Drell-Yan qT resummation of fiducial power corrections at N3LL

We consider Drell-Yan production pp -> (VX)-X-* -> LX at small q(T) << Q, where q(T) 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 q(T)/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 q(T) spectrum, they constitute the complete linear power corrections. We thus obtain predictions for the fiducial q(T) spectrum to (NLL)-L-3 and next-to-leading-power in q(T)/Q. Matching to full NNLO (alpha s2), 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 q(T) less than or similar to 40 GeV. We also discuss the implications for more complicated observables, and provide predictions for the fiducial phi (*) spectrum at (NLL)-L-3+NNLO. We find excellent agreement with ATLAS and CMS measurements of q(T) and phi (*). We also consider the pTl spectrum. We show that it develops leptonic power corrections in q(T)/(Q - 2pTl), which diverge near the Jacobian peak pTl similar to 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 pTl spectrum around the Jacobian peak at (NLL)-L-3+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/gamma (*) -> ll or W -> l nu 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 q(T) 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.

Automated summary

The study shows that linear power corrections are dominant for the fiducial q(T) spectrum and can be predicted and accumulated to the same order as the leading power contribution through factorization. The complete tensor decomposition method provides a rigorous theoretical basis for recoil schemes and accurate angular decomposition for complex cases such as Z/gamma (*) -> ll or W -> l nu.