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Related papers: Factorizing two-loop vacuum sum-integrals

200 papers

Electromagnetic corrections to the $n$-point functions of lattice QCD can be evaluated using a position-space photon propagator defined in infinite volume. Here we address the computational challenge arising from the volume-squared sum over…

High Energy Physics - Lattice · Physics 2026-03-16 Dominik Erb , Harvey B. Meyer , Konstantin Ottnad

Based on the Simplified Differential Equations approach, we present results for the two-loop non-planar hexa-box families of master integrals. We introduce a new approach to obtain the boundary terms and establish a one-dimensional integral…

High Energy Physics - Phenomenology · Physics 2022-05-25 Adam Kardos , Costas G. Papadopoulos , Alexander V. Smirnov , Nikolaos Syrrakos , Christopher Wever

We present a set of algebraic functions for evaluating the coefficients of the scalar integral basis of a general one-loop amplitude. The functions are derived from unitarity cuts, but the complete cut-integral procedure has been carried…

High Energy Physics - Phenomenology · Physics 2008-11-26 Ruth Britto , Bo Feng

Monte Carlo simulations of systems with a complex action are known to be extremely difficult. A new approach to this problem based on a factorization property of distribution functions of observables has been proposed recently. The method…

High Energy Physics - Lattice · Physics 2010-02-03 J. Ambjorn , K. N. Anagnostopoulos , J. Nishimura , J. J. M. Verbaarschot

We analytically evaluate the master integrals for the second type of planar contributions to the massive two-loop Bhabha scattering in QED using differential equa- tions with canonical bases. We obtain results in terms of multiple…

High Energy Physics - Phenomenology · Physics 2021-10-04 Claude Duhr , Vladimir A. Smirnov , Lorenzo Tancredi

It is proved that each of compact linear groups of one special type admits a polynomial factorization map onto a real vector space. More exactly, the group is supposed to be non-commutative one-dimensional and to have two connected…

Algebraic Geometry · Mathematics 2014-11-24 O. G. Styrt

We evaluate a new 3-loop sum-integral which contributes to the Debye screening mass in hot QCD. While we manage to derive all divergences analytically, its finite part is mapped onto simple integrals and evaluated numerically.

High Energy Physics - Phenomenology · Physics 2015-06-05 I. Ghisoiu , Y. Schroder

The large double logarithm in loop-induced processes is one kind of logarithm at subleading power, which has a different origin from Sudakov double logarithms. We develop a method with soft-collinear effective theory to resum these large…

High Energy Physics - Phenomenology · Physics 2019-12-24 Jian Wang

We recompute the functions describing the collinear factorization of one-loop amplitudes using the unitarity-based method. We present the results in a form suitable for use as an ingredient in two-loop calculations. We also present a…

High Energy Physics - Phenomenology · Physics 2008-11-26 David A. Kosower , Peter Uwer

Fully analytical results for the first two moments of the heavy-quark vacuum polarisation function at four loops in quantum chromo-dynamics are presented.

High Energy Physics - Phenomenology · Physics 2008-11-26 Bernd A. Kniehl , Anatoly V. Kotikov

Loop amplitudes are conveniently expressed in terms of master integrals whose coefficients carry the process dependent information. Similarly before integration, the loop integrands may be expressed as a linear combination of propagator…

High Energy Physics - Theory · Physics 2016-12-28 Harald Ita

We present analytic results of the two-loop master integrals for hadronic $tW$ production that contain two massive propagators. For the planar integral family, we succeed in constructing the canonical basis, so the results are written in…

High Energy Physics - Phenomenology · Physics 2023-02-17 Jian Wang , Yefan Wang

Extending the method successful for one-loop integrals, the computation of two-loop diagrams with general internal masses is discussed. For the two-loop vertex of non-planar type, as an example, we show a calculation related to…

High Energy Physics - Phenomenology · Physics 2011-03-02 J. FUJIMOTO , Y. SHIMIZU , K. KATO , T. KANEKO

We review recent progress that we have achieved in evaluating the class of fully massive vacuum integrals at five loops. After discussing topics that arise in classification, evaluation and algorithmic codification of this specific set of…

High Energy Physics - Phenomenology · Physics 2016-12-21 Thomas Luthe , York Schroder

We compute the two-loop master integrals for non-leptonic heavy-to-heavy decays analytically in a recently-proposed canonical basis. For this genuine two-loop, two-scale problem we first derive a basis for the master integrals that…

High Energy Physics - Phenomenology · Physics 2015-05-20 Tobias Huber , Susanne Krankl

For a large class of two-loop selfenergy- and vertex-type diagrams with only one non-zero mass ($M$) and the vertices also with only one non-zero external momentum squared ($q^2$) the first few expansion coefficients are calculated by the…

High Energy Physics - Phenomenology · Physics 2008-11-26 J. Fleischer , A. V. Kotikov , O. L. Veretin

We apply Soft-Collinear Effective Theory to prove at leading power in Lambda_QCD/m_b a factorization formula for the radiative leptonic decay B -> gamma l nu. Large logarithms entering the hard-scattering kernel are systematically resummed…

High Energy Physics - Phenomenology · Physics 2011-09-13 Stefan W. Bosch

We present numerical results which are needed to evaluate all non-trivial master integrals for four-loop massless propagators, confirming the recent analytic results of[1]and evaluating an extra order in $\ep$ expansion for each master…

High Energy Physics - Phenomenology · Physics 2014-11-20 A. V. Smirnov , M. Tentyukov

Renormalization-group methods in soft-collinear effective theory are used to perform the resummation of large perturbative logarithms for deep-inelastic scattering in the threshold region x->1. The factorization theorem for the structure…

High Energy Physics - Phenomenology · Physics 2010-10-27 Thomas Becher , Matthias Neubert , Ben D. Pecjak

We propose a framework for calculating two-loop Feynman diagrams which appear within a renormalizable theory in the general mass case and at finite external momenta. Our approach is a combination of analytical results and of high accuracy…

High Energy Physics - Phenomenology · Physics 2009-10-30 A. Ghinculov , Y. -P. Yao