Three-Loop Gluon Scattering in QCD and the Gluon Regge Trajectory

Caola, Fabrizio; Chakraborty, Amlan; Gambuti, Giulio; Manteuffel, Andreas von; Tancredi, Lorenzo

doi:10.1103/physrevlett.128.212001

Cited by 30 publications

(36 citation statements)

References 74 publications

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“…(6.12) enter at one loop order higher than the quantities on its l.h.s. Substituting the available perturbative data into this equation, namely the ABDK/BDS ansatz [60,87] expression for the four-point MHV amplitude, the known expression for F 4 up to two loops, and the three-loop all-plus four-point amplitude [27,84,85] into this equation, we find perfect agreement.…”

Section: Jhep07(2022)057mentioning

confidence: 74%

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Symmetry properties of Wilson loops with a Lagrangian insertion

Chicherin

Henn

2022

J. High Energ. Phys.

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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.

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Section: Jhep07(2022)057mentioning

confidence: 74%

“…Here the finite remainder H YM n is known for n = 4 up to the three-loop order [84,85]. The infrared divergences are taken into account by the factor Z YM IR , which implements the minimal subtraction.…”

Section: Jhep07(2022)057mentioning

confidence: 99%

Symmetry properties of Wilson loops with a Lagrangian insertion

Chicherin

Henn

2022

J. High Energ. Phys.

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“…A second issue is that due to dual conformal symmetry [18], non-trivial amplitudes that can be studied in N = 4 sYM have at least n ≥ 6 particles, and they depend on (3n − 15) dimensionless kinematic variables. This is to be compared with amplitudes in QCD, which depend on (3n − 11) kinematic variables, and where already the cases n = 4, 5 are of enormous current interest, see for example [19,20] and references therein. It would therefore be desirable to have a relevant observable in N = 4 sYM that, for the same number of particles, has similar variable dependence as QCD amplitudes, and ideally could be computed in four dimensions, to fully exploit the novel integrand insights.…”

Section: Jhep07(2022)038 1 Introductionmentioning

confidence: 99%

Pentagon Wilson loop with Lagrangian insertion at two loops in $$ \mathcal{N} $$ = 4 super Yang-Mills theory

Chicherin

Henn

2022

J. High Energ. Phys.

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We compute the two-loop result for the null pentagonal Wilson loop with a Lagrangian insertion (normalized by the Wilson loop without insertion) in planar, maximally supersymmetric Yang-Mills theory. This finite observable is closely related to the Amplituhedron, and it is reminiscent of finite parts of planar two-loop five-particle scattering amplitudes. We verify that, up to this loop order, the leading singularities are given by the same conformally invariant expressions that appear in all-plus pure Yang-Mills amplitudes. The accompanying weight-four transcendental functions are expressed in terms of the pentagon functions space known from planar two-loop five-particle amplitudes, but interestingly only a subset of the functions appears. Being a function of four dimensionless variables, the observable has interesting asymptotic limits. We verify that our analytic result is consistent with soft and collinear limits, and find an intriguingly simple pattern in the multi-Regge limit. Thanks to the new result we can also conjecturally predict, for general kinematics, the maximal weight piece of the planar three-loop five-particle all-plus amplitude in pure Yang-Mills theory. Motivated by the Amplituhedron geometry, we investigate positivity properties of the integrated answer. Generalizing previous results at four particles, we find numerical evidence that the two-loop five-particle result has uniform sign in a kinematic region suggested by the loop Amplituhedron.

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“…This defines a scheme to extract the two-loop impact factors (2) and the three-loop Regge trajectory (3) by matching eq. ( 17), where M NF → is identified with M MR → , with fixed-order calculations [31][32][33][34][35]. Here, we take a different point of view following refs.…”

Section: Pos(ll2022)044mentioning

confidence: 99%

High-energy limit of 2->2 scattering amplitudes at NNLL

Milloy¹,

Falcioni²,

Gardi³

et al. 2022

Proceedings of Loops and Legs in Quantum Field Theory — PoS(LL2022)

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The high-energy limit of 2 → 2 scattering amplitudes offers an excellent setting to explore the universal features of gauge theories. At Leading Logarithmic (LL) accuracy the partonic amplitude is governed by Regge poles in the complex angular momentum plane. Beyond LL, Regge cuts in this plane begin to play an important role. Specifically, the real part of the amplitude at Next-to-Next-to-Leading Logarithmic (NNLL) accuracy presents for the first time both a Regge pole and a Regge cut. Analysing this tower of logarithms and computing it explicitly through four loops we are able to systematically separate between the Regge pole and the Regge cut. The former involves two fundamental parameters, namely the gluon Regge trajectory and impact factors. We explain how to consistently define the impact factors at two loops and the Regge trajectory at three loops. We confirm that the singularities of the trajectory are given by the cusp anomalous dimension. We also show that the Regge-cut contribution at four loop is nonplanar.

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Three-Loop Gluon Scattering in QCD and the Gluon Regge Trajectory

Cited by 30 publications

References 74 publications

Symmetry properties of Wilson loops with a Lagrangian insertion

Symmetry properties of Wilson loops with a Lagrangian insertion

Pentagon Wilson loop with Lagrangian insertion at two loops in $$ \mathcal{N} $$ = 4 super Yang-Mills theory

High-energy limit of 2->2 scattering amplitudes at NNLL

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