Why and how to use a differential equation method to calculate multi-loop integrals

A short pedagogical introduction to a differential method used to calculate multi-loop scalar integrals is presented. As an example it is shown how to obtain, using the method, large mass expansion of the two loop sunrise master integrals.Comment: 9 p., presented at XXV International Conference on Theoretical Physics "Particle Physics and Astrophysics in the Standard Models and Beyond", Ustron, Poland, September 200

Radiative return at NLO and the measurement of the hadronic cross-section in electron-positron annihilation

Electron-positron annihilation into hadrons plus an energetic photon from initial state radiation allows the hadronic cross-section to be measured over a wide range of energies. The full next-to-leading order QED corrections for the cross-section for e^+ e^- annihilation into a real tagged photon and a virtual photon converting into hadrons are calculated where the tagged photon is radiated off the initial electron or positron. This includes virtual and soft photon corrections to the process e^+ e^- \to \gamma +\gamma^* and the emission of two real hard photons: e^+ e^- \to \gamma + \gamma + \gamma^*. A Monte Carlo generator has been constructed, which incorporates these corrections and simulates the production of two charged pions or muons plus one or two photons. Predictions are presented for centre-of-mass energies between 1 and 10 GeV, corresponding to the energies of DAPHNE, CLEO-C and B-meson factories.Comment: 13 pages, 15 figure

Electron-positron annihilation into phi f_{0}(980) and clues for a new 1^{--} resonance

We study the e^{+}e^{-} to phi pi pi reaction for pions in an isoscalar s-wave which is dominated by loop mechanisms. For kaon loops we start from the conventional RCHPT, but use the unitarized amplitude for KbarK-pipi scattering and the full kaon form factor instead of the lowest order terms. We study also effects of vector mesons using RCHPT supplemented with the conventional anomalous term for VVP interactions and taking into account the effects of heavy vector mesons in the K*K transition form factor. We find a peak in the dipion invariant mass around the f_{0}(980) as in the experiment. Selecting the phi f_{0}(980) contribution as a function of the e^{+}e^{-} energy we also reproduce the experimental data except for a narrow peak, yielding support to the existence of a 1^{--} resonance above the phi f_{0}(980) threshold, coupling strongly to this state.Comment: 18 pages, 4 figure

Proton-nucleus cross section at high energies

Cross sections for proton inelastic collision with different nuclei are described within the Glauber and multiple scattering approximations. A significant difference between approximate `Glauber' formula and exact calculations with a geometrical scaling assumption for very high-energy cross section is shown. Experimental values of proton-proton cross sections obtained using extensive air shower data are based on the relationship of proton-proton and respective proton-air absorption cross sections. According to obtained results values reported by the Akeno and Fly's Eye experimental groups are about 10% overestimated. The proper energy dependence of absorption cross section for collisions with air nuclei is of a great importance for studies of high energy cosmic rays using the Monte Carlo technique.Comment: 9pp (9 eps figures

Master Equations for Master Amplitudes

The general lines of the derivation and the main properties of the master equations for the master amplitudes associated to a given Feynman graph are recalled. Some results for the 2-loop self-mass graph with 4 propagators are then presented