Evaluating the last missing ingredient for the three-loop quark static potential by differential equations

被引:0
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作者
Roman N. Lee
Vladimir A. Smirnov
机构
[1] Budker Institute of Nuclear Physics,Skobeltsyn Institute of Nuclear Physics
[2] Moscow State University,undefined
来源
Journal of High Energy Physics | / 2016卷
关键词
NLO Computations; QCD Phenomenology;
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摘要
We analytically evaluate the three-loop Feynman integral which was the last missing ingredient for the analytical evaluation of the three-loop quark static potential. To evaluate the integral we introduce an auxiliary parameter y, which corresponds to the residual energy in some of the HQET propagators. We construct a differential system for 109 master integrals depending on y and fix boundary conditions from the asymptotic behaviour in the limit y → ∞. The original integral is recovered from the limit y → 0. To solve these linear differential equations we try to find an ϵ-form of the differential system. Though this step appears to be, strictly speaking, not possible, we succeed to find an ϵ-form of all irreducible diagonal blocks, which is sufficient for solving the differential system in terms of an ϵ expansion. We find a solution up to weight six in terms of multiple polylogarithms and obtain an analytical result for the required three-loop Feynman integral by taking the limit y → 0. As a by-product, we obtain analytical results for some Feynman integrals typical for HQET.
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