The leading power asymptotic behaviour of the dimensionally regularized massless on-shell planar triple box diagram in the Regge limit t/s → 0 is analytically evaluated. E-mail: [email protected] Systematical analytical evaluation of two-loop Feynman diagrams with four external lines within dimensional regularization [1] began three years ago. In the pure massless case with all end-poi...

We calculate radiative corrections to the Lamb shift of order α3(Zα)5m and radiative corrections to hyperfine splitting of order α(Zα)EF generated by the diagrams with insertions of radiative photons and electron polarization loops in the graphs with two external photons. We also obtain the radiativerecoil correction to hyperfine splitting in muonium generated by the diagrams with the τ polariz...

We apply ideas motivated by string theory to improve the calculational efficiency of one-loop weak interaction processes with massive external gauge bosons. In certain cases " supersymmetry " relations between diagrams with a fermion loop and with a gauge boson loop hold. This is explicitly illustrated for a particular one-loop standard model process with four-external gauge bosons. The supersy...

Single mass scale diagrams: construction of a basis for the ε-expansion. Abstract Exploring the idea of Broadhurst on the " sixth root of unity " we present an ansatz for construction of a basis of transcendental numbers for the ε-expansion of single mass scale diagrams with two particle massive cut. As example, several new two-and three-loop master integrals are calculated.

We introduce a new technique to generate scattering amplitudes at one loop. Traditional tree algorithms, which handle diagrams with fixed momenta, are promoted to generators of loop-momentum polynomials that we call open loops. Combining open loops with tensor-integral and Ossola-Papadopoulos-Pittau reduction results in a fully flexible, very fast, and numerically stable one-loop generator. As ...

We present a full two-loop O(g6) perturbative field theoretic calculation of the expectation value of two circular Maldacena-Wilson loops in D = 4 N = 4 supersymmetric U(N) gauge theory. It is demonstrated that, after taking into account very subtle cancellations of bulk and boundary divergences, the result is completely finite without any renormalization. As opposed to previous lower order cal...

We study the unwheeled rational Kontsevich integral of torus knots. We give a precise formula for these invariants up to loop degree 3 and show that they appear as colorings of simple diagrams. We show that they behave under cyclic branched coverings in a very simple way. Our proof is combinatorial: it uses the results of Wheels and Wheelings and new decorations of diagrams.

This paper describes the impetus behind and design of a quasi-casual math puzzle game with the goal of crowdsourcing formal software verification through the analysis of loop invariants. This game, Xylem: The Code of Plants, presents players with puzzles derived from data produced by loops in a particular piece of software. Solving these puzzles involves finding and expressing a loop invariant ...

New developments concerning the extension of the recently introduced (1) Feynman diagram analyser DIANA are presented. Recent high precision experiments require, on the side of the theory, high-precision calculations resulting in the evaluation of higher loop diagrams in the Standard Model. For specific processes thousands of multiloop Feynman diagrams do contribute. Of course, the contribution...

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 package is used for the calculation of special types of diagrams. A method of calculation of higher order ε-expansion of master integrals is demonstrated. Nowada...