Beyond cusp anomalous dimension from integrability

Abstract:We use the principle of maximal transcendentality and the universal nature of subleading infrared poles to extract the analytic value of the four-loop collinear anomalous dimension in planar N = 4 super-Yang-Mills theory from recent QCD results, obtaininĝ G (4) 0 = −300ζ 7 − 256ζ 2 ζ 5 − 384ζ 3 ζ 4 . This value agrees with a previous numerical result to within 0.2%. It also provides the Regge trajectory, threshold soft anomalous dimension and rapidity anomalous dimension through four loops.

Section: Jhep01(2018)075mentioning

confidence: 99%

Section: The Computationmentioning

confidence: 99%

The principle of maximal transcendentality and the four-loop collinear anomalous dimension

Dixon

2018

“…The virtual scaling function, B L (g), appearing in (1.2) explicitly depends on the twist L and it is less obvious that it remains unaffected by wrapping effects. The integral equation corresponding to B L (g) has been derived in [25], see also [26][27][28]. Interestingly, the solution to this equation may be related to the solution of the integral equation determining f (g).…”

Section: Jhep02(2010)050mentioning

confidence: 99%

From weak coupling to spinning strings

Freyhult

Rej

Zieme

2010

We identify the gauge theory dual of a spinning string of minimal energy with spins S 1 , S 2 on AdS 5 and charge J on S 5 . For this purpose we focus on a certain set of local operators with two different types of covariant derivatives acting on complex scalar fields. We analyse the corresponding nested Bethe equations for the ground states in the limit of large spins. The auxiliary Bethe roots form certain string configurations in the complex plane, which enable us to derive integral equations for the leading and subleading contribution to the anomalous dimension. The results can be expressed through the observables of the sl(2) sub-sector, i.e. the cusp anomaly f (g) and the virtual scaling function B L (g), rendering the strong-coupling analysis straightforward. Furthermore, we also study a particular sub-class of these operators specialising to a scaling limit with finite values of the second spin at weak and strong coupling.

“…[19][20][21][22][23][24], with very recent progress towards four loops [25][26][27][28][29][30][31][32][33] (even more is known in maximally supersymmetric Yang-Mills theory, see e.g. [34][35][36][37][38][39]). Despite this impressive progress, there remains several unresolved questions regarding the anomalous dimensions governing single-logarithmic corrections and their universality, some of which we address below.…”

Section: Introductionmentioning

confidence: 99%

Relating amplitude and PDF factorisation through Wilson-line geometries

Falcioni

Gardi

Milloy

2019

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