Drell-Yan $q_T$ Resummation of Fiducial Power Corrections at N${}^3$LL

Abstract

We consider Drell-Yan production $pp\to V^{\ast }X\to LX$ at small $q_T\ll Q$. Experimental measurements require fiducial cuts on the leptonic state $L$, which 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. We thus obtain predictions for the fiducial $q_T$ spectrum to N3LL and next-to-leading-power in $q_T/Q$. Matching to full NNLO (${\alpha }_s^2$), we find that the linear power corrections are indeed the dominant ones, and the remaining fixed-order corrections become almost negligible below $q_T\lesssim 40$ GeV. We also discuss the implications for more complicated observables, and provide predictions for the fiducial ${\varphi }^{\ast }$ spectrum at N3LL+NNLO. We find excellent agreement with ATLAS and CMS measurements of $q_T$ and ${\varphi }^{\ast }$. We also consider the $p_T^{\ell }$ spectrum. We show that it develops leptonic power corrections in $q_T/(Q-2p_T^{\ell })$, which diverge near the Jacobian peak $p_T^{\ell }\sim Q/2$ 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 $p_T^{\ell }$ spectrum around the Jacobian peak at N3LL+NNLO. Our method is based on performing a complete tensor decomposition for hadronic and leptonic tensors. 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 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. We also discuss the application to $q_T$ subtractions.

Comments: 81 pages + appendices, beautiful figures [abstract abridged]; v2: more beautiful figures (illustration of Born lepton projection, comparisons to normalized CMS spectra); v3: journal version (added figure with uncertainty breakdown)