HYPERgeometric functions DIfferential REduction: MATHEMATICA based packages for differential reduction of generalized hypergeometric functions: Horn hypergeometric functions of two variables

HYPERDIRE is a project devoted to the creation of a set of Mathematica-based programs for the differential reduction of hypergeometric functions. The current version allows for manipulations involving the full set of Horn-type hypergeometric functions of two variables, including 30 functions.

When epsilon-expansion of hypergeometric functions is expressible in terms of multiple polylogarithms: the two-variables examples

In this talk, we discuss the algorithm for the construction of analytical coefficients of higher order epsilon expansion of some Horn type hypergeometric functions of two variables around rational values of parameters.

Annihilation of $bar p+pto e^++e^-+ pi^0$ and $bar p+pto gamma + pi^0$ through $omega$-meson intermediate state

The s-channel annihilation of proton and antiproton into a neutral pion and a real or virtual photon followed by lepton pair emission is studied. Such mechanism is expected to play a role at moderate values of the total energy $sqrt{s}$, when the pion is emitted around $90^{circ}$ in the center of mass. A fair comparison with the existing data is obtained taking into account scattering and annihilation channels. The cross section is calculated and numerical results are given in the kinematical range accessible in the PANDA experiment at FAIR.

Differential reduction of generalized hypergeometric functions from Feynman diagrams: One-variable case

The differential-reduction algorithm, which allows one to express generalized hypergeometric functions with parameters of arbitrary values in terms of such functions with parameters whose values differ from the original ones by integers, is discussed in the context of evaluating Feynman diagrams. Where this is possible, we compare our results with those obtained using standard techniques. It is shown that the criterion of reducibility of multiloop Feynman integrals can be reformulated in terms of the criterion of reducibility of hypergeometric functions. The relation between the numbers of master integrals obtained by differential reduction and integration by parts is discussed.

Differential Reduction Algorithms for Hypergeometric Functions Applied to Feynman Diagram Calculation

We describe the application of differential reduction algorithms for Feynman Diagram calculation. We illustrate the procedure in the context of generalized hypergeometric functions, and give an example for a type of q-loop bubble diagram.