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Register a new userA Toolbox for $q_T$ and $0$-Jettiness Subtractions at N$^3$LO
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We derive the leading-power singular terms at three loops for both $q_T$ and 0-jettiness, $cal{T}_0$, for generic color-singlet processes. Our results provide the complete set of differential subtraction terms for $q_T$ and $cal{T}_0$ subtractions at N$^3$LO, which are an important ingredient for matching 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 $q_T$ and $cal{T}_0$ at N$^3$LL$$ and 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 $q_T$ and $cal{T}_0$ beam function coefficients at N$^3$LO in the $zto 1$ threshold limit, and we also estimate the size of the unknown terms beyond threshold.
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Kinematic selection cuts and isolation requirements are a necessity in experimental measurements for identifying prompt leptons and photons that originate from the hard-interaction process of interest. We analyze how such cuts affect the application of the $q_T$ and $N$-jettiness subtraction methods for fixed-order calculations. We consider both fixed-cone and smooth-cone isolation methods. We find that kinematic selection and isolation cuts both induce parametrically enhanced power corrections with considerably slower convergence compared to the standard power corrections that are already present in inclusive cross sections without additional cuts. Using analytic arguments at next-to-leading order we derive their general scaling behavior as a function of the subtraction cutoff. We also study their numerical impact for the case of gluon-fusion Higgs production in the $Htogammagamma$ decay mode and for $pptogammagamma$ direct diphoton production. We find that the relative enhancement of the additional cut-induced power corrections tends to be more severe for $q_T$, where it can reach an order of magnitude or more, depending on the choice of parameters and subtraction cutoffs. We discuss how all such cuts can be incorporated without causing additional power corrections by implementing the subtractions differentially rather than through a global slicing method. We also highlight the close relation of this formulation of the subtractions to the projection-to-Born method.
$N$-jettiness subtractions provide a general approach for performing fully-differential next-to-next-to-leading order (NNLO) calculations. Since they are based on the physical resolution variable $N$-jettiness, $mathcal{T}_N$, subleading power corrections in $tau=mathcal{T}_N/Q$, with $Q$ a hard interaction scale, can also be systematically computed. We study the structure of power corrections for $0$-jettiness, $mathcal{T}_0$, for the $ggto H$ process. Using the soft-collinear effective theory we analytically compute the leading power corrections $alpha_s tau lntau$ and $alpha_s^2 tau ln^3tau$ (finding partial agreement with a previous result in the literature), and perform a detailed numerical study of the power corrections in the $gg$, $gq$, and $qbar q$ channels. This includes a numerical extraction of the $alpha_stau$ and $alpha_s^2 tau ln^2tau$ corrections, and a study of the dependence on the $mathcal{T}_0$ definition. Including such power suppressed logarithms significantly reduces the size of missing power corrections, and hence improves the numerical efficiency of the subtraction method. Having a more detailed understanding of the power corrections for both $qbar q$ and $gg$ initiated processes also provides insight into their universality, and hence their behavior in more complicated processes where they have not yet been analytically calculated.
We compute the unpolarized quark and gluon transverse-momentum dependent fragmentation functions (TMDFFs) at next-to-next-to-next-to-leading order (N$^3$LO) in perturbative QCD. The calculation is based on a relation between the TMDFF and the limit of the semi-inclusive deep inelastic scattering cross section where all final-state radiation becomes collinear to the detected hadron. The required cross section is obtained by analytically continuing our recent computation of the Drell-Yan and Higgs boson production cross section at N$^3$LO expanded around the limit of all final-state radiation becoming collinear to one of the initial states. Our results agree with a recent independent calculation by Luo et al.
We compute the quark and gluon transverse momentum dependent parton distribution functions at next-to-next-to-next-to-leading order (N$^3$LO) in perturbative QCD. Our calculation is based on an expansion of the differential Higgs boson and Drell-Yan production cross sections about their collinear limit. This method allows us to employ cutting edge techniques for the computation of cross sections to extract the universal building blocks in question. The corresponding perturbative matching kernels for all channels are expressed in terms of simple harmonic polylogarithms up to weight five. As a byproduct, we confirm a previous computation of the soft function for transverse momentum factorization at N$^3$LO. Our results are the last missing ingredient to extend the $q_T$ subtraction methods to N$^3$LO and to obtain resummed $q_T$ spectra at N$^3$LL$^prime$ accuracy both for gluon as well as for quark initiated processes.
We present a $q_T$-resummed calculation of diphoton production at order N$^3$LL$^prime$+NNLO. To reach the primed level of accuracy we have implemented the recently published three-loop $mathcal{O}(alpha_s^3)$ virtual corrections in the $qbar{q}$ channel and the three-loop transverse momentum dependent beam functions and combined them with the existing infrastructure of CuTe-MCFM, a code performing resummation at order N$^3$LL. While the primed predictions are parametrically not more accurate, one typically observes that they are the dominant effect of the next order. We include in both the $qbar{q}$ and loop-induced $gg$ channel the hard contributions consistently together at order $alpha_s^3$ and find that the resummed $qbar{q}$ channel without matching stabilizes indeed. Due to large matching corrections and large contributions and uncertainties from the $gg$ channel, the overall improvements are small though. We furthermore study the effect of hybrid-cone photon isolation and hard-scale choice on our fully matched results to describe the ATLAS 8 TeV data and find that the hybrid-cone isolation destroys agreement at small $q_T$.
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