arXiv subjects
Publications and source records attributed to P. A. Baikov.
The integration by parts recurrence relations allow to reduce some Feynman integrals to more simple ones (with some lines missing). Nevertheless the possibility of such reduction for the given particular integral was unclear. The recently proposed technique for studying the recurrence relations as by-product provides with simple criterion of the irreducibility.
The systematic approach to solving the recurrence relations for multi-loop integrals is described. In particular, the criteria of their reducibility is suggested.
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 CompHEP package was developed for calculations of decay and high energy collision processes with, correspondingly, up to 5 and 4 final particles in the lowest order (tree) approximation. The main idea put into CompHEP was to make available passing from the Lagrangian to final distributions efficiently with high level automation what is extremely needed in collider physics. The present talk describes a general structure of the CompHEP facilities and reports some physical results obtained with its help. The main purpose of the talk is to attract the attention of high energy physicists to this user-friendly package which is completely aimed at making easier their routine and tedious calculations in the TeV region.
The approach to the constructing explicit solutions of the recurrence relations for multi-loop integrals are suggested. The resulting formulas demonstrate a high efficiency, at least for 3-loop vacuum integrals case. They also produce a new type of recurrence relations over the space-time dimension.
Explicit formulas for solutions of recurrence relations for 3--loop vacuum integrals are generalized for the $n$-loop case.
Explicit formulas for the solutions of the recurrence relations for 3--loop vacuum integrals are suggested. This formulas can be used for direct calculations and demonstrate a high efficiency. They also produce a new type of recurrence relations over the space--time dimension.
Three--loop contributions to massive QED vacuum polarization are evaluated by a combination of analytical and numerical techniques. The first three Taylor coefficients, at small $q^2$, are obtained analytically, using $d$\/--dimensional recurrence relations. Combining these with analytical input at threshold, and at large $q^2$, an accurate Padé approximation is obtained, for all $q^2$. Inserting this in the one--loop diagram for the muon anomalous magnetic moment, we find reasonable agreement with four--loop, single--electron--loop, muon--anomaly contributions, recently re--evaluated by Kinoshita, using 8--dimensional Monte--Carlo integration. We believe that our new method is at least two orders of magnitude more accurate than the Monte--Carlo approach, whose uncertainties appear to have been underestimated, by a factor of 6.
The coefficient functions of the gluon condensate $ $, in the correlators of heavy-quark vector, axial, scalar and pseudoscalar currents, are obtained analytically, to two loops, for all values of $z=q^2/4m^2$. In the limiting cases $z\to0$, $z\to1$, and $z\to-\infty$, comparisons are made with previous partial results. Approximation methods, based on these limiting cases, are critically assessed, with a view to three-loop work. High accuracy is achieved using a few moments as input. A {\em single} moment, combined with only the {\em leading} threshold and asymptotic behaviours, gives the two-loop corrections to better than 1% in the next 10 moments. A two-loop fit to vector data yields $<\frac{α_{\rm s}}πG^2>\approx0.021$ GeV$^4$.