Next-to-leading power corrections to V+1 jet production in N -jettiness subtraction

Abstract

We discuss the subleading power corrections to one-jet production processes in N -jettiness subtraction using vector-boson plus jet production as an example. We analytically derive the next-to-leading power leading logarithmic corrections (NLP-LL) through O(α S ) in perturbative QCD, and outline the calculation of the next-to-leading logarithmic corrections (NLP-NLL). Our result is differential in the jet transverse momentum and rapidity, and in the vector boson momentum squared and rapidity. We present simple formulae that separate the NLP corrections into universal factors valid for any one-jet cross section and process-dependent matrix-element corrections. We discuss in detail features of the NLP corrections such as the process independence of the leading-logarithmic result that occurs due to the factorization of matrix elements in the subleading soft limit, the occurrence of poles in the non-hemisphere soft function at NLP and the cancellation of potential T 1 /Q corrections to the N -jettiness factorization theorem. We validate our analytic result by comparing them to numerically-fitted coefficients, finding good agreement for both the inclusive and the differential cross sections.arXiv:1907.12213v2 [hep-ph] 6 Aug 2019 separate the power corrections into process-independent terms valid for any one-jet production process and process-dependent matrix element correction factors. Important aspects of our results are summarized below.• We make use of the expansion by regions [32,33] to perform the computation of the cross section. In particular, we split the phase space into two beam regions, a jet region and a soft region.• We show that all NLP-LL corrections at NLO arise from the emission of soft partons, as in the case of color-singlet production [1, 2], and show how to obtain such subleading soft corrections by making use of the subleading soft theorem [34]. This allows us to write the NLP-LL result in a universal form valid for all one-jet processes.• We show that the non-hemisphere soft contributions defined in [35], which are finite at leading power, contribute to poles when extended to next-to-leading power. These poles are necessary for the consistency of the result at NLP.• We demonstrate the cancellation of potential power corrections suppressed only by T /Q, where T is the one-jettiness event shape variable and Q is a generic hard scale.Our paper is organized as follows. In Section II we discuss the Born-level process for V + j production and introduce the notation used in the remainder of the manuscript. We discuss our strategy for the computation of the NLP corrections in Section III, and illustrate the separation of the phase space into different regions. In Section IV, we write down a general expression for the phase space that is valid in every region, separating the case where the two final-state partons are measured as two separate jets from the case where they are part of the same jet.We then proceed to expand the phase space in each region, listing all the relevant expansion coefficients in t...

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].…”

Impact of isolation and fiducial cuts on qT and N-jettiness subtractions

“…(5.5) is the calculation of the reference cross section σ(X (0) ) using differential τ subtractions. Since it involves the same reference measurement X (0) everywhere, the difference dσ(X (0) ) − dσ sub (X (0) ) does not involve any cut-induced power corrections, hence reducing the problem of power corrections to the normal and well-studied case, and for which the power corrections can be systematically calculated if necessary [70][71][72][73][74][75][76]. In particular, if the implementation of the differential τ subtractions proves too difficult in practice, this contribution could be calculated with the slicing approach (see below).…”

“…In particular, for inclusive Higgs and Drell-Yan production the leading-logarithmic (LL) corrections at NNLO at next-to-leading power (NLP) are known for T 0 [70][71][72]. At NLO, the full NLP corrections are known for T 0 [73,74], q T [75], and T 1 [76].…”

Single-jet inclusive rates with exact color at $$ \mathcal{O} $$ ($$ {\alpha}_s^4 $$)

“…The calculation of a cross section at NNLO in QCD requires a method to handle infrared (IR) singularities occurring in contributions of different final state multiplicities. Apart from the already mentioned antenna subtraction scheme, there are several other methods currently being developed for this purpose: the CoLoRfulNNLO scheme [29][30][31][32][33], q T -slicing [34,35], N -jettiness slicing [36][37][38][39][40][41][42][43], sector-improved residue subtraction [44][45][46] and its spin-off called nested soft-collinear subtraction scheme [47][48][49], the projection-to-Born method [50,51], local analytic sector subtraction [52] and geometric IR subtraction [53]. The results that we report in section 3 have been obtained with our implementation of the sector-improved residue subtraction in the C++ library Stripper (SecToR Improved Phase sPacE for real Radiation).…”