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Zihao Wu

Bio: Zihao Wu is an academic researcher from University of Science and Technology of China. The author has contributed to research in topics: Physics & Reduction (complexity). The author has an hindex of 1, co-authored 3 publications receiving 24 citations.

Papers
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Journal ArticleDOI
TL;DR: In this paper, an improved version of Leinartas' multivariate partial fraction algorithm is presented, and an efficient method to shorten the analytic integration-by-parts reduction coefficients of multi-loop Feynman integrals.
Abstract: We present an efficient method to shorten the analytic integration-by-parts (IBP) reduction coefficients of multi-loop Feynman integrals. For our approach, we develop an improved version of Leinartas’ multivariate partial fraction algorithm, and provide a modern implementation based on the computer algebra system Singular. Furthermore, we observe that for an integral basis with uniform transcendental (UT) weights, the denominators of IBP reduction coefficients with respect to the UT basis are either symbol letters or polynomials purely in the spacetime dimension D. With a UT basis, the partial fraction algorithm is more efficient both with respect to its performance and the size reduction. We show that in complicated examples with existence of a UT basis, the IBP reduction coefficients size can be reduced by a factor of as large as ∼ 100. We observe that our algorithm also works well for settings without a UT basis.

35 citations

Journal ArticleDOI
TL;DR: In this paper, an improved version of Leinartas' multivariate partial fraction algorithm is presented, and an efficient method to shorten the analytic integration-by-parts reduction coefficients of multi-loop Feynman integrals.
Abstract: We present an efficient method to shorten the analytic integration-by-parts (IBP) reduction coefficients of multi-loop Feynman integrals. For our approach, we develop an improved version of Leinartas' multivariate partial fraction algorithm, and provide a modern implementation based on the computer algebra system Singular. Furthermore, We observe that for an integral basis with uniform transcendental (UT) weights, the denominators of IBP reduction coefficients with respect to the UT basis are either symbol letters or polynomials purely in the spacetime dimension $D$. With a UT basis, the partial fraction algorithm is more efficient both with respect to its performance and the size reduction. We show that in complicated examples with existence of a UT basis, the IBP reduction coefficients size can be reduced by a factor of as large as $\sim 100$. We observe that our algorithm also works well for settings without a UT basis.

12 citations

15 May 2023
TL;DR: The NeatIBP as mentioned in this paper package automatically generates small-size integration-by-parts (IBP) identities for Feynman integrals, which can subsequently be used for either finite field reduction or analytic reduction.
Abstract: In this work, we present the package {\sc NeatIBP}, which automatically generates small-size integration-by-parts (IBP) identities for Feynman integrals. Based on the syzygy and module intersection techniques, the generated IBP identities' propagator degree is controlled and thus the size of the system of IBP identities is shorter than that generated by the standard Laporta algorithm. This package is powered by the computer algebra systems {\sc Mathematica} and {\sc Singular}, and the library {\sc SpaSM}. It is parallelized on the level of Feynman integral sectors. The generated small-size IBP identities can subsequently be used for either finite field reduction or analytic reduction. We demonstrate the capabilities of this package on several multi-loop IBP examples.

3 citations

Posted Content
TL;DR: In this article, a large scale parallel implementation of the improved Leinartas' algorithm was developed, based on the GPI-Space framework, for the reduction of two-loop five-point Feynman integrals with degree-five numerators.
Abstract: In this paper, we show that with the state-of-art module intersection IBP reduction method and our improved Leinartas' algorithm, IBP relations for very complicated Feynman integrals can be solved and the analytic reduction coefficients can be dramatically simplified. We develop a large scale parallel implementation of our improved Leinartas' algorithm, based on the \textsc{Singular}/\textsc{GPI-Space} framework. We demonstrate our method by the reduction of two-loop five-point Feynman integrals with degree-five numerators, with a simple and sparse IBP system. The analytic reduction result is then greatly simplified by our improved Leinartas' algorithm to a usable form, with a compression ratio of two order of magnitudes. We further discover that the compression ratio increases with the complexity of the Feynman integrals.

Cited by
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Journal ArticleDOI
TL;DR: The precision frontier in collider physics is being pushed at impressive speed, from both the experimental and the theoretical side as discussed by the authors, and the aim of this review is to give an overview of recent developments in precision calculations within the Standard Model of particle physics, in particular in the Higgs sector.

140 citations

Journal ArticleDOI
TL;DR: AMFlow as mentioned in this paper is a Mathematica package to numerically compute dimensionally regularized Feynman integrals via the recently proposed auxiliary mass flow method, which can be obtained by constructing and solving differential systems with respect to this parameter, in an automatic way.

65 citations

Journal ArticleDOI
TL;DR: In this article, an analytic analysis of the gluon-initiated contribution to diphoton plus jet production at hadron colliders up to two loops in QCD is presented.
Abstract: We present an analytic computation of the gluon-initiated contribution to diphoton plus jet production at hadron colliders up to two loops in QCD. We reconstruct the analytic form of the finite remainders from numerical evaluations over finite fields including all colour contributions. Compact expressions are found using the pentagon function basis. We provide a fast and stable implementation for the colour- and helicity-summed interference between the one-loop and two-loop finite remainders in C++ as part of the NJet library.

52 citations

Journal ArticleDOI
TL;DR: In this article, all planar contributions to the two-loop massless helicity amplitudes for the LHC process were calculated in terms of the functional basis proposed by Chicherin and Sotnikov.
Abstract: We calculate all planar contributions to the two-loop massless helicity amplitudes for the process $$ q\overline{q} $$ → γγγ. The results are presented in fully analytic form in terms of the functional basis proposed recently by Chicherin and Sotnikov. With this publication we provide the two-loop contributions already used by us in the NNLO QCD calculation of the LHC process pp → γγγ [Chawdhry et al. (2019)]. Our results agree with a recent calculation of the same amplitude [Abreu et al. (2020)] which was performed using different techniques. We combine several modern computational techniques, notably, analytic solutions for the IBP identities, finite-field reconstruction techniques as well as the recent approach [Chen (2019)] for efficiently projecting helicity amplitudes. Our framework appears well-suited for the calculation of two-loop multileg amplitudes for which complete sets of master integrals exist.

50 citations

Journal ArticleDOI
TL;DR: In this article, the authors presented an analytic analysis of the two-loop QCD corrections to an on-shell W$ boson using the leading color and massless bottom quark approximations, and identified an independent basis of special functions that allows an analytic subtraction of the infrared and ultraviolet poles.
Abstract: We present an analytic computation of the two-loop QCD corrections to $u\overline{d}\ensuremath{\rightarrow}{W}^{+}b\overline{b}$ for an on-shell $W$ boson using the leading color and massless bottom quark approximations. We perform an integration-by-parts reduction of the unpolarized squared matrix element using finite field reconstruction techniques and identify an independent basis of special functions that allows an analytic subtraction of the infrared and ultraviolet poles. This basis is valid for all planar topologies for five-particle scattering with an off-shell leg.

40 citations