Four-pion production in e+ e- annihilation

We calculate the processes e+ e- -> 4 pions and tau -> nu_tau + 4 pions to O(p^4) in the low-energy expansion of the standard model. The chiral amplitudes of O(p^4) can be extended via resonance exchange to energies around 1 GeV. Higher-order effects have been included in the form of omega, a_1 and double rho exchange and by performing a resummation of the pion form factor. The predicted cross sections and the branching ratios BR(rho -> 4 pions) are in good agreement with available data.Comment: 24 pages, 8 figures, small changes in the text, results and conclusions unchanged, version to appear in EPJ

Low-energy expansion of the pion-nucleon Lagrangian

The renormalized pion-nucleon Lagrangian is calculated to O(p^3) in heavy baryon chiral perturbation theory. By suitably chosen transformations of the nucleon field, the Lagrangian is brought to a standard form.Comment: 10 pages, Latex, 1 figure in uuencoded postscript file embedded with epsfig.st

Parabolic methods for the construction of spacelike slices of prescribed mean curvature in cosmological spacetimes

Spacelike hypersurfaces of prescribed mean curvature in cosmological space times are constructed as asymptotic limits of a geometric evolution equation. In particular, an alternative, constructive proof is given for the existence of maximal and constant mean curvature slices

Four-pion production

Starting from the low-energy structure derived from QCD, we extend the amplitudes for four-pion production in e+ e- annihilation and tau decays up to invariant four-pion masses of 1 GeV. Cross sections and branching ratios BR(rho^0 -> 4 pi) are compared with available data.Comment: 4 pages, 3 figures, contribution to Proc. of QCD'02, Montpellier, July 2002, misprints correcte

Renormalization of chiral perturbation theory to order p^6

The renormalization of chiral perturbation theory is carried out to next-to-next-to-leading order in the meson sector. We calculate the divergent part of the generating functional of Green functions of quark currents to O(p^6) for chiral SU(n), involving one- and two-loop diagrams. The renormalization group equations for the renormalized low-energy constants of O(p^6) are derived. We compare our results with previous two-loop calculations in chiral perturbation theory.Comment: 43 pages, LaTeX2e, 1 figur

Radiative Semileptonic Kaon Decays

We evaluate the matrix elements for the radiative kaon decays $K^+ \to l^+\nu_l\gamma$, $l^+ \nu_l l'^+ l'^-$ and $K \to \pi l \nu_l\gamma$ \ ($l,\ l' = e,\mu$) to next-to-leading order in chiral perturbation theory. We calculate total rates and rates with several kinematical cuts and confront the results with existing data. Measurements at future kaon facilities will allow for a more detailed comparison between theory and experiment.Comment: LaTeX, 40 pages, 5 figures (not included), CERN-TH 6625/92, BUTP-92/3