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.

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We derive the leading-power singular terms at three loops for both $$q_T$$ q T and 0-jettiness, $$\mathcal {T}_0$$ T 0 , for generic color-singlet processes. Our results provide the complete set of differential subtraction terms for $$q_T$$ q T and $$\mathcal {T}_0$$ T 0 subtractions at $$\hbox {N}^3\hbox {LO}$$ N 3 LO , which are an important ingredient for matching $$\hbox {N}^3\hbox {LO}$$ N 3 LO calculations with parton showers. We obtain the full three-loop structure of the relevant beam and soft functions, which are necessary ingredients for the resummation of $$q_T$$ q T and $$\mathcal {T}_0$$ T 0 at $$\hbox {N}^3\hbox {LL}'$$ N 3 LL ′ and $$\hbox {N}^4\hbox {LL}$$ N 4 LL order, and which constitute important building blocks in other contexts as well. The nonlogarithmic boundary coefficients of the beam functions, which contribute to the integrated subtraction terms, are not yet fully known at three loops. By exploiting consistency relations between different factorization limits, we derive results for the $$q_T$$ q T and $$\mathcal {T}_0$$ T 0 beam function coefficients at $$\hbox {N}^3\hbox {LO}$$ N 3 LO in the $$z\rightarrow 1$$ z → 1 threshold limit, and we also estimate the size of the unknown terms beyond threshold.

We consider Drell-Yan production pp → Z/γ * → + − with the simultaneous measurement of the Z-boson transverse momentum q T and 0-jettiness T 0 . Since both observables resolve the initial-state QCD radiation, the double-differential cross section in q T and T 0 contains Sudakov double logarithms of both q T /Q and T 0 /Q, where Q ∼ m Z is the dilepton invariant mass. We simultaneously resum the logarithms in q T and T 0 to next-tonext-to-leading logarithmic order (NNLL) matched to next-to-leading fixed order (NLO). Our results provide the first genuinely two-dimensional analytic Sudakov resummation for initial-state radiation. Integrating the resummed double-differential spectrum with an appropriate scale choice over either T 0 or q T recovers the corresponding single-differential resummation for the remaining variable. We discuss in detail the required effective field theory setups and their combination using two-dimensional resummation profile scales. We also introduce a new method to perform the q T resummation where the underlying resummation is carried out in impact-parameter space, but is consistently turned off depending on the momentum-space target value for q T . Our methods apply at any order and for any color-singlet production process, such that our results can be systematically extended when the relevant perturbative ingredients become available.1 Yet another case, which will not be relevant here, arises when different infrared-sensitive measurements are performed in different regions of phase space, which may require the resummation of nonglobal logarithms [40][41][42][43][44][45].

Gluon-induced processes such as Higgs production typically exhibit large perturbative corrections. These partially arise from large virtual corrections to the gluon form factor, which at timelike momentum transfer contains Sudakov logarithms evaluated at negative arguments ln 2 (−1) = −π 2 . It has been observed that resumming these terms in the timelike form factor leads to a much improved perturbative convergence for the total cross section. We discuss how to consistently incorporate the resummed form factor into the perturbative predictions for generic cross sections differential in the Born kinematics, including in particular the Higgs rapidity spectrum. We verify that this indeed improves the perturbative convergence, leading to smaller and more reliable perturbative uncertainties, and that this is not affected by cancellations between resummed and unresummed contributions. Combining both fixed-order and resummation uncertainties, the perturbative uncertainty for the total cross section at N 3 LO+N 3 LL ϕ is about a factor of two smaller than at N 3 LO. The perturbative uncertainty of the rapidity spectrum at NNLO+NNLL ϕ is similarly reduced compared to NNLO. We also study the analogous resummation for quark-induced processes, namely Higgs production through bottom quark annihilation and the Drell-Yan rapidity spectrum. For the former the resummation leads to a small improvement, while for the latter it confirms the already small uncertainties of the fixed-order predictions.