Drell-Yan qT resummation of fiducial power corrections at N3LL

Abstract

We consider Drell-Yan production pp → V*X → LX at small qT ≪ Q, where qT and Q are the total transverse momentum and invariant mass of the leptonic final state L. Experimental measurements require fiducial cuts on L, which in general introduce enhanced, linear power corrections in qT/Q. We show that they can be unambiguously predicted from factorization, and resummed to the same order as the leading-power contribution. For the fiducial qT spectrum, they constitute the complete linear power corrections. We thus obtain predictions for the fiducial qT spectrum to N3LL and next-to-leading-power in qT/Q. Matching to full NNLO ($$ {\alpha}_s^2 $$ α s 2 ), we find that the linear power corrections are indeed the dominant ones, and once included by factorization, the remaining fixed-order corrections become almost negligible below qT ≲ 40 GeV. We also discuss the implications for more complicated observables, and provide predictions for the fiducial ϕ* spectrum at N3LL+NNLO. We find excellent agreement with ATLAS and CMS measurements of qT and ϕ*. We also consider the $$ {p}_T^{\mathrm{\ell}} $$ p T ℓ spectrum. We show that it develops leptonic power corrections in qT/(Q − 2$$ {p}_T^{\mathrm{\ell}} $$ p T ℓ ), which diverge near the Jacobian peak $$ {p}_T^{\mathrm{\ell}} $$ p T ℓ ∼ Q/2 and must be kept to all powers to obtain a meaningful result there. Doing so, we obtain for the first time an analytically resummed result for the $$ {p}_T^{\mathrm{\ell}} $$ p T ℓ spectrum around the Jacobian peak at N3LL+NNLO. Our method is based on performing a complete tensor decomposition for hadronic and leptonic tensors. We show that in practice this is equivalent to often-used recoil prescriptions, for which our results now provide rigorous, formal justification. Our tensor decomposition yields nine Lorentz-scalar hadronic structure functions, which for Z/γ* → ℓℓ or W → ℓν directly map onto the commonly used angular coefficients, but also holds for arbitrary leptonic final states. In particular, for suitably defined Born-projected leptons it still yields a LO-like angular decomposition even when including QED final-state radiation. Finally, we also discuss the application to qT subtractions. Including the unambiguously predicted fiducial power corrections significantly improves their performance, and in particular makes them applicable near kinematic edges where they otherwise break down due to large leptonic power corrections.

The qT and ∆ϕ spectra in W and Z production at the LHC at N3LL′+N2LO

“…[96,[103][104][105][106][107][108][109], whilst the authors in refs. [91,92,[110][111][112] have accomplished N 3 LL very recently. Thanks to the developments in fixed-order perturbative calculations, the cusp anomalous dimension has achieved fourloop accuracy [113] and the fixed-order ingredients (including the non-singlet quark form factor [114], soft [102,115] and beam functions [116][117][118]) at N 3 LO are available now.…”

“…Very recently, a systematic classification has been carried out in ref. [112] as to the leptonic power corrections.…”

Unpolarized quark and gluon TMD PDFs and FFs at N3LO

“…Using rapidity regulators, direct computation of TMD PDFs and FFs at NNLO have since become available [23][24][25][26][27][28]. The progress in NNLO calculation for TMD distributions have allowed many cutting-edge calculations for phenomenology, including fixed-order calculation at NNLO and beyond [29][30][31][32][33][34] and resummation for large logarithms at small q T at unprecedented N 3 LL accuracy [34][35][36][37][38][39][40][41]. We also note that perturbative calculation for TMD quantities suitable for lattice calculation [42][43][44][45] has also made important progress recently [46].…”

Drell-Yan angular lepton distributions at small x from TMD factorization.

“…As to the rest of angular coefficients, more details about quark TMDs and at least some guesses about quark-quark-gluon TMDs are necessary to make quantitative predictions. Also, one needs to take into account fiducial power corrections, see recent paper [19] for a review. This bring us to the second question, namely how much we can learn about proton structure from Z-boson experiments.…”

“…These cuts introduce linear power corrections in q ⊥ /Q, see the discussion in ref. [19]. In this paper we do not consider fiducial power corrections.…”