Feynman integrals(FIs)serve as fundamental components of perturbative quantum field theory.The study of FIs is important for both exploring the mysteries of quantum field theories and their phenomenological applicatio...Feynman integrals(FIs)serve as fundamental components of perturbative quantum field theory.The study of FIs is important for both exploring the mysteries of quantum field theories and their phenomenological applications,particularly in particle physics.A significant amount of effort has been devoted to analytically calculating FIs,with the goal of expressing them as linear combinations of special functions.展开更多
We extend the auxiliary-mass-flow(AMF) method originally developed for Feynman loop integration to calculate integrals which also involve phase-space integration.The flow of the auxiliary mass from the boundary(∞) to...We extend the auxiliary-mass-flow(AMF) method originally developed for Feynman loop integration to calculate integrals which also involve phase-space integration.The flow of the auxiliary mass from the boundary(∞) to the physical point(0+) is obtained by numerically solving differential equations with respective to the auxiliary mass.For problems with two or more kinematical invariants,the AMF method can be combined with the traditional differential-equation method,providing systematic boundary conditions and a highly nontrivial self-consistency check.The method is described in detail using a pedagogical example of e+e-→γ*→tt+X at NNLO.We show that the AMF method can systematically and efficiently calculate integrals to high precision.展开更多
We study the triply heavy baryonsΩ_(QQQ)(Q=c,b)in the QCD sum rules by performing the first calculation of the next-to-leading order(NLO)contribution to the perturbative QCD part of the correlation functions.Compared...We study the triply heavy baryonsΩ_(QQQ)(Q=c,b)in the QCD sum rules by performing the first calculation of the next-to-leading order(NLO)contribution to the perturbative QCD part of the correlation functions.Compared with the leading order(LO)result,the NLO contribution is found to be very important to theΩ_(QQQ).This is because the NLO not only results in a large correction but also reduces the parameter dependence,making the Borel platform more distinct,especially for the Q_(bbb)in the MS scheme,where the platform appears only at NLO but not at LO.Particularly,owing to the inclusion of the NLO contribution,the renormalization schemes(MS and On-Shell)dependence and the scale dependence are significantly reduced.Consequently,after including the NLO contribution to the perturbative part in the QCD sum rules,the masses are estimated to be 4.53_)0.11)^(+0.26) GeV forΩ_(ccc) and14.27_(-0.32)^(+0.33) GeV forΩ_(bbb),where the results are obtained atμ=M_(B) with errors including those from the variation of the renormalization scaleμin the range(0.8-1.2)M_(B).A careful study of theμdependence in a wider range is further performed,which shows that the LO results are very sensitive to the choice ofμwhereas the NLO results are considerably better.In addition to theμ=M_(B) result,a more stable value,(4.75-4.80)GeV,for theΩ_(ccc) mass is found in the range ofμ=(1.2-2.0)M_(B),which should be viewed as a more relevant prediction in our NLO approach because of μ dependence.展开更多
基金supported by the National Natural Science Foundation of China(12325503,and 11975029)the National Key Research and Development Program of China(2020YFA0406400)+1 种基金the China Postdoctoral Science Foundation(2023M733123,and 2023TQ0282)the Postdoctoral Fellowship Program of China Postdoctoral Science Foundation。
文摘Feynman integrals(FIs)serve as fundamental components of perturbative quantum field theory.The study of FIs is important for both exploring the mysteries of quantum field theories and their phenomenological applications,particularly in particle physics.A significant amount of effort has been devoted to analytically calculating FIs,with the goal of expressing them as linear combinations of special functions.
基金Supported in part by the National Natural Science Foundation of China(11875071,11975029)the High-performance Computing Platform of Peking University。
文摘We extend the auxiliary-mass-flow(AMF) method originally developed for Feynman loop integration to calculate integrals which also involve phase-space integration.The flow of the auxiliary mass from the boundary(∞) to the physical point(0+) is obtained by numerically solving differential equations with respective to the auxiliary mass.For problems with two or more kinematical invariants,the AMF method can be combined with the traditional differential-equation method,providing systematic boundary conditions and a highly nontrivial self-consistency check.The method is described in detail using a pedagogical example of e+e-→γ*→tt+X at NNLO.We show that the AMF method can systematically and efficiently calculate integrals to high precision.
基金Supported in part by the National Natural Science Foundation of China(11875071,11975029)the National Key Research and Development Program of China(2020YFA0406400)。
文摘We study the triply heavy baryonsΩ_(QQQ)(Q=c,b)in the QCD sum rules by performing the first calculation of the next-to-leading order(NLO)contribution to the perturbative QCD part of the correlation functions.Compared with the leading order(LO)result,the NLO contribution is found to be very important to theΩ_(QQQ).This is because the NLO not only results in a large correction but also reduces the parameter dependence,making the Borel platform more distinct,especially for the Q_(bbb)in the MS scheme,where the platform appears only at NLO but not at LO.Particularly,owing to the inclusion of the NLO contribution,the renormalization schemes(MS and On-Shell)dependence and the scale dependence are significantly reduced.Consequently,after including the NLO contribution to the perturbative part in the QCD sum rules,the masses are estimated to be 4.53_)0.11)^(+0.26) GeV forΩ_(ccc) and14.27_(-0.32)^(+0.33) GeV forΩ_(bbb),where the results are obtained atμ=M_(B) with errors including those from the variation of the renormalization scaleμin the range(0.8-1.2)M_(B).A careful study of theμdependence in a wider range is further performed,which shows that the LO results are very sensitive to the choice ofμwhereas the NLO results are considerably better.In addition to theμ=M_(B) result,a more stable value,(4.75-4.80)GeV,for theΩ_(ccc) mass is found in the range ofμ=(1.2-2.0)M_(B),which should be viewed as a more relevant prediction in our NLO approach because of μ dependence.
