We present results for the relation between a heavy quark mass defined in on-shell and minimal subtraction (MS[over ¯]) scheme to four-loop order. The method compute integral is briefly described new are used establish relations various short-distance masses MS[over ¯] next-to-next-to-next-to-leading order accuracy. These play an important role accurate determination of masses.

We compute the form factors of photon-quark-anti-quark vertex and effective a Higgs-boson two gluons to three-loop order within massless perturbative quantum chromodynamics. These results provide building blocks for many third-order cross sections. Furthermore, this is first calculation complete corrections.

We compute the three-loop corrections to potential of two heavy quarks. In particular we consider in this Letter purely gluonic contribution which provides combination with fermion Ref. \cite{Smirnov:2008pn} complete answer at three loops.

One of the two existing strategies resolving singularities multifold Mellin-Barnes integrals in dimensional regularization parameter, or a parameter analytic regularization, is formulated modified form. The corresponding algorithm implemented as Mathematica code MBresolve.m

We demonstrate that pure N=4 supergravity is ultraviolet divergent at four loops. The form of the divergence suggests it due to rigid U(1) duality-symmetry anomaly theory. This first known example an in a ungauged theory dimensions. use duality between color and kinematics construct integrand four-loop four-point amplitude, whose then extracted by standard integration techniques.

We evaluate a Laurent expansion in dimensional regularization parameter $ε=(4-d)/2$ of all the master integrals for four-loop massless propagators up to transcendentality weight twelve, using recently developed method one present coauthors (R.L.) and extending thereby results by Baikov Chetyrkin obtained at seven. observe only multiple zeta values our results. Therefore, we conclude that propagator integrals, with any integer powers numerators propagators, have their epsilon expansions twelve.

We present an algorithm that reveals relevant contributions in non-threshold-type asymptotic expansion of Feynman integrals about a small parameter. It is shown the problem reduces to finding convex hull set points multidimensional vector space.

In this paper we compute the relation between heavy quark masses defined in modified minimal subtraction and on-shell scheme. Detailed results are presented for all coefficients of SU$(N_c)$ colour factors. The reduction four-loop integrals is performed a general QCD gauge parameter. Some about 380 master computed analytically, others with high numerical precision based on Mellin-Barnes representations, rest numerically help {\tt FIESTA}. We discuss detail precise evaluation integrals....

We compute the four-loop QCD corrections to massless quark-anti-quark-photon form factor F q in large-N c limit. From pole part we extract analytic expressions for corresponding cusp and collinear anomalous dimensions.

A bstract We analytically compute the four-loop QCD corrections for colour structure ( d F abcd ) 2 to massless non-singlet quark form factor. The computation involves non-trivial non-planar integral families which have master integrals in top sector. by introducing a second mass scale and solving differential equations with respect ratio of two scales. present details our calculational procedure. Analytical results cusp collinear anomalous dimensions, finite part factor are presented. also...

We compute the potential-photon contributions to classical relativistic scattering angle of two charged nonspinning bodies in electrodynamics through fifth order coupling. use amplitudes framework, effective field theory, and multiloop integration techniques based on by parts differential equations. At order, result is expressed terms cyclotomic polylogarithms. Our calculation demonstrates feasibility corresponding calculations general relativity, including evaluation encountered four-loop integrals.

We consider the three-loop corrections to static potential which are induced by a closed fermion loop. For reduction of occurring integrals combination Gröbner and Laporta algorithm has been used evaluation master performed with help Mellin–Barnes technique. The fermionic amount 2% tree-level result for top quarks, 8% bottom quarks 27% charm quark system.

We describe several techniques for the calculation of multi-loop integrals and their application to heavy quark current correlators. As new results, we present four-loop correction second third physical moment in low-energy expansions vector, axial-vector scalar Using a Ward identity, obtain fourth pseudo-scalar correlator. briefly discuss impact these results on determination charm mass strong coupling constant using lattice simulations correlators charm- bottom-quark from experimental data...