The pseudothreshold expansion of the 2-loop sunrise selfmass master amplitudes

Caffo, M.; Czyż, Henryk; Remiddi, E.

doi:10.1016/s0550-3213(00)00274-1

Cited by 43 publications

(74 citation statements)

References 12 publications

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“…We carry out the calculation by employing the technique based on the Laporta algorithm [75][76][77][78] and the differential equation method [79][80][81][82][83][84][85][86], already used in [73,74]. The calculation of the leading color coefficient in the gluon fusion does not require the calculation of any new master integrals beyond the ones obtained in the two previous works, such that we do not discuss the calculational method in full detail.…”

Section: Jhep01(2011)102mentioning

confidence: 99%

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Two-loop leading color corrections to heavy-quark pair production in the gluon fusion channel

Bonciani

Ferroglia

Gehrmann

et al. 2011

J. High Energ. Phys.

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Abstract:We evaluate the two-loop QCD diagrams contributing to the leading color coefficient of the heavy-quark pair production cross section in the gluon fusion channel. We obtain an analytic expression, which is valid for any value of the Mandelstam invariants s and t and of the heavy-quark mass m. Our findings agree with previous analytic results in the small-mass limit and with recent results for the coefficients of the IR poles.

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Section: Jhep01(2011)102mentioning

confidence: 99%

“…The resulting scalar loop integrals are reduced to a set of Master Integrals (MIs) employing the technique based upon the Laporta algorithm [75][76][77][78]. Then, the MIs can be evaluated analytically by means of the differential equation method [79][80][81][82][83][84][85][86].…”

Section: Calculationmentioning

confidence: 99%

Two-loop leading color corrections to heavy-quark pair production in the gluon fusion channel

Bonciani

Ferroglia

Gehrmann

et al. 2011

J. High Energ. Phys.

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“…The values of the master integrals at the threshold can be obtained in a way similar to the way followed for the values at the pseudothreshold [9] and we will discuss here mostly those points of the derivation which are different from the pseudothreshold case. If the values at the threshold are written as…”

Section: The Threshold Values Of the Master Amplitudesmentioning

confidence: 99%

“…With the configuration space technique the expansion around threshold was investigated also in [8]. The expansion around one of the pseudothresholds (the others are straightforwardly given by a cyclic permutation of the masses) was obtained in analytical form in [9].…”

Section: Introductionmentioning

confidence: 99%

The threshold expansion of the 2-loop sunrise self-mass master amplitudes

2001

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“…From these equations the analytic expressions for their first order expansion were completed at the special points [4,8,9,5]:…”

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confidence: 99%

Numerical evaluation of general massive 2-loop self-mass master integrals from differential equations

Caffo

Czyż

Remiddi

2003

Nuclear Instruments and Methods in Physics Research Section A:

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The system of 4 differential equations in the external invariant satisfied by the 4 master integrals of the general massive 2-loop sunrise self-mass diagram is solved by the Runge-Kutta method in the complex plane. The method offers a reliable and robust approach to the direct and precise numerical evaluation of Feynman graph integrals.The relevance of the higher order calculations for the comparison with nowadays precision measurements in high energy physics is well known and comprehensively presented by G. Passarino in this conference.Therefore can be of some interest the exploitation of an alternative method (but still in the context of the integration by part identities and master integrals (MI) [1]) to the more common direct integration method for the numerical evaluation of the MI.The method uses directly the differential equations. Starting from the integral representation of the MI, related to a certain Feynman graph, by derivation with respect to one of the internal masses [2] or one of the external invariants [3] and with the repeated use of the integration by part identities, a system of independent first order partial differential equations is obtained in a number equal to the number of the MI (master differential equations).Enlarging the number of loops and legs grows the number of parameters, MI and equations, but does not change or spoil the method.

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The pseudothreshold expansion of the 2-loop sunrise selfmass master amplitudes

Abstract: The values at pseudothreshold of two loop sunrise master amplitudes with arbitrary masses are obtained by solving a system of differential equations. The expansion at pseudothreshold of the amplitudes is constructed and some lowest terms are explicitly presented.

Cited by 43 publications

References 12 publications

Two-loop leading color corrections to heavy-quark pair production in the gluon fusion channel

Two-loop leading color corrections to heavy-quark pair production in the gluon fusion channel

The threshold expansion of the 2-loop sunrise self-mass master amplitudes

Numerical evaluation of general massive 2-loop self-mass master integrals from differential equations

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