N3LO corrections to jet production in deep inelastic scattering using the Projection-to-Born method

Abstract

Computations of higher-order QCD corrections for processes with exclusive final states require a subtraction method for real-radiation contributions. We present the first-ever generalisation of a subtraction method for third-order (N 3 LO) QCD corrections. The Projection-to-Born method is used to combine inclusive N 3 LO coefficient functions with an exclusive second-order (NNLO) calculation for a final state with an extra jet. The input requirements, advantages, and potential applications of the method are discussed, and validations at lower orders are performed. As a test case, we compute the N 3 LO corrections to kinematical distributions and production rates for single-jet production in deep inelastic scattering in the laboratory frame, and compare them with data from the ZEUS experiment at HERA. The corrections are small in the central rapidity region, where they stabilize the predictions to sub per-cent level. The corrections increase substantially towards forward rapidity where large logarithmic effects are expected, thereby yielding an improved description of the data in this region.

Numerical Loop-Tree Duality: contour deformation and subtraction

“…Traditionally, the computation of these two components is performed using very different approaches and the deep connection relating their degenerate infrared degrees of freedom is only realised through dimensional regularisation [3][4][5] at the very end of the computation. Indeed, real-emission contributions are typically computed numerically through the introduction of subtraction counterterms [6][7][8][9][10][11][12][13][14][15][16][17] or some form of phase-space slicing [18][19][20][21][22][23][24][25], whereas the evaluation of their virtual counterparts is mostly carried out purely analytically, thus realising the cancellation of infrared singularities at the integrated level. A notable exception is the computation of inclusive Higgs production at N 3 LO accuracy [26], which was performed through reverse-unitarity [27,28].…”

A subtraction scheme for massive QED

“…First steps towards extending universal schemes beyond NNLO have been made in QCD [30]. The simplicity of FKS 2 suggests that this paradigm is a promising starting point for further extension to N 3 LO in massive QED, provided that all matrix elements are known.…”

“…n (ξ c ) = dΦ n M (3) n +Ê(ξ c )M(2) The auxiliary integrals I(1) , J and K cancel as do the explicit 1/ǫ poles in the first line. The other contributions in(30) are also separately finite. Thus, after setting d = 4 the explicit expressions of the separately finite parts of (30) are given by(31) with dσ…”

Second-order QCD corrections to event shape distributions in deep inelastic scattering

“…It combines the contributions from four-parton production at tree-level [31][32][33], three-parton production at one loop [34][35][36][37] and twoparton production at two loops [38][39][40][41], using the antenna subtraction method [42][43][44] to isolate infrared singular terms from the different contributions, which are then combined to yield numerically finite predictions for arbitrary infrared-safe observables constructed from the parton momenta. Besides for di-jet production at NNLO, the same ingredients and setup have been used previously in the computation of N 3 LO corrections to single jet production in DIS [45], in extractions of the strong coupling constant from DIS jet data [46,47], and in studies of diffractive di-jet production [48]. The calculations have also been extended to jet production in charged current DIS [49,50] at the same perturbative orders.…”

“…Event selection cuts on the lepton variables and on h E h are applied according to the H1 [23] and ZEUS [24] analyses, and events are then classified into the different kinematical bins of Tables 1 and 2. The total hadronic DIS cross section for each kinematical bin (required for the normalization of the event shape distributions and mean values) is obtained to NNLO from NNLOJET, based on the one-jet calculation to this order [45]. Central renormalization and factorization scales are used for the normalization.…”