Drell-Yan $q_T$ spectrum and its uncertainty at N$^3$LL$'$and approximate N$^4$LL

Billis, Georgios; Ebert, Markus A.; Tackmann, Frank; Michel, Johannes K. L.

Preprint

PUBDB-2023-03807

Drell-Yan $q_T$ spectrum and its uncertainty at N$^3$LL$'$and approximate N$^4$LL

Billis, G. ; Ebert, M. A. ; Tackmann, F.DESY* ; Michel, J. K. L. (Corresponding author)

2024

[10.3204/PUBDB-2023-03807]

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Please use a persistent id in citations: doi:10.3204/PUBDB-2023-03807

Report No.: DESY-23-081; arXiv:2411.16004

Abstract: We consider Drell-Yan production $pp\to V^* X \to L X$ at small$q_T \ll Q$, where $q_T$ and $Q$ arethe 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 linearpower corrections.We thus obtain predictions for the fiducial $q_T$ spectrum to N$^3$LL andnext-to-leading-power in $q_T/Q$.Matching to full NNLO ($\alpha_s^2$), we find that the linear powercorrections are indeed the dominant ones, and once included by factorization,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 $\phi^*$ spectrum at N$^3$LL$+$NNLO.We find excellent agreement with ATLAS and CMS measurements of $q_T$ and $\phi^*$.We also consider the $p_T^\ell$ spectrum. We show that it developsleptonic power corrections in $q_T/(Q - 2p_T^\ell)$, which diverge near the Jacobianpeak $p_T^\ell \sim Q/2$ 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 N$^3$LL$+$NNLO.%Our method is based on performing a complete tensor decomposition for hadronicand leptonic tensors. We show that in practice this is equivalent tooften-used recoil prescriptions, for which our results now provide rigorous, formaljustification.Our tensor decomposition yields nine Lorentz-scalar hadronic structure functions, whichfor $Z/\gamma^* \to \ell\ell$ or $W\to\ell\nu$ directly map ontothe 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-likeangular decomposition even when including QED final-state radiation.Finally, we also discuss the application to $q_T$ subtractions. Including theunambiguously predicted fiducial power corrections significantly improves theirperformance, and in particular makes them applicable near kinematic edgeswhere they otherwise break down due to large leptonic power corrections.

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