Regge analysis of pion-pion (and pion-kaon) scattering for energy s^{1/2}>1.4 GeV

We perform a detailed Regge analysis of NN, pion-N and pion-pion scattering. From it, we find expressions that represent the pion-pion scattering amplitudes with an accuracy of a few percent, for exchange of isospin zero, and $\sim15$ for exchange of isospin 1, and this for energies s^{1/2}> 1.4 GeV and for momentum transfers |t|^{1/2}< 0.4 GeV. These Regge formulas are perfectly compatible with the low energy (s^{1/2}< 1.4 GeV) scattering amplitudes deduced from pion-pion phase shift analyses as well as with higher energy (s^{1/2}>1.4 GeV) experimental pion-pion cross sections. They are also compatible with NN and pion-N experimental cross sections using factorization, a property that we check with great precision. This contrasts with results from phase shift analyses of the pion-pion scattering amplitude which bear little resemblance to reality in the region $1.4<s^{1/2}<2 GeV$, as they are not well defined and increasingly violate a number of physical requirements as energy grows. Pion-kaon scattering is also considered, and we present a Regge analysis for these processes valid for energies s^{1/2}>1.7 GeV. As a byproduct of our analysis we present also a fit of $NN$, $\pi N$ and $KN$ cross sections valid from c.m. kinetic energy $E_{\rm kin}\simeq1$ GeV to multi TeV energies.Comment: New section added, extending the pion-nucleon and nucleon nucleon Regge description to Multi TeV energies. Conclusions on pion-pion scattering unchange

Consistency checks of pion-pion scattering data and chiral dispersive calculations

We have evaluated forward dispersion relations for scattering amplitudes that follow from direct fits to several sets of pion-pion scattering experiments, together with the precise K decay results, and high to energy data. We find that some of the most commonly used experimental sets, as well as some recent theoretical analyses based on Roy equations, do not satisfy these constraints by several standard deviations. Finally, we provide a consistent pion-pion amplitude by improving a global fit to data with these dispersion relations.Comment: Talk presented by F. J. Yndurain at ``Quark confinement and the Hadron Spectrum", Sardinia, Sept. 200

Fast and slow light in zig-zag microring resonator chains

We analyze fast and slow light transmission in a zig-zag microring resonator chain. This novel device permits the operation in both regimes. In the superluminal case, a new ubiquitous light transmission effect is found whereby the input optical pulse is reproduced in an almost simultaneous manner at the various system outputs. When the input carrier is tuned to a different frequency, the system permits to slow down the propagating optical signal. Between these two extreme cases, the relative delay can be tuned within a broad range

Rho and Sigma Mesons in Unitarized Thermal ChPT

We present our recent results for the rho and sigma mesons considered as resonances in pion-pion scattering in a thermal bath. We use chiral perturbation theory to fourth order in p for the low energy behaviour, then extend the analysis via the unitarization method of the Inverse Amplitude into the resonance region. The width of the rho broadens about twice the amount required by phase space considerations alone, its mass staying practically constant up to temperatures of order 150 MeV. The sigma meson behaves in accordance to chiral symmetry restoration expectations.Comment: Proc. Workshop Strong and Electroweak Matter 02, Heidelberg, German

New dispersion relations in the description of ππ\pi\pi scattering amplitudes

We present a set of once subtracted dispersion relations which implement crossing symmetry conditions for the $\pi\pi$ scattering amplitudes below 1 GeV. We compare and discuss the results obtained for the once and twice subtracted dispersion relations, known as Roy's equations, for three $\pi\pi$ partial JI waves, S0, P and S2. We also show that once subtracted dispersion relations provide a stringent test of crossing and analyticity for $\pi\pi$ partial wave amplitudes, remarkably precise in the 400 to 1.1 GeV region, where the resulting uncertainties are significantly smaller than those coming from standard Roy's equations, given the same input.Comment: 8 pages, 2 figures, to appear in the Proceedings of the Meson 2008 conference, June 6-10, 2008, Cracow, Polan