Exact results for three- and four-point ladder diagrams with an arbitrary number of rungs

Ussyukina, N.I.; Davydychev, Andrei I.

doi:10.1016/0370-2693(93)91118-7

Cited by 223 publications

(279 citation statements)

References 22 publications

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“…There it was noticed that these two diagrams, as well as the ones produced by the rung rule, satisfy some intriguing conformality properties [22,23] that have been studied recently in [24]. This new insight, together with some generalized unitarity arguments developed in [25,26,27,28], might lead to a systematic way of generating the diagrams at any order in perturbation theory.…”

Section: Structure Of the L-loop Four-gluon Amplitudementioning

confidence: 73%

Four-loop cusp anomalous dimension from obstructions

2007

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We introduce a method for extracting the cusp anomalous dimension at L loops from four-gluon amplitudes in N = 4 Yang-Mills without evaluating any integrals that depend on the kinematical invariants. We show that the anomalous dimension only receives contributions from the obstructions introduced in hep-th/0601031. We illustrate this method by extracting the two-and three-loop anomalous dimensions analytically and the four-loop one numerically. The four-loop result was recently guessed to be f (4) = − 4ζ 3 2 + 24ζ 2 ζ 4 + 50ζ 6 − 4(1 + r)ζ 2 3 with r = −2 using integrability and string theory arguments in hep-th/0610251. Simultaneously, f (4) was computed numerically in hep-th/0610248 from the four-loop amplitude obtaining, with best precision at the symmetric point s = t, r = −2.028(36). Our computation is manifestly s/t independent and improves the precision to r = −2.00002(3), providing strong evidence in favor of the conjecture. The improvement is possible due to a large reduction in the number of contributing terms, as well as a reduction in the number of integration variables in each term.

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Section: Structure Of the L-loop Four-gluon Amplitudementioning

confidence: 73%

Four-loop cusp anomalous dimension from obstructions

2007

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“…The case where all the a i are zero gives a three-point horizontal ladder integral. 1 This series of integrals can be expressed in terms of classical polylogarithms [15]. The simplest example of all is where the word is empty and corresponds to the one-loop ladder integral (or triangle integral).…”

Section: Jhep02(2013)092mentioning

confidence: 99%

“…Thus an alternative to the approach we have followed here is to start from the coeffcients L w (z,z) defined by 15) and build solutions of the differential equation (2.15) from them. Note that unlike for L(z,z) the differential equation we want is not automatic because the action of ∂z introduces the y letters on the right instead of the x letters.…”

Section: Jhep02(2013)092mentioning

confidence: 99%

Generalised ladders and single-valued polylogs

Drummond

2013

J. High Energ. Phys.

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We introduce and solve an infinite class of loop integrals which generalises the well-known ladder series. The integrals are described in terms of single-valued polylogarithmic functions which satisfy certain differential equations. The combination of the differential equations and single-valued behaviour allow us to explicitly construct the polylogarithms recursively. For this class of integrals the symbol may be read off from the integrand in a particularly simple way. We give an explicit formula for the simplest generalisation of the ladder series. We also relate the generalised ladder integrals to a class of vacuum diagrams which includes both the wheels and the zigzags.

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“…To this end, we make use of the known two-loop result [9,10] in terms of Euclidean scalar box integrals Φ ð1Þ and Φ ð2Þ whose explicit form can be found in Refs. [9][10][11]. All that we need for our purposes is their Mellin transforms [11] M ð1Þ ðj 1 ;…”

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confidence: 99%

Energy-Energy Correlations inN=4Supersymmetric Yang-Mills Theory

et al. 2014

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We present a new approach to computing energy-energy correlations in gauge theories that exploits their relation to correlation functions and bypasses the use of scattering amplitudes. We illustrate its power by calculating energy-energy correlations in the maximally supersymmetric Yang-Mills theory in the next-toleading order approximation. Introduction.-In this Letter we study a particular class of observables, the so-called energy-energy correlations (EEC), which were first introduced in the context of QCD for the process of electron-positron annihilation into hadrons. EEC played a crucial role in precision tests of QCD as the theory of strong interactions. EEC measures the differential angular distribution of the energy that flows through two calorimeters separated by the relative angle χ. It is defined [1] as the energy-weighted sum over pairs of particles produced in the final states of e þ e − → V → a þ bþ everything (with V being a virtual photon γ Ã or a Z 0 boson):

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Exact results for three- and four-point ladder diagrams with an arbitrary number of rungs

Cited by 223 publications

References 22 publications

Four-loop cusp anomalous dimension from obstructions

Four-loop cusp anomalous dimension from obstructions

Generalised ladders and single-valued polylogs

Energy-Energy Correlations inN=4Supersymmetric Yang-Mills Theory

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