Master integrals with 2 and 3 massive propagators for the 2-loop electroweak form factor - planar case

We compute the master integrals containing 2 and 3 massive propagators entering the planar amplitudes of the 2-loop electroweak form factor. The masses of the $W$, $Z$ and Higgs bosons are assumed to be degenerate. This work is a continuation of our previous evaluation of master integrals containing at most 1 massive propagator. The 1/\epsilon poles and the finite parts are computed exactly in terms of a {\it new} class of 1-dimensional harmonic polylogarithms of the variable x, with \epsilon=2-D/2 and D the pace-time dimension. Since thresholds and pseudothresholds in s=\pm 4m^2 do appear in addition to the old ones in s=0,\pm m^2, an extension of the basis function set involving complex constants and radicals is introduced, together with a set of recursion equations to reduce integrals with semi-integer powers. It is shown that the basic properties of the harmonic polylogarithms are maintained by the generalization. We derive small-momentum expansions |s| << m^2 of all the 6-denominator amplitudes. We also present large momentum expansions |s| >> m^2 of all the 6-denominator amplitudes which can be represented in terms of ordinary harmonic polylogarithms. Comparison with previous results in the literature is performed finding complete agreement.Comment: 68 pages, 7 figure

The Uehling correction to the energy levels in a pionic atom

We consider a correction to energy levels in a pionic atom induced by the Uehling potential, i.e., by a free electron vacuum-polarization loop. The calculation is performed for circular states (l=n-1). The result is obtained in a closed analytic form as a function of $Z\alpha$ and the pion-to-electron mass ratio. Certain asymptotics of the result are also presented

Explicit results for all orders of the epsilon-expansion of certain massive and massless diagrams

An arbitrary term of the epsilon-expansion of dimensionally regulated off-shell massless one-loop three-point Feynman diagram is expressed in terms of log-sine integrals related to the polylogarithms. Using magic connection between these diagrams and two-loop massive vacuum diagrams, the epsilon-expansion of the latter is also obtained, for arbitrary values of the masses. The problem of analytic continuation is also discussed.Comment: 8 pages, late

Final State Radiative Effects for the Exact O(alpha) YFS Exponentiated (Un)Stable W+W- Production At and Beyond LEP2 Energies

We present the LL final state radiative effects for the exact O(alpha) YFS exponentiated (un)stable WW pair production at LEP2/NLC energies using Monte Carlo event generator methods. The respective event generator, version 1.12 of the program YFSWW3, wherein both Standard Model and anomalous triple gauge boson couplings are allowed, generates n(\gamma) radiation both from the initial state and from the intermediate W+ W- and generates the LL final state W decay radiative effects. Sample Monte Carlo data are illustrated.Comment: 16 pages, 8 figures, 2 table

The Two Loop Crossed Ladder Vertex Diagram with Two Massive Exchanges

We compute the (three) master integrals for the crossed ladder diagram with two exchanged quanta of equal mass. The differential equations obeyed by the master integrals are used to generate power series expansions centered around all the singular (plus some regular) points, which are then matched numerically with high accuracy. The expansions allow a fast and precise numerical calculation of the three master integrals (better than 15 digits with less than 30 terms in the whole real axis). A conspicuous relation with the equal-mass sunrise in two dimensions is found. Comparison with a previous large momentum expansion is made finding complete agreement.Comment: 42 pages, 1 figur