Analytic results for two-loop planar master integrals for Bhabha scattering

Duhr, Claude; Smirnov, Vladimir A.; Tancredi, Lorenzo

doi:10.1007/jhep09(2021)120

Cited by 20 publications

(19 citation statements)

References 69 publications

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“…These analytic results were obtained in a recent paper [34] using differential equations with canonical bases. This is a two-loop example, but it already demonstrates well the advancement from FIESTA4 to FIESTA5.…”

Section: Physical Kinematics Comparing Versions and Options Of The Ne...mentioning

confidence: 56%

FIESTA5: numerical high-performance Feynman integral evaluation

Smirnov,

Shapurov,

Vysotsky

2021

Preprint

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In this paper we present a new release of the FIESTA program (Feynman Integral Evaluation by a Sector decomposiTion Approach). FIESTA5 is performance-oriented -we implemented improvements of various kinds in order to make Feynman integral evaluation faster. We plugged in two new integrators, the Quasi Monte Carlo and Tensor Train. At the same time the old code of FIESTA4 was upgraded to the C++17 standard and mostly rewritten without self-made structures such as hash tables. There are also several essential improvements which are most relevant for complex integrations -the new release is capable of producing results where previously impossible.

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Section: Physical Kinematics Comparing Versions and Options Of The Ne...mentioning

confidence: 56%

FIESTA5: numerical high-performance Feynman integral evaluation

Smirnov,

Shapurov,

Vysotsky

2021

Preprint

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“…Conversely, it remains unclear whether other mechanism of generating functional relations between elliptic dilogarithms exist (although see [128,282] for work on this topic). Techniques for reducing elliptic multiple polylogarithms to multiple polylogarithms (when possible) also remain relatively unexplored, although there exist examples in which Feynman integrals containing multiple non-rationalizable square roots have been found to be expressible in terms of multiple polylogarithms [269,[284][285][286]. Importantly, methods for directly constructing the integrands of amplitudes using generalized unitarity [287][288][289] have also recently been extended to the elliptic sector.…”

Section: Iterated Integrals Involving Elliptic Curvesmentioning

confidence: 99%

Functions Beyond Multiple Polylogarithms for Precision Collider Physics

Bourjaily¹,

Broedel²,

Chaubey³

et al. 2022

Preprint

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Feynman diagrams constitute one of the essential ingredients for making precision predictions for collider experiments. Yet, while the simplest Feynman diagrams can be evaluated in terms of multiple polylogarithms-whose properties as special functions are well understood-more complex diagrams often involve integrals over complicated algebraic manifolds. Such diagrams already contribute at NNLO to the self-energy of the electron, t t production, γγ production, and Higgs decay, and appear at two loops in the planar limit of maximally supersymmetric Yang-Mills theory. This makes the study of these more complicated types of integrals of phenomenological as well as conceptual importance.In this white paper contribution to the Snowmass community planning exercise, we provide an overview of the state of research on Feynman diagrams that involve special functions beyond multiple polylogarithms, and highlight a number of research directions that constitute essential avenues for future investigation.

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“…Even in cases where the canonical " d log"-form of DEs can be obtained, it can be difficult, if not impossible, to find MPL solutions if the symbol alphabet contains non-rationalizable square roots [42,[54][55][56][57]. Very importantly, even when these attempts did succeed, it was frequently observed that the numerical evaluation in the physical scattering regions is very challenging [26,27,42,58]. In addition, contrary to naïve expectations, the physical properties may even be more obscured due to the presence of spurious branch cuts, which are instead absent in the iterated integral representation.…”

Section: Jhep01(2022)096 1 Introductionmentioning

confidence: 99%

Pentagon functions for one-mass planar scattering amplitudes

Chicherin

Sotnikov

Zoia

2022

J. High Energ. Phys.

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We present analytic results for all planar two-loop Feynman integrals contributing to five-particle scattering amplitudes with one external massive leg. We express the integrals in terms of a basis of algebraically-independent transcendental functions, which we call one-mass pentagon functions. We construct them by using the properties of iterated integrals with logarithmic kernels. The pentagon functions are manifestly free of unphysical branch cuts, do not require analytic continuation, and can be readily evaluated over the whole physical phase space of the massive-particle production channel. We develop an efficient algorithm for their numerical evaluation and present a public implementation suitable for direct phenomenological applications.

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Analytic results for two-loop planar master integrals for Bhabha scattering

Cited by 20 publications

References 69 publications

FIESTA5: numerical high-performance Feynman integral evaluation

FIESTA5: numerical high-performance Feynman integral evaluation

Functions Beyond Multiple Polylogarithms for Precision Collider Physics

Pentagon functions for one-mass planar scattering amplitudes

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