New results for two-loop off-shell three-point diagrams

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

doi:10.1016/0370-2693(94)90874-5

Cited by 96 publications

(124 citation statements)

References 27 publications

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“…It reproduces the results presented in [26], [27] since the indices of the lines in the left-hand side of (51) are changed by means of the star-triangle symmetries (21). …”

supporting

confidence: 84%

Multi-loop Feynman integrals and conformal quantum mechanics

Исаев¹

2003

Nuclear Physics B

110

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New algebraic approach to analytical calculations of D-dimensional integrals for multi-loop Feynman diagrams is proposed. We show that the known analytical methods of evaluation of multi-loop Feynman integrals, such as integration by parts and star-triangle relation methods, can be drastically simplified by using this algebraic approach. To demonstrate the advantages of the algebraic method of analytical evaluation of multi-loop Feynman diagrams, we calculate ladder diagrams for the massless φ 3 theory. Using our algebraic approach we show that the problem of evaluation of special classes of Feynman diagrams reduces to the calculation of the Green functions for specific quantum mechanical problems. In particular, the integrals for ladder massless diagrams in the φ 3 scalar field theory are given by the Green function for the conformal quantum mechanics.

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“…It reproduces the results presented in [26], [27] since the indices of the lines in the left-hand side of (51) are changed by means of the star-triangle symmetries (21). …”

supporting

confidence: 84%

Multi-loop Feynman integrals and conformal quantum mechanics

Исаев¹

2003

Nuclear Physics B

110

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“…The same constants appear in the (2 − 2ε)-dimensional Feynman integrals [14], as one should expect due to algebraic relations between diagrams with shifted dimension [3]. We also note that Cl 2 π 3 2 appears in the two-loop non-planar three-point diagram [15], when internal lines are massless, whereas all external momenta squared are off shell and equal. Unfortunately, a large number of elements (more than 4000) makes it difficult to define the complete basis of "sixth root of unity" at the weight 4.…”

Section: Introductionsupporting

confidence: 71%

New results for the ε-expansion of certain one-, two- and three-loop Feynman diagrams

Davydychev

Kalmykov²

2001

Nuclear Physics B

164

228

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For certain dimensionally-regulated one-, two-and three-loop diagrams, problems of constructing the ε-expansion and the analytic continuation of the results are studied. In some examples, an arbitrary term of the ε-expansion can be calculated. For more complicated cases, only a few higher terms in ε are obtained. Apart from the oneloop two-and three-point diagrams, the examples include two-loop (mainly on-shell) propagator-type diagrams and three-loop vacuum diagrams. As a by-product, some new relations involving Clausen function, generalized log-sine integrals and certain Euler-Zagier sums are established, and some useful results for the hypergeometric functions of argument 1 4 are presented.

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“…We consider three point graphs with incoming momenta q 1 , q 2 , and −(q 1 + q 2 ) and identify one momentum as large, say q 1 . The ordinary large momentum procedure is used to find an expansion with respect to q Using the described method we found very good numerical agreement with the analytical results for the one loop vertex corrections given in [21,22] and the one and two loop scalar three point integrals given in [23] by computing only 4 to 6 terms of the expansion.…”

Section: Methods Of the Calculationsupporting

confidence: 56%

Two-loop QCD vertices and three-loop MOM β functions

Chetyrkin

Seidensticker

2000

Physics Letters B

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We present numerical results for the two loop QCD corrections to the ghost gluon vertex, the quark gluon vertex, and the triple gluon vertex in the massless limit at the symmetric point. We restrict ourselves to the tensor structures existing in the tree level. The corrections are used to examine different coupling constant definitions in momentum subtraction schemes and the corresponding three-loop β functions.

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New results for two-loop off-shell three-point diagrams

Cited by 96 publications

References 27 publications

Multi-loop Feynman integrals and conformal quantum mechanics

Multi-loop Feynman integrals and conformal quantum mechanics

New results for the ε-expansion of certain one-, two- and three-loop Feynman diagrams

Two-loop QCD vertices and three-loop MOM β functions

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