. The dependence on the lepton mass is then expanded such that potentially large logarithmic contributions are kept. After determining all boundary constants, we give the coefficients of the Taylor series around four space-time dimensions in terms of generalized polylogarithms up to weight four. Keywords: Scattering Amplitudes, Perturbative QCD ArXiv ePrint: 2004.14908
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP11(2020)107
JHEP11(2020)107
Master integrals for the mixed QCD-QED corrections to the Drell-Yan production of a massive lepton pair
Contents 1
2 Notation
3
3 Differential equations
4
4 -factorized form
5
5 Solution 5.1 Boundary conditions 5.2 Consistency checks
8 9 10
6 Conclusions
11
1
Introduction
The Drell-Yan (DY) processes, depicted at leading order in figure 1, have big cross sections and clean experimental signatures, and thus are one of the best-studied processes at the LHC. In particular they can be used to determine important parameters in the electroweak (EW) sector like the weak mixing angle and W boson mass [1, 2]. The DY processes are also playing an important role as standard candles for the LHC in the form of luminosity measurements and detector calibrations. Furthermore the abundance of clean data make the DY processes a perfect place to determine parton distribution functions and search for Beyond Standard Model (BSM) physics. All these applications rely on a precise theoretical description of the DY processes, making it crucial for the physics program at the LHC. The perturbative corrections to the Drell-Yan processes can be divided into two classes. The pure QCD corrections only occur in the initial state of the DY processes, due to the colorless nature of the leptonic final state. These corrections are known differentially up to next-to-next-to leading order (NNLO) [3, 4] and inclusively at next-to-next-to-nextto-leading order (NNNLO) [5]. In contrast the EW corrections can involve both the quarkonic initial and leptonic final state. These corrections have been computed at nextto-leading order (NLO) [6–17] and there is an ongoing effort to extend the computation to NNLO [18–21]. Starting at NNLO the EW and QCD corrections start to mix and are currently assumed to be the largest unknown correction in the high energy region [22]. These mixed corrections can be furt
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