Large-n contributions to the four-loop splitting functions in QCD

We study long-distance singularities governing different physical quantities involving massless partons in perturbative QCD by using factorisation in terms of Wilson-line correlators. By isolating the process-independent hard-collinear singularities from quark and gluon form factors, and identifying these with the ones governing the elastic limit of the perturbative Parton Distribution Functions (PDFs)δ(1 − x) in the large-x limit of DGLAP splitting functions -we extract the anomalous dimension controlling soft singularities of the PDFs, verifying that it admits Casimir scaling. We then perform an independent diagrammatic computation of the latter using its definition in terms of Wilson lines, confirming explicitly the above result through two loops. By comparing our eikonal PDF calculation to that of the eikonal form factor by Erdogan and Sterman and the classical computation of the closed parallelogram by Korchemsky and Korchemskaya, a consistent picture emerges whereby all singularities emerge in diagrammatic configurations localised at the cusps or along lightlike lines, but where distinct contributions to the anomalous dimensions are associated with finite (closed) lightlike segments as compared to infinite (open) ones. Both are relevant for resumming large logarithms in physical quantities, notably the anomalous dimension controlling Drell-Yan or Higgs production near threshold on the one hand, and the gluon Regge trajectory controlling the high-energy limit of partonic scattering on the other. Isolating hard-collinear singularitiesThe contribution of Γ J in eq. (2.18) is associated to the soft singularities of J i , which cancel in the ratio of J i and J i eq. (2.9). It is therefore convenient to focus on the poles of pure hard-collinear origin, defined aswhere J i | pole means only the poles of the jet function. We extract the function J i/J for i = q and i = g from the form factor of the quark and of the gluon, respectively, thus providing the process-independent components containing the purely collinear singularities associated with massless external partons. In order to determine J i/J , we isolate the pole part of the jet function J i , by replacing in eq. (2.18) the function G(1, α s , ǫ) with γ G , according to the

Section: Definitionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Relating amplitude and PDF factorisation through Wilson-line geometries

Falcioni

Gardi

Milloy

2019

“…The four-loop cusp anomalous is also known numerically[51,52], and largely analytically[53][54][55][56][57][58][59][60].…”

mentioning

confidence: 99%

Renormalization and matching for the Collins-Soper kernel from lattice QCD

Ebert

Stewart

Zhao

2020

The Collins-Soper kernel, which governs the energy evolution of transversemomentum dependent parton distribution functions (TMDPDFs), is required to accurately predict Drell-Yan like processes at small transverse momentum, and is a key ingredient for extracting TMDPDFs from experiment. Earlier we proposed a method to calculate this kernel from ratios of the so-called quasi-TMDPDFs determined with lattice QCD, which are defined as hadronic matrix elements of staple-shaped Euclidean Wilson line operators. Here we provide the one-loop renormalization of these operators in a regularizationindependent momentum subtraction (RI /MOM) scheme, as well as the conversion factor from the RI /MOM-renormalized quasi-TMDPDF to the MS scheme. We also propose a procedure for calculating the Collins-Soper kernel directly from position space correlators, which simplifies the lattice determination.

“…[×] [12,13] [ 14] [×] [15] [15] [15] ( [17] [×] [16,18] * [19,20] [17] [12,16] [×] Table 1. Four-loop contributions to Γ cusp (φ) and its limits in QCD as well as the HQET field anomalous dimension γ h .…”

mentioning

confidence: 99%

Matter dependence of the four-loop QCD cusp anomalous dimension: from small angles to all angles

Brüser

Grozin

Henn

et al. 2019

We compute the fermionic contributions to the cusp anomalous dimension in QCD at four loops as an expansion for small cusp angle. As a byproduct we also obtain the respective terms of the four-loop HQET wave function anomalous dimension. Our new results at small angles provide stringent tests of a recent conjecture for the exact angle dependence of the matter terms in the four-loop cusp anomalous dimension. We find that the conjecture does not hold for two of the seven fermionic color structures, but passes all tests for the remaining terms. This provides strong support for the validity of the corresponding conjectured expressions with full angle dependence. Taking the limit of large Minkowskian angle, we extract novel analytic results for certain terms of the light-like cusp anomalous dimension. They agree with the known numerical results. Finally, we study the anti-parallel lines limit of the cusp anomalous dimension. In a conformal theory, the latter is proportional to the static quark-antiquark potential. We use the new four-loop results to determine parts of the conformal anomaly term.