Related papers: HQET heavy-heavy vertex diagram with two velocitie…
Differential equations for the one-loop HQET vertex diagram with arbitrary self-energy insertions and arbitrary residual energies are reduced to the $\varepsilon$ form and used to obtain the $\varepsilon$ expansion in terms of Goncharov…
Methods of calculation of loop diagrams in Heavy Quark Effective Theory (HQET) are presented.
Three-loop vertex diagrams in HQET needed for sum rules for B^0 - \bar{B}^0 mixing are considered. They depend on two residual energies. An algorithm of reduction of these diagrams to master integrals has been constructed. All master…
After a brief introduction to Heavy Quark Effective Theory, we discuss $\alpha$ representation in HQET and methods of calculation of some kinds of HQET diagrams up to three loops.
Recent results and methods of three-loop calculations in HQET are reviewed.
Recently, algorithms for calculation of 3-loop propagator diagrams in HQET and on-shell QCD with a heavy quark have been constructed and implemented. These algorithms (based on integration by parts recurrence relations) reduce an arbitrary…
We give a complete analytical computation of three-point one-loop integrals with one heavy propagator, up to the third tensor rank, for arbitrary values of external momenta and masses.
We review algorithmic methods for two-loop calculations in HQET, and the analogous methods for on-shell QCD, needed for matching HQET to QCD.
An algorithm for calculation of three-loop propagator diagrams in HQET, based on integration-by-parts recurrence relations, is constructed and implemented as a REDUCE package Grinder, and in Axiom.
Effective field theories such as Heavy Quark Effective Theory (HQET) are indispensable tools in controlling the effects of the strong interaction. The increasing experimental precision requires the knowledge of higher dimensional operators.…
Three-loop propagator diagrams in HQET can be reduced, using integration by parts, to 8 basis integrals: 5 trivial ones, two expressible via 3F2, and one only known up to \epsilon^0. Calculation of the heavy-quark propagator in HQET is…
We determine the master integrals for vertex and propagator diagrams that appear in effective field theories containing heavy fields. The integrals involve at least one heavy line, and the standard lines include an arbitrary mass scale. The…
Small momentum expansion of the "sunset" diagram with three different masses is obtained. Coefficients at powers of $p^2$ are evaluated explicitly in terms of dilogarithms and elementary functions. Also some power expansions of "sunset"…
The perturbative contribution to the correlator of two HQET heavy-light currents expanded in light-quark masses up to quadratic terms is calculated up to 4 loops. The leading large-$\beta_0$ limit is also considered, so that terms with the…
We give a complete analytical computation of three and two-point loop integrals occurring in heavy-particle theories, involving a velocity change, for arbitrary real values of the external masses and residual momenta.
We present a calculation of the renormalized heavy-light and heavy-heavy currents in HQET at order O(1/m_Q^2).
Extending the method successful for one-loop integrals, the computation of two-loop diagrams with general internal masses is discussed. For the two-loop vertex of non-planar type, as an example, we show a calculation related to…
A weighted graph is a graph in which every edge is assigned a non-negative real number. In a weighted graph, the weight of a path is the sum of the weights of its edges, and the weighed degree of a vertex is the sum of the weights of the…
Problems occurring in physically important non-trivial examples of loop calculations are discussed. A procedure of deriving expansions of two-loop self-energy diagrams with different masses is constructed. The cases of small and large…
We give the results of complete analytical computations of two- and three-point loop integrals ocurring in heavy particle theories, with and without velocity change, for arbitrary values of external momenta and masses.