The analytical values of the sunrise master integrals for one of the masses equal to zero

Czyż, Henryk; Grzelińska, Agnieszka; Zabawa, R.

doi:10.1016/s0370-2693(02)01992-5

Cited by 13 publications

(16 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(15). The larger errors (or less efficiency in calculations) come from the zero mass contributions, for which an approach based entirely on analytical expressions is in preparation [17]. Furthermore the choice of equal values for two or even all the three masses, reduces the number of the independent equations in the system of differential equations, generating potential numerical problems, although less serious than those for the zero mass.…”

Section: Tests and Comparisonsmentioning

confidence: 99%

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

2002

Self Cite

View full text Add to dashboard Cite

show abstract

Section: Tests and Comparisonsmentioning

confidence: 99%

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

2002

Self Cite

View full text Add to dashboard Cite

show abstract

“…[28,29,30,31]). The classical (or genuine) two-loop sunrise diagram with different values of the internal masses has recently been studied in some detail using the traditional momentum space approach (see e.g.…”

Section: Introductionmentioning

confidence: 99%

On the evaluation of a certain class of Feynman diagrams in x-space: Sunrise-type topologies at any loop order

2007

View full text Add to dashboard Cite

We review recently developed new powerful techniques to compute a class of Feynman diagrams at any loop order, known as sunrise-type diagrams. These sunrise-type topologies have many important applications in many different fields of physics and we believe it to be timely to discuss their evaluation from a unified point of view. The method is based on the analysis of the diagrams directly in configuration space which, in the case of the sunrise-type diagrams and diagrams related to them, leads to enormous simplifications as compared to the traditional evaluation of loops in momentum space. We present explicit formulae for their analytical evaluation for arbitrary mass configurations and arbitrary dimensions at any loop order. We discuss several limiting cases of their kinematical regimes which are e.g. relevant for applications in HQET and NRQCD. We completely solve the problem of renormalization using simple formulae for the counterterms within dimensional regularization. An important application is the computation of the multi-particle phase space in D-dimensional space-time which we discuss. We present some examples of their functions. We discuss the use of recurrence relations naturally emerging in configuration space for the calculation of special series of integrals of the sunrise topology. We finally report on results for the computation of an extension of the basic sunrise topology, namely the spectacle topology and the topology with an irreducible loop addition.

show abstract

“…(3.15) of [8] for k = 0 and Eq. (27) of [4] for k = 1. The case of k = 9, which we have checked numerically, agrees with Eq.…”

Section: Conementioning

confidence: 99%

“…The relations from [32] have been implemented independently using FORM [43]. The expansions around s = 0 were also derived using the methods of [3,20] and numerical results have been compared with the results from analytical expressions of [4,24,27].…”

Section: Introductionmentioning

confidence: 99%

An analytic approach to sunset diagrams in chiral perturbation theory: Theory and practice

Ananthanarayan¹,

Bijnens²,

Ghosh³

et al. 2016

Eur. Phys. J. A

View full text Add to dashboard Cite

We demonstrate the use of several code implementations of the Mellin-Barnes method available in the public domain to derive analytic expressions for the sunset diagrams that arise in the two-loop contribution to the pion mass and decay constant in three-flavoured chiral perturbation theory. We also provide results for all possible two-mass configurations of the sunset integral, and derive a new one-dimensional integral representation for the one mass sunset integral with arbitrary external momentum. Thoroughly annotated Mathematica notebooks are provided as ancillary files, which may serve as pedagogical supplements to the methods described in this paper.

show abstract

The analytical values of the sunrise master integrals for one of the masses equal to zero

Abstract: The analytical values of the sunrise master amplitudes were found for one mass equal to zero, two other arbitrary masses and an arbitrary external four momentum. Differential equations in the square of the external four momentum and masses were used to obtain the master integrals.

Cited by 13 publications

References 15 publications

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

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

On the evaluation of a certain class of Feynman diagrams in x-space: Sunrise-type topologies at any loop order

An analytic approach to sunset diagrams in chiral perturbation theory: Theory and practice

Contact Info

Product

Resources

About