Cusp and Collinear Anomalous Dimensions in Four-Loop QCD from Form Factors

Manteuffel, Andreas von; Panzer, Erik; Schabinger, Robert M.

doi:10.1103/physrevlett.124.162001

Cited by 134 publications

(109 citation statements)

References 112 publications

(170 reference statements)

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“…The cusp anomalous dimension is now known to fourloop order [61][62][63][64][65][66][67][68][69][70][71][72][73][74], and the QCD β-function is as well [75]. The hard and jet functions are known through three-loop order [45,[75][76][77][78][79][80][81], as they are relevant for resummation of a broad class of observables.…”

Section: Mmdt Grooming and Factorization Theoremmentioning

confidence: 99%

Two- and three-loop data for the groomed jet mass

2020

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We discuss the status of resummation of large logarithmic contributions to groomed event shapes of hadronic final states in electron-positron annihilation. We identify the missing ingredients needed for nextto-next-to-next-to-leading logarithmic (NNNLL) resummation of the modified mass mass drop tagger (mMDT) groomed jet mass in e þ e − collisions: the low-scale collinear-soft constants at two-loop accuracy, c ð2Þ S c , and the three-loop noncusp anomalous dimension of the global soft function, γ ð2Þ S. We present a method for extracting those constants using fixed-order codes: the EVENT2 program to obtain the color coefficients of c ð2Þ S c , and MCCSM for extracting γ ð2Þ S. We present all necessary formulae for resummation of the mMDT groomed heavy jet mass distribution at NNNLL accuracy.

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Section: Mmdt Grooming and Factorization Theoremmentioning

confidence: 99%

Two- and three-loop data for the groomed jet mass

2020

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“…Reduze and LiteRed [5][6][7][8][9][10][11][12][13][14][15][16], based on the Laporta algorithm [17] and/or the algebra structures of IBP relations [18][19][20]. In recent years, many new ideas and programs have appeared for use in the computation of complicated multi-loop IBP reductions, for example, syzygy approach [21][22][23][24][25][26], finite-field interpolation [27][28][29][30][31], module intersection [32,33], intersection theory [34][35][36][37], η expansion [38][39][40][41][42] and direct solution of IBP recursive relations [43].…”

Section: Introductionmentioning

confidence: 99%

IBP reduction coefficients made simple

Boehm

Wittmann

et al. 2020

J. High Energ. Phys.

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We present an efficient method to shorten the analytic integration-by-parts (IBP) reduction coefficients of multi-loop Feynman integrals. For our approach, we develop an improved version of Leinartas’ multivariate partial fraction algorithm, and provide a modern implementation based on the computer algebra system Singular. Furthermore, we observe that for an integral basis with uniform transcendental (UT) weights, the denominators of IBP reduction coefficients with respect to the UT basis are either symbol letters or polynomials purely in the spacetime dimension D. With a UT basis, the partial fraction algorithm is more efficient both with respect to its performance and the size reduction. We show that in complicated examples with existence of a UT basis, the IBP reduction coefficients size can be reduced by a factor of as large as ∼ 100. We observe that our algorithm also works well for settings without a UT basis.

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“…[50]. At four loops, one finds the first occurence of higher-order Casimir operators of the gauge algebra, which have recently been computed in the case of the cusp anomalous dimension [61,62]: the interplay of this class of contributions to the cusp with similar contributions to multi-particle correlators is a very interesting open problem, with subtle connections to the factorisation of collinear poles. We note that an interesting alternative approach to IR exponentiation, focusing not on diagrammatics but on the symmetries and renormalisation properties of Wilson-line correlators, was developed in refs.…”

Section: Jhep03(2021)188mentioning

confidence: 95%

“…Together with Bose symmetry, they allow to reduce the form of the soft anomalous dimension matrix to a relatively simple parametrisation in terms of a few scalar functions. Of particular interest is the appearance, at four loops, of contributions proportional to quartic Casimir operators of the gauge algebra, which are fully known for the simple case of two Wilson lines [61,62,79,80], but, as yet, undetermined in the general case, although partial results have begun to emerge [53,81]. Our results provide all the necessary colour ingredients for the complete four-loop calculation, and other tools are available for the study of colour structures at high orders, such as the effective vertex analysis of ref.…”

Section: Jhep03(2021)188mentioning

confidence: 99%

Cwebs beyond three loops in multiparton amplitudes

Agarwal

Magnea

Pal

et al. 2021

J. High Energ. Phys.

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Correlators of Wilson-line operators in non-abelian gauge theories are known to exponentiate, and their logarithms can be organised in terms of collections of Feynman diagrams called webs. In [1] we introduced the concept of Cweb, or correlator web, which is a set of skeleton diagrams built with connected gluon correlators, and we computed the mixing matrices for all Cwebs connecting four or five Wilson lines at four loops. Here we complete the evaluation of four-loop mixing matrices, presenting the results for all Cwebs connecting two and three Wilson lines. We observe that the conjuctured column sum rule is obeyed by all the mixing matrices that appear at four-loops. We also show how low-dimensional mixing matrices can be uniquely determined from their known combinatorial properties, and provide some all-order results for selected classes of mixing matrices. Our results complete the required colour building blocks for the calculation of the soft anomalous dimension matrix at four-loop order.

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Cusp and Collinear Anomalous Dimensions in Four-Loop QCD from Form Factors

Cited by 134 publications

References 112 publications

Two- and three-loop data for the groomed jet mass

Two- and three-loop data for the groomed jet mass

IBP reduction coefficients made simple

Cwebs beyond three loops in multiparton amplitudes

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