Two-loop master integrals for jets: the planar topologies

Gehrmann, Thomas; Remiddi, E.

doi:10.1016/s0550-3213(01)00057-8

Cited by 354 publications

(563 citation statements)

References 42 publications

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“…The two-loop matrix elements are given, to all orders in the dimensional regulator, in terms of the master integrals of refs. [39,40], where the complete set of master integrals was evaluated in terms of harmonic polylogarithms (HPLs) and two-dimensional harmonic polylogarithms (2dHPLs) [39,41] up to transcendental weight four. This is sufficient to compute the corresponding matrix elements up to finite terms (some of the master integrals are known to all orders in ǫ, see, e.g., ref.…”

Section: Jhep02(2015)077mentioning

confidence: 99%

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Two-loop splitting amplitudes and the single-real contribution to inclusive Higgs production at N3LO

Duhr

Gehrmann

Jaquier

2015

J. High Energ. Phys.

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The factorisation of QCD matrix elements in the limit of two external partons becoming collinear is described by process-independent splitting amplitudes, which can be expanded systematically in perturbation theory. Working in conventional dimensional regularisation, we compute the two-loop splitting amplitudes for all simple collinear splitting processes, including subleading terms in the regularisation parameter. Our results are then applied to derive an analytical expression for the two-loop single-real contribution to inclusive Higgs boson production in gluon fusion to fourth order (N 3 LO) in perturbative QCD.

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Section: Jhep02(2015)077mentioning

confidence: 99%

“…We have therefore explicitly computed all the master integrals of refs. [39,40] up to transcendental weight five using the method of differential equations [42][43][44]. We choose a canonical basis of master integrals where all the master integrals are of uniform transcendental weight [45].…”

Section: Jhep02(2015)077mentioning

confidence: 99%

Two-loop splitting amplitudes and the single-real contribution to inclusive Higgs production at N3LO

Duhr

Gehrmann

Jaquier

2015

J. High Energ. Phys.

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“…Therefore the whole problem decomposes into two parts: the construction of a reduction algorithm and the evaluation of the master Feynman integrals. There were several recent attempts to make the reduction procedure systematic: (i) Using the fact that the total number of IBP equations grows faster than the number of independent Feynman integrals, when one increases the total power of the numerator and denominator, one can sooner or later obtain an overdetermined system of equations [3,4] which can be solved. (There is a public version of implementing the corresponding algorithm on a computer [5].…”

Section: Introductionmentioning

confidence: 99%

Applying Gröbner bases to solve reduction problems for Feynman integrals

Smirnov

2006

J. High Energy Phys.

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We describe how Gröbner bases can be used to solve the reduction problem for Feynman integrals, i.e. to construct an algorithm that provides the possibility to express a Feynman integral of a given family as a linear combination of some master integrals. Our approach is based on a generalized Buchberger algorithm for constructing Gröbner-type bases associated with polynomials of shift operators. We illustrate it through various examples of reduction problems for families of one-and two-loop Feynman integrals. We also solve the reduction problem for a family of integrals contributing to the three-loop static quark potential.

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“…In the case of massless two-loop four-point diagrams with one leg off-shell the problem of the evaluation has been solved in [9,10], with subsequent applications [11] to the process e + e − → 3jets. (See [12] for recent reviews of the present status of NNLO calculations.…”

Section: Introductionmentioning

confidence: 99%

“…p 2 i = 0, i = 1, 2, 3, 4, the problem of analytical evaluation of two-loop four-point diagrams in expansion in ǫ = (4 − d)/2, where d is the space-time dimension, has been completely solved in [2,3,4,5,6,7]. The corresponding analytical algorithms have been successfully applied to the evaluation of two-loop virtual corrections to various scattering processes [8] in the zero-mass approximation.In the case of massless two-loop four-point diagrams with one leg off-shell the problem of the evaluation has been solved in [9,10], with subsequent applications [11] to the process e + e − → 3jets. (See [12] for recent reviews of the present status of NNLO calculations.…”

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confidence: 99%

The leading power Regge asymptotic behaviour of dimensionally regularized massless on-shell planar triple box

Smirnov

2002

Physics Letters B

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The leading power asymptotic behaviour of the dimensionally regularized massless on-shell planar triple box diagram in the Regge limit t/s → 0 is analytically evaluated.1 E-mail: smirnov@theory.sinp.msu.ru Systematical analytical evaluation of two-loop Feynman diagrams with four external lines within dimensional regularization [1] began three years ago. In the pure massless case with all end-points on-shell, i.e. p 2 i = 0, i = 1, 2, 3, 4, the problem of analytical evaluation of two-loop four-point diagrams in expansion in ǫ = (4 − d)/2, where d is the space-time dimension, has been completely solved in [2,3,4,5,6,7]. The corresponding analytical algorithms have been successfully applied to the evaluation of two-loop virtual corrections to various scattering processes [8] in the zero-mass approximation.In the case of massless two-loop four-point diagrams with one leg off-shell the problem of the evaluation has been solved in [9,10], with subsequent applications [11] to the process e + e − → 3jets. (See [12] for recent reviews of the present status of NNLO calculations. See [13] for a brief review of results on the analytical evaluation of various double-box Feynman integrals and the corresponding methods of evaluation.) For another three-scale calculational problem, where all four legs are on-shell and there is a non-zero internal mass, a first analytical result was obtained in [14] for the scalar master double box.The purpose of this paper is to turn attention to three-loop on-shell massless four-point diagrams. As a first step, the leading power asymptotic behaviour of the dimensionally regularized massless on-shell planar triple box diagram shown in Fig. 1 in the Regge limit t/s → 0 will be analytically evaluated. This calculation will demonstrate that a three-loop BFKL analysis [15] (at least its virtual part which can be reduced to the evaluation of Regge asymptotics) is possible 2 . The calculation will be based on the technique of alpha parameters and MellinBarnes (MB) representation which was successfully used in [2,4,9,14] and reduces, due to taking residues and shifting contours, to a decomposition of a given MB integral into pieces where a Laurent expansion of the integrand in ǫ becomes possible. At a final stage, summation formulae for series of S 1 (n)S 3 (n)/n 2 , ψ ′′ (n + 1)S 2 (n)/n etc., where S k (n) = n j=1 j −k , are used. A table of such formulae is presented in Appendix.2 In three loops, non-planar diagrams as well as higher terms of expansion of double boxes in ǫ are also needed. 1The general planar triple box Feynman integral without numerator takes the formwhere s = (p 1 + p 2 ) 2 and t = (p 2 + p 3 ) 2 are Mandelstam variables, and k, l and r are loop momenta. Usual prescriptions k 2 = k 2 + i0, s = s + i0, etc. are implied.To evaluate the leading power asymptotic behaviour of the master triple box (1), i.e. for all a i = 1, in the limit t/s → 0 one can use the strategy of expansion by regions [16,17,18]. It shows that in the leading power only (1c-1c-1c) and (2c-2c-2c) region...

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Two-loop master integrals for jets: the planar topologies

Cited by 354 publications

References 42 publications

Two-loop splitting amplitudes and the single-real contribution to inclusive Higgs production at N3LO

Two-loop splitting amplitudes and the single-real contribution to inclusive Higgs production at N3LO

Applying Gröbner bases to solve reduction problems for Feynman integrals

The leading power Regge asymptotic behaviour of dimensionally regularized massless on-shell planar triple box

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