Four Pion Final States with Tagged Photons at Electron Positron Colliders

A Monte Carlo generator has been constructed to simulate the reaction e^+e^- \to \gamma + 4 \pi, where the photon is assumed to be observed in the detector. Only initial state radiation is considered. Additional collinear photon radiation has been incorporated with the technique of structure functions. Predictions are presented for cms energies of 1GeV, 3GeV and 10GeV, corresponding to the energies of DAPHNE, BEBC and of B-meson factories. The event rates are sufficiently high to allow for a precise measurement of R(Q^2) in the region of Q between approximately 1GeV and 2.5GeV. For the construction of the program we employ isospin relations between the amplitudes governing tau decays into four pions and electron positron annihilation into four pions. Estimates of the kinematic breaking of these isospin relations as a consequence of the \pi^- -- \pi^0 mass difference are given.Comment: LATEX, 27 pages, 9 figures, discussion of the kinematic breaking of isospin relations extended, typos corrected, some formulations change

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

Precision measurement of the hadronic cross-section through the radiative return method

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 at high luminosity meson factories. Weighted integrals over this cross-section are a decisive input for electroweak precision tests. A Monte Carlo event generator called PHOKHARA has been developed, which simulates $e^+ e^- \to$ hadrons + photon(s) at the NLO accuracy. The latest tests and upgrades are presented in this paper.Comment: Talk given at 7th International Workshop on Tau Lepton Physics (TAU 02), Santa Cruz, California, 10-13 Sep 2002. TAU-2002-WE06. 10 pages, 12 figure

Radiative return method as a tool in hadronic physics

A short review of both theoretical and experimental aspects of the radiative return method is presented. It is emphasised that the method gives not only possibility of the independent from the scan method measurement of the hadronic cross section, but also can provide information concerning details of the hadronic interactions. New developments in the PHOKHARA event generator are also reviewed. The 3 pion and kaon pair production is implemented within the version 5.0 of the program, together with contributions of the radiative phi decays to the 2 pion final states. Missing NLO radiative corrections to the e+e- -> mu+ mu- gamma process will be implemented in the forthcoming version of the generator

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