M.Yu. Kalmykov

Massive Feynman diagrams and inverse binomial sums

Abstract When calculating higher terms of the ɛ -expansion of massive Feynman diagrams, one needs to evaluate particular cases of multiple inverse binomial sums. These sums are related to the derivatives of certain hypergeometric functions with respect to their parameters. Exploring this connection and using it together with an approach based on generating functions, we analytically calculate a number of such infinite sums, for an arbitrary value of the argument which corresponds to an arbitrary value of the off-shell external momentum. In such a way, we find a number of new results for physically important Feynman diagrams. Considered examples include two-loop two- and three-point diagrams, as well as three-loop vacuum diagrams with two different masses. The results are presented in terms of generalized polylogarithmic functions. As a physical example, higher-order terms of the ɛ -expansion of the polarization function of the neutral gauge bosons are constructed.

New results for the ε-expansion of certain one-, two- and three-loop Feynman diagrams

Abstract For certain dimensionally-regulated one-, two- and three-loop diagrams, problems of constructing the e -expansion and the analytic continuation of the results are studied. In some examples, an arbitrary term of the e -expansion can be calculated. For more complicated cases, only a few higher terms in e are obtained. Apart from the one-loop two- and three-point diagrams, the examples include two-loop (mainly on-shell) propagator-type diagrams and three-loop vacuum diagrams. As a by-product, some new relations involving Clausen function, generalized log-sine integrals and certain Euler–Zagier sums are established, and some useful results for the hypergeometric functions of argument 1 4 are presented.

vs. pole masses of gauge bosons II: two-loop electroweak fermion corrections

We have calculated the fermion contributions to the shift of the position of the poles of the massive gauge boson propagators at two-loop order in the Standard Model. Together with the bosonic contributions calculated previously the full two-loop corrections are available. This allows us to investigate the full correction in the relationship between MS and pole masses of the vector bosons Z and W. Two-loop renormalization and the corresponding renormalization group equations are discussed. Analytical results for the master-integrals appearing in the massless fermion contributions are given. A new approach of summing multiple binomial sums has been developed.Abstract We have calculated the fermion contributions to the shift of the position of the poles of the massive gauge boson propagators at two-loop order in the Standard Model. Together with the bosonic contributions calculated previously the full two-loop corrections are available. This allows us to investigate the full correction in the relationship between MS and pole masses of the vector bosons Z and W . Two-loop renormalization and the corresponding renormalization group equations are discussed. Analytical results for the master-integrals appearing in the massless fermion contributions are given. A new approach of summing multiple binomial sums has been developed.

Pole masses of quarks in-dimensional reduction

Abstract Pole masses of quarks in quantum chromodynamics are calculated to two-loop order in the framework of the regularization by dimensional reduction. For the diagram with a light quark loop, the non-Euclidean asymptotic expansion is constructed with the external momentum on the mass shell of a heavy quark.

MS vs. pole masses of gauge bosons: electroweak bosonic two-loop corrections

The relationship between MS and pole masses of the vector bosons Z and W is calculated at the two-loop level in the Standard Model. We only consider the purely bosonic contributions which represent a gauge invariant subclass of diagrams. All calculations were performed in the linear Rξ gauge with three arbitrary gauge parameters utilizing the method of asymptotic expansions. The results are presented in analytic form as series in the small parameters sin 2 �W and the mass ratio m 2 /m 2 . We also present the corresponding on-shell mass counter-terms for the massive gauge bosons, which will be needed for the calculation of observables at two-loops in the on-shell renormalization scheme.The relationship between MS and pole masses of the vector bosons Z and W is calculated at the two-loop level in the Standard Model. We only consider the purely bosonic contributions which represents a gauge invariant subclass of diagrams. All calculations were performed in the linear

The O(ααs) correction to the pole mass of the t-quark within the Standard Model

R_\xi

Single-scale diagrams and multiple binomial sums

gauge with three arbitrary gauge parameters utilizing the method of asymptotic expansions. The results are presented in analytic form as series in the small parameters

Two-loop self-energy master integrals on shell

\sin^2\theta_W

ON-SHELL2: FORM based package for the calculation of two-loop self-energy single scale Feynman diagrams occurring in the Standard Model

and mass ratio

Single-mass-scale diagrams: construction of a basis for the ε-expansion

m_Z^2/m_H^2