Analytic Form of the Three-loop Four-gluon Scattering Amplitudes in Yang-Mills Theory

We compute the three-loop leading-colour corrections to the Yang-Mills Regge trajectory and gluon impact factor. Conjecturing that, in analogy with $$ \mathcal{N} $$ N = 4 super Yang-Mills (SYM), in a suitable scheme Nc-subleading terms are absent from the three-loop Regge trajectory, we understand our result as the first computation of the pure gauge, or nf = 0, part of the QCD three-loop Regge trajectory. The results are presented both for the bare and renormalised amplitudes and are consistent with predictions from infrared factorisation along with reproducing known results in planar $$ \mathcal{N} $$ N = 4 SYM through a maximal weight truncation. We also include the dependence on a Regge factorisation scale to facilitate future applications in BFKL theory at next-to-next-to leading logarithmic accuracy.

“…where we have used the cyclic invariance of colour-ordered amplitudes to match the helicity configuration of the last colour-ordered amplitude in eq. ( 2.3) to the ones given in [48].…”

Section: Jhep01(2022)149mentioning

confidence: 79%

Section: Jhep01(2022)149mentioning

confidence: 99%

Section: The Antisymmetric Octet At Three-loop Ordermentioning

confidence: 99%

Section: Jhep01(2022)149mentioning

confidence: 99%

Section: Jhep01(2022)149mentioning

confidence: 99%

See 3 more Smart Citations

The gluon Regge trajectory at three loops from planar Yang-Mills theory

Duca

Marzucca²,

Verbeek

2022

Gluonic evanescent operators: two-loop anomalous dimensions

Jin

Ren

Yang

et al. 2023

Evanescent operators are a special class of operators that vanish in four-dimensional spacetime but are non-zero in d = 4−2ϵ dimensions. In this paper, we continue our systematic study of the evanescent operators in the pure Yang-Mills theory and focus on their two-loop renormalization. We develop an efficient strategy to compute the two-loop divergences of form factors of high-dimensional and high-length operators by combining the d-dimensional unitarity method and the improved tensor reduction techniques. Two-loop anomalous dimensions are obtained for the dimension-10 basis in the planar YM theory, for which both the $$ \overline{\textrm{MS}} $$ MS ¯ scheme and the finite-renormalization scheme are used. We verify that the two-loop anomalous dimensions are the same in these two schemes at the Wilson-Fisher conformal fixed point. Our computation shows that the evanescent operators are indispensable in order to obtain the correct two-loop anomalous dimensions. This work provides a first computation of the two-loop anomalous dimensions of the complete set of dimension-10 operators. The method we use is also expected to provide an efficient strategy for the two-loop renormalization of general high-dimensional operators.

Symmetry properties of Wilson loops with a Lagrangian insertion

Chicherin

Henn

2022

Null Wilson loops in $$ \mathcal{N} $$ N = 4 super Yang-Mills are dual to planar scattering amplitudes. This duality implies hidden symmetries for both objects. We consider closely related infrared finite observables, defined as the Wilson loop with a Lagrangian insertion, normalized by the Wilson loop itself. Unlike ratio and remainder functions studied in the literature, this observable is non-trivial already for four scattered particles and bears close resemblance to (finite parts of) scattering processes in non-supersymmetric Yang-Mills theory. Moreover, by integrating over the insertion point, one can recover information on the amplitude, as was recently done to compute the full four-loop cusp anomalous dimension. We study the general structure of the Wilson loop with a Lagrangian insertion, focusing in particular on its leading singularities and their (hidden) symmetry properties. Thanks to the close connection of the observable to integrands of MHV amplitudes, it is natural to expect that its leading singularities can be written as certain Grassmannian integrals. The latter are manifestly dual conformal. They also have a conformal symmetry, up to total derivatives. We find that, surprisingly, the conformal symmetry becomes an invariance in the frame where the Lagrangian insertion point is sent to infinity. Furthermore, we use integrability methods to study how higher Yangian charges act on the Grassmannian integral. We evaluate the n-particle observable both at tree- and at one-loop level, finding compact analytic formulas. These results are explicitly written in the form of conformal leading singularities, multiplied by transcendental functions. We then compare these formulas to known expressions for all-plus amplitudes in pure Yang-Mills theory. We find a remarkable new connection: the Wilson loop with Lagrangian insertion in $$ \mathcal{N} $$ N = 4 super Yang-Mills appears to predict the maximal weight terms of the planar pure Yang-Mills all-plus amplitude. We test this relationship for the two-loop n-point Yang-Mills amplitude, as well as for the three-loop four-point amplitude.