Webs and posets

Dukes, Mark; Gardi, Einan; McAslan, Heather; Scott, Darren J.; White, Chris D.

doi:10.1007/jhep01(2014)024

Cited by 32 publications

(55 citation statements)

References 84 publications

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“…This has been further used in refs. [105,106] to establish a relation with partially ordered sets, and deduce all-order solutions for certain classes of webs.…”

Section: Jhep04(2014)044mentioning

confidence: 99%

“…Progress was achieved there owing to the replica trick of statistical physics which led to a general algorithm for determining web mixing matrices. The study of these [93,[103][104][105][106] proceeded using both combinatorial methods and the connection with the renormalizability of the Wilson-line vertex. The most striking feature of webs is that -despite the fact that they contain disconnected, often reducible diagrams -their colour factors always correspond to connected graphs [93].…”

Section: Jhep04(2014)044mentioning

confidence: 99%

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From webs to polylogarithms

Gardi

2014

J. High Energ. Phys.

186

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We compute a class of diagrams contributing to the multi-leg soft anomalous dimension through three loops, by renormalizing a product of semi-infinite non-lightlike Wilson lines in dimensional regularization. Using non-Abelian exponentiation we directly compute contributions to the exponent in terms of webs. We develop a general strategy to compute webs with multiple gluon exchanges between Wilson lines in configuration space, and explore their analytic structure in terms of α ij , the exponential of the Minkowski cusp angle formed between the lines i and j. We show that beyond the obvious inversion symmetry α ij → 1/α ij , at the level of the symbol the result also admits a crossing symmetry α ij → −α ij , relating spacelike and timelike kinematics, and hence argue that in this class of webs the symbol alphabet is restricted to α ij and 1 − α 2 ij . We carry out the calculation up to three gluons connecting four Wilson lines, finding that the contributions to the soft anomalous dimension are remarkably simple: they involve pure functions of uniform weight, which are written as a sum of products of polylogarithms, each depending on a single cusp angle. We conjecture that this type of factorization extends to all multiple-gluon-exchange contributions to the anomalous dimension.

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“…This has been further used in refs. [105,106] to establish a relation with partially ordered sets, and deduce all-order solutions for certain classes of webs.…”

Section: Jhep04(2014)044mentioning

confidence: 99%

Section: Jhep04(2014)044mentioning

confidence: 99%

From webs to polylogarithms

Gardi

2014

J. High Energ. Phys.

186

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“…The work of Ref. [17][18][19][20][21][22][23] shows that it does in fact generalise but in a rather non-trivial way. A few hints can already be drawn from the simple example above: first, it is convenient to consider together sets of diagrams which are related by permutation of the order of gluon attachments to the Wilson lines; we refer to the entire set as a single web.…”

Section: Pos(radcor 2013)043mentioning

confidence: 99%

“…This was done in the context of a Wilson loop, or two Wilson lines, corresponding to a colour singlet form factor (for a review see [16]). The generalization to a product of more than two Wilson lines, as relevant for QCD hard scattering, was only made over the last three years [17][18][19][20][21][22][23].…”

Section: The Non-abelian Exponentiation Theoremmentioning

confidence: 99%

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Progress on soft gluon exponentiation and long-distance singularities

Gardi¹

2014

Proceedings of 11th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology) —

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I review the recent progress in studying long-distance singularities in gauge-theory scattering amplitudes in terms of Wilson lines. The non-Abelian exponentiation theorem, which has been recently generalised to the case of multi-leg amplitudes, states that diagrams exponentiate such that the colour factors in the exponent are fully connected. After a brief review of the diagrammatic approach to soft gluon exponentiation, I sketch the method we used to prove the theorem and illustrate how connected colour factors emerge in the exponent in webs that are formed by sets of multiple-gluon-exchange diagrams. In the second part of the talk I report on recent progress in evaluating the corresponding integrals, where a major simplification is achieved upon formulating the calculation in terms of subtracted webs. I argue that the contributions of all multiplegluon-exchange diagrams to the soft anomalous dimension take the form of products of specific polylogarithmic functions, each depending on a single cusp angle.11th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology)

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Color-kinematics duality for QCD amplitudes

Johansson

Ochirov

2016

J. High Energ. Phys.

170

290

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We show that color-kinematics duality is present in tree-level amplitudes of quantum chromodynamics with massive flavored quarks. Starting with the color structure of QCD, we work out a new color decomposition for n-point tree amplitudes in a reduced basis of primitive amplitudes. These primitives, with k quark-antiquark pairs and (n − 2k) gluons, are taken in the (n − 2)!/k! Melia basis, and are independent under the color-algebra Kleiss-Kuijf relations. This generalizes the color decomposition of Del Duca, Dixon, and Maltoni to an arbitrary number of quarks. The color coefficients in the new decomposition are given by compact expressions valid for arbitrary gauge group and representation. Considering the kinematic structure, we show through explicit calculations that color-kinematics duality holds for amplitudes with general configurations of gluons and massive quarks. The new (massive) amplitude relations that follow from the duality can be mapped to a well-defined subset of the familiar BCJ relations for gluons. They restrict the amplitude basis further down to (n − 3)!(2k − 2)/k! primitives, for two or more quark lines. We give a decomposition of the full amplitude in that basis. The presented results provide strong evidence that QCD obeys the color-kinematics duality, at least at tree level. The results are also applicable to supersymmetric and D-dimensional extensions of QCD.

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Webs and posets

Cited by 32 publications

References 84 publications

From webs to polylogarithms

From webs to polylogarithms

Progress on soft gluon exponentiation and long-distance singularities

Color-kinematics duality for QCD amplitudes

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