Results 1 to 10 of about 29,966 (283)
The unpolarized two-loop massive pure singlet Wilson coefficients for deep-inelastic scattering [PDF]
Nuclear Physics B, 2019 We calculate the massive two–loop pure singlet Wilson coefficients for heavy quark production in the unpolarized case analytically in the whole kinematic region and derive the threshold and asymptotic expansions.
J. Blümlein +3 more
doaj +3 more sources
Iterated Shimura integrals [PDF]
Moscow Mathematical Journal, 2005 In this paper I continue the study of iterated integrals of modular forms and noncommutative modular symbols for $\Gamma \subset SL(2,\bold{Z})$ started in [Ma3].
Manin, Yu. I.
core +4 more sources
Algorithms and tools for iterated Eisenstein integrals
Journal of High Energy Physics, 2020 We present algorithms to work with iterated Eisenstein integrals that have recently appeared in the computation of multi-loop Feynman integrals. These algorithms allow one to analytically continue these integrals to all regions of the parameter space ...
Claude Duhr, Lorenzo Tancredi
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The ice cone family and iterated integrals for Calabi-Yau varieties
Journal of High Energy Physics, 2023 We present for the first time fully analytic results for multi-loop equal-mass ice cone graphs in two dimensions. By analysing the leading singularities of these integrals, we find that the maximal cuts in two dimensions can be organised into two copies ...
Claude Duhr +3 more
doaj +2 more sources
Iterated binomial sums and their associated iterated integrals [PDF]
Journal of Mathematical Physics, 2014 We consider finite iterated generalized harmonic sums weighted by the binomial \documentclass[12pt]{minimal}\begin{document}$\binom{2k}{k}$\end{document}2kk in numerators and denominators. A large class of these functions emerges in the calculation of massive Feynman diagrams with local operator insertions starting at 3-loop order in the coupling ...
Ablinger, J. +3 more
openaire +6 more sources
Optimization of the mean-square approximation procedures for iterated Stratonovich stochastic integrals of multiplicities 1 to 3 with respect to components of the multi-dimensional Wiener process based on Multiple Fourier–Legendre series [PDF]
MATEC Web of Conferences, 2022 The article is devoted to approximation of iterated Ito and Stratonovich stochastic integrals of multiplicities 1 to 3 by the method of multiple Fourier–Legendre series.
Kuznetsov Dmitriy, Kuznetsov Mikhail
doaj +1 more source
Poincaré series for modular graph forms at depth two. Part I. Seeds and Laplace systems
Journal of High Energy Physics, 2022 We derive new Poincaré-series representations for infinite families of non-holomorphic modular invariant functions that include modular graph forms as they appear in the low-energy expansion of closed-string scattering amplitudes at genus one.
Daniele Dorigoni +2 more
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Homogeneous Approximation of One- Dimensional Series of Iterated Integrals and Time Optimality
Journal of Optimization, Differential Equations and Their Applications, 2023 In the paper we consider nonlinear systems depending linearly on control with one-dimensional output. As is well known, under the analyticity requirement, the output can be expressed as a series of iterated integrals of controls with scalar coefficients.
Daria M. Andreieva +1 more
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Massive kite diagrams with elliptics
Nuclear Physics B, 2021 We present the results for two-loop massive kite master integrals with elliptics in terms of iterated integrals with algebraic kernels. The key ingredients are new integral representations for sunset subgraphs in d=4−2ε and d=2−2ε dimensions together ...
M.A. Bezuglov +2 more
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Journal of High Energy Physics, 2021 We present a complete set of analytic helicity amplitudes for top quark pair production via gluon fusion at two-loops in QCD. For the first time, we include corrections due to massive fermion loops which give rise to integrals over elliptic curves.
Simon Badger +3 more
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