Related papers: Quark mass relations to four-loop order
In this contribution we discuss the four-loop relation between the on-shell and $\bar{\rm MS}$ definition of heavy quark masses which is applied to the top, bottom and charm case. We also present relations between the $\bar{\rm MS}$ quark…
In this paper we compute the relation between heavy quark masses defined in the modified minimal subtraction and on-shell scheme. Detailed results are presented for all coefficients of the SU$(N_c)$ colour factors. The reduction of the…
The relation between the on-shell quark mass and the mass defined in the modified minimal subtraction scheme is computed up to order \alpha_s^3. Implications for the numerical values of the top and bottom quark masses are discussed. We show…
The relation between the on-shell and $\bar{\rm MS}$ mass can be expressed through scalar and vector part of the quark propagator. In principle these two-point functions have to be evaluated on-shell which is a non-trivial task at…
We discuss a practical approach to compute master integrals entering physical quantities which depend on one parameter. As an example we consider four-loop QCD corrections to the relation between a heavy quark mass defined in the…
We compute the relation between the pole mass and the kinetic mass of a heavy quark to three loops. Using the known relation between the pole and the $\overline{\rm MS}$ mass we obtain precise conversion relations between the $\overline{\rm…
We compute three-loop corrections to the relation between the heavy quark masses defined in the pole and kinetic schemes. Using known relations between the pole and $\overline{\rm MS}$ quark masses we can establish precise relations between…
The asymptotic structure of the QCD perturbative relation between the on-shell and $\overline{\rm{MS}}$ heavy quark masses is studied. We estimate the five and six-loop contributions to this relation by three different techniques. First,…
In this paper, we explore the properties of the bottom-quark on-shell mass ($M_b$) by using its relation to the $\overline{\rm MS}$ mass (${\overline m}_b$). At present, this $\overline{\rm MS}$-on-shell relation has been known up to…
The analytic relation between the \bar {MS} and the pole quark masses is computed to O(\alpha_s^3) in QCD. Using this exact result, the accuracy of the large \beta_0 approximation is critically examined and the implications of the obtained…
We describe a method to numerically compute multi-loop integrals, depending on one dimensionless parameter $x$ and the dimension $d$, in the whole kinematic range of $x$. The method is based on differential equations, which, however, do not…
The one-loop off-shell massive quark contribution to the three-gluon vertex is calculated in an arbitrary space-time dimension. The results for all relevant on-shell and symmetric limits are obtained directly from the general off-shell…
In these proceedings we discuss the relation between the kinetic and the on-shell schemes for the bottom and the charm quarks and present the methods for the calculation of the mass relation to higher orders in perturbative QCD. The bottom…
The summary of the available semi-analytical results for the three-loop corrections to the QCD static potential and for the $\mathcal{O}(\alpha_s^4)$ contributions to the ratio of the running and pole heavy quark masses are presented. The…
We present the three-loop QCD+QED mixed corrections to the on-shell quark mass and wave-function renormalization constants through orders $\mathcal{O}(\alpha_s^m\alpha^n)$ with $m+n=3$. We further derive the three-loop relation between the…
We estimate the presently unknown constant in the 4-loop relation between the quark pole mass and the MSbar mass, by requiring stability of the perturbative prediction for E_tot(r)=2m_pole+V_QCD(r) in the intermediate-distance region. The…
The QCD/HQET matching coefficient for the heavy-quark field is calculated up to four loops. It must be finite; this requirement produces analytical results for some terms in the four-loop on-shell heavy-quark field renormalization constant…
We combine the known asymptotic behaviour of the QCD perturbation series expansion, which relates the pole mass of a heavy quark to the MSbar mass, with the exact series coefficients up to the four-loop order to determine the ultimate…
The effective charges motivated method is applied to the relation between pole and $\rm{\overline{MS}}$-scheme heavy quark masses to study high order perturbative QCD corrections in the observable quantities proportional to the running…
The impact of recent multi-loop calculations on precise determinations of charm- and bottom-quark masses and the strong coupling constant is discussed.