Gauged linear sigma model and pion-pion scattering

A simple gauged linear sigma model with several parameters to take the symmetry breaking and the mass differences between the vector meson and the axial vector meson into account is considered here as a possibly useful template for the role of a light scalar in QCD as well as for (at a different scale) an effective Higgs sector for some recently proposed walking technicolor models. An analytic procedure is first developed for relating the Lagrangian parameters to four well established (in the QCD application) experimental inputs. One simple equation distinguishes three different cases:1. QCD with axial vector particle heavier than vector particle, 2. possible technicolor model with vector particle heavier than the axial vector one, 3. the unphysical QCD case where both the KSRF and Weinberg relations hold. The model is applied to the s-wave pion-pion scattering in QCD. Both the near threshold region and (with an assumed unitarization) theglobal region up to about 800 MeV are considered. It is noted that there is a little tension between the choice of bare sigma mass parameter for describing these two regions. If a reasonable globa fit is made, there is some loss of precision in the near threshold region.Comment: 19 pages, 9 figure

The pion-pion scattering amplitude. III: Improving the analysis with forward dispersion relations and Roy equations

We complete and improve the fits to experimental $\pi\pi$ scattering amplitudes, both at low and high energies, that we performed in the previous papers of this series. We then verify that the corresponding amplitudes satisfy analyticity requirements, in the form of partial wave analyticity at low energies, forward dispersion relations (FDR) at all energies, and Roy equations below$\bar{K}K$ threshold; the first by construction, the last two, inside experimental errors. Then we repeat the fits including as constraints FDR and Roy equations. The ensuing central values of the various scattering amplitudes verify very accurately FDR and, especially, Roy equations, and change very little from what we found by just fitting data, with the exception of the D2 wave phase shift, for which one parameter moves by $1.5 \sigma$. These improved parametrizations therefore provide a reliable representation of pion-pion amplitudes with which one can test various physical relations. We also present a list of low energy parameters and other observables. In particular, we find $a_0^{(0)}=0.223\pm0.009 M^{-1}_\pi$, $a_0^{(2)}=-0.0444\pm0.0045 M^{-1}_\pi$ and $\delta_0^{(0)}(m^2_K)-\delta_0^{(2)}(m^2_K)=50.9\pm1.2^{\rm o}$.Comment: Plain TeX. 29 figures. Version to be published in PRD, with improved P and F wave

Thermal rates for baryon and anti-baryon production

We use a form of the fluctuation-dissipation theorem to derive formulas giving the rate of production of spin-1/2 baryons in terms of the fluctuations of either meson or quark fields. The most general formulas do not assume thermal or chemical equilibrium. When evaluated in a thermal ensemble we find equilibration times on the order of 10 fm/c near the critical temperature in QCD.Comment: 22 pages, 4 tables and 2 figures, REVTe

A MASTER FORMULA FOR CHIRAL SYMMETRY BREAKING

We derive a master formula for chiral $SU(2)\times SU(2)$ breaking, based on the Veltman-Bell equations and the Peierls-Dyson relation. Our approach does not rely on the use of the soft pion limit or an expansion around the chiral limit, and yields exact results for on-shell pions. Threshold theorems for $\pi N\rightarrow \pi N$, $\gamma N\rightarrow \pi N$, $\pi N\rightarrow\pi\pi N$, $\gamma N\rightarrow \gamma\pi N$, $\gamma N\rightarrow \pi\pi N$ and $\pi N\rightarrow \pi\gamma N$ are recovered, and corrections to them are given. The reactions $\pi\rightarrow e\nu \gamma$, $\pi\rightarrow e\nu e^+e^-$, $\gamma\pi\rightarrow \gamma\pi$ and $\gamma\gamma\rightarrow \pi\pi$ are also discussed. A general formula for $\pi\pi$ scattering and a new one loop effective action are obtained. The new effective action reproduces the KSFR relation, and yields specific estimates for the pion polarisabilities. A detailed comparison with baryon-free chiral perturbation theory to one loop is made. An extension of our effective action to two loops is outlined.Comment: 119 pages + 7 Figures available from (I.Zahed

Quark Mass dependence at Two Loops for Meson Properties

This talks contains a short introduction to Chiral Perturbation Theory and the existing calculations to two-loop order in the mesonic sector. I include a discussion on which quantities the expansion can be organized in. The present best values of the Low-Energy-Constants as determined from continuum physics are given as well as the assumptions underlying the fits to experimental data. I present plots of masses, decay constants and $f_+(0)$ in $K_{\ell3}$ as a function of quark or meson masses. The talk ends with a list of things for which it would be extremely useful to have good results from lattice QCD calculations.Comment: 15 pages, plenary talk at T he XXV International Symposium on Lattice Field Theory, July 30 - August 4 2007, Regensburg, Germany. v2: some clarifying statements adde

On the spectral functions of scalar mesons

In this work we study the spectral functions of scalar mesons in one- and two-channel cases. When the propagators satisfy the K\"allen-Lehman representation a normalized spectral function is obtained, allowing to take into account finite-width effects in the evaluation of decay rates. In the one-channel case, suitable to the light sigma and k mesons, the spectral function can deviate consistently from a Breit-Wigner shape. In the two-channel case with one subthreshold channel the evaluated spectral function is well approximated by a Flatte' distribution; when applying the study to the a_0(980) and f_0(980) mesons the tree-level forbidden KK decay is analysed.Comment: 13 pages, 7 figure

Parameters of scalar resonances from the combined analysis of data on processes ππ→ππ,KKˉ,ηη\pi\pi\to\pi\pi,K\bar{K},\eta\eta and J/ψJ/\psi decays

A combined analysis of data on isoscalar S-wave processes $\pi\pi\to\pi\pi,K\overline{K},\eta\eta$ and on decays $J/\psi\to\phi\pi\pi,\phi K\overline{K}$ from the DM2, Mark III and BESIII collaborations is performed to study $f_0$ mesons. The method of analysis is based on analyticity and unitarity and uses an uniformization procedure. In the analysis limited only to the multi-channel $\pi\pi$-scattering data, two possible sets of parameters of the $f_0(500)$ were found: in both cases the mass was about 700 MeV but the total width was either about 600 or 930 MeV. The extension of the analysis using only the DM2 and Mark III data on the $J/\psi$ decays does not allow to choose between these sets. However, the data from BESIII on the di-pion mass distribution in the decay $J/\psi\to\phi\pi^+\pi^-$ clearly prefers the wider $f_0(500)$ state. Spectroscopic implications from results of the analysis are also discussed.Comment: the formalism is also described (text overlap) in arXiv:1108.3725; new extended analysis of data; revised PRD versio

Further Analysis on \sigma-particle Properties

In a previous work, we have reanalyzed the I=0 S-wave \pi\pi-scattering phase-shift through a new method of Interfering Breit-Wigner amplitudes, and have shown the existence of a light scalar, \sigma particle, accompanied by a negative "repulsive core"-type background phase-shift, whose origin may have some correspondence to a ``compensating'' \pi\pi contact interaction. In this work we make further analysis on the phase shift under KKbar threshold from the same standpoint, to determine precise values of \sigma mass and width, so far as present experimental data are concerned.Comment: Updated with recent progres