Related papers: Calculating three-loop diagrams in Heavy Quark Eff…
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…
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…
Methods of calculation of loop diagrams in Heavy Quark Effective Theory (HQET) are presented.
I discuss methods of calculation of propagator diagrams (massless, those of Heavy Quark Effective Theory, and massive on-shell diagrams) up to 3 loops. Integration-by-parts recurrence relations are used to reduce them to linear combinations…
We review algorithmic methods for two-loop calculations in HQET, and the analogous methods for on-shell QCD, needed for matching HQET to QCD.
We use dimensional recurrence relations and analyticity to calculate four-loop propagator-type master integrals in the heavy-quark effective theory. Compared to previous applications of the DRA method, we apply a new technique of fixing…
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.
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…
Higher order calculations in perturbative Quantum Field Theories often produce coupled linear systems of differential equations which factorize to first order. Here we present an algorithm to solve such systems in terms of iterated…
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.
Recent results and methods of three-loop calculations in HQET are reviewed.
The implementation of an algorithm for three-loop massive vacuum integrals, based on the explicit solution of the recurrence relations, in REDUCE and FORM is described.
The one-loop HQET heavy-heavy vertex diagram with arbitrary powers of all three denominators and arbitrary residual energies is investigated. Various particular cases in which the result becomes simpler are considered.
We consider the currents formed by a heavy and a light quark within Quantum Chromodynamics and compute the matching to Heavy Quark Effective Theory to three-loop accuracy. As an application we obtain the third-order perturbative corrections…
An exact expression for the master integral I_2 arising in three-loop on-shell HQET propagator diagrams with mass is derived and its analytical expansion in the dimensional regularization parameter epsilon is given.
A recently proposed method of calculating scalar two-loop propagator and vertex functions with massive particles is illustrated with simple examples. A double integral representation is derived with the example of a propagator function. An…
A set of recurrence relations for on-shell two-loop self-energy diagrams with one mass is presented, which allows to reduce the diagrams with arbitrary indices (powers of scalar propagators) to a set of the master integrals. The SHELL2…
An algorithm for calculating two-loop propagator type Feynman diagrams with arbitrary masses and external momentum is proposed. Recurrence relations allowing to express any scalar integral in terms of basic integrals are given. A minimal…
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…
A new approach is presented to evaluate multi-loop integrals, which appear in the calculation of cross-sections in high-energy physics. It relies on a fully numerical method and is applicable to a wide class of integrals with various mass…