Meson-meson scattering within one loop Chiral Perturbation Theory and its unitarization

We present the complete one-loop calculation of all the two meson scattering amplitudes within the framework of SU(3) Chiral Perturbation Theory, which includes pions, kaons and the eta. In addition, we have unitarized these amplitudes with the coupled channel Inverse Amplitude Method, which ensures simultaneously the good low energy properties of Chiral Perturbation Theory and unitarity. We show how this method provides a remarkable description of meson-meson scattering data up to 1.2 GeV including the scattering lengths and the generation of seven light resonances, which is consistent with previous determination of the chiral parameters. Particular attention is paid to discuss the differences and similarities of this work with previous analysis in the literature.Comment: 20 pages, 5 figures. Comments on sigma, kappa and eta', as well as some references added. Final version to appear in Phys.Rev.

Relativistic Effects in the Scalar Meson Dynamics

A separable potential formalism is used to describe the $\pi\pi$ and $K\overline{K}$ interactions in the scalar-isoscalar states in the energy range from the $\pi\pi$ threshold up to 1.4 GeV. Introduction of relativistic propagators into a system of Lippmann-Schwinger equations leads to a very good description of the data ($\chi^{2}=0.93$ per one degree of freedom). Three poles are found in this energy region: fo(500) ($M=506\pm 10$ MeV, $\Gamma=494\pm 5$ MeV), fo(975) ($M=973\pm 2$ MeV, $\Gamma=29\pm 2$ MeV) and fo(1400) ($M=1430\pm 5$ MeV, $\Gamma=145\pm 25$ MeV). The fo(975) state can be interpreted as a $K\overline{K}$ bound state. The fo(500) state may be associated with the often postulated very broad scalar resonance under the $K\overline{K}$ threshold (sometimes called $\sigma$ or $\epsilon$ meson). The scattering lengths in the $\pi\pi$ and $K\overline{K}$ channels have also been obtained. The relativistic approach provides qualitatively new results (e.g. the appearance of the fo(500)) in comparison with previously used nonrelativistic approach.Comment: 30 pages in LaTeX + 5 figures available on request. Preprint Orsay No IPNO/TH 93-3

A low-lying scalar meson nonet in a unitarized meson model

A unitarized nonrelativistic meson model which is successful for the description of the heavy and light vector and pseudoscalar mesons yields, in its extension to the scalar mesons but for the same model parameters, a complete nonet below 1 GeV. In the unitarization scheme, real and virtual meson-meson decay channels are coupled to the quark-antiquark confinement channels. The flavor-dependent harmonic-oscillator confining potential itself has bound states epsilon(1.3 GeV), S(1.5 GeV), delta(1.3 GeV), kappa(1.4 GeV), similar to the results of other bound-state qqbar models. However, the full coupled-channel equations show poles at epsilon(0.5 GeV), S(0.99 GeV), delta(0.97 GeV), kappa(0.73 GeV). Not only can these pole positions be calculated in our model, but also cross sections and phase shifts in the meson-scattering channels, which are in reasonable agreement with the available data for pion-pion, eta-pion and Kaon-pion in S-wave scattering.Comment: A slightly revised version of Zeitschrift fuer Physik C30, 615 (1986

A partial wave analysis of the centrally produced pi0pi0 system in pp interactions at 450 GeV/c

A partial wave analysis of the centrally produced pi0pi0 channel has been performed in pp collisions using an incident beam momentum of 450 GeV/c. An unambiguous physical solution has been found. Evidence is found for the f0(980), f0(1300) and f0(1500) in the the S-wave. and the f2(1270) is observed dominantly in the D0-wave. In addition, there is evidence for a broad enhancement in the D-wave below 1 GeV.Comment: 12 pages, Latex, 4 Figure

A partial wave analysis of the centrally produced pi+pi- system in pp interactions at 450 GeV/c

A partial wave analysis of the centrally produced pi+pi- channel has been performed in pp collisions using an incident beam momentum of 450 GeV/c. An unambiguous physical solution has been found. Evidence is found for the f0(980), f0(1300), f0(1500) and fJ(1710) with J = 0 in the the S-wave. The rho(770) is observed dominantly in the P0-wave and the f2(1270) is observed dominantly in the D0-wave. In addition, there is evidence for a broad enhancement in the D-wave below 1 GeV.Comment: 12 pages, Latex, 4 Figure

A partial wave analysis of the π0π0\pi ^0\pi ^0 system produced in π−p\pi ^-p charge exchange collisions

A partial wave analysis of the of the $\pi ^0\pi ^0$ system produced in the charge exchange reaction: $\pi ^-p\to \pi ^0\pi ^0n$ at an incident momentum of $18.3 GeV/c$ is presented as a function of ${\pi ^0\pi ^0}$ invariant mass, $m_{\pi^0\pi^0}$, and momentum transfer squared, $| {t} |$, from the incident $\pi^-$ to the outgoing ${\pi ^0\pi ^0}$ system.Comment: 24 pages total,8 pages text, 14 figures, 1 table. Submitted to Phys Rev

Quark-gluonium content of the scalar-isoscalar states f_0(980), f_0(1300), f_0(1500), f_0(1750), f_0(1420 ^{+150}_{- 70}) from hadronic decays

On the basis of the decay couplings f_0 -> \pi\pi, K\bar K, \eta\eta, \eta\eta', which had been found before, in the study of analytical (IJ^{PC}=00^{++})-amplitude in the mass range 450-1900 MeV, we analyse the quark-gluonium content of resonances f_0(980), f_0(1300), f_0(1500), f_0(1750) and the broad state f_0(1420 ^{+ 150}_{-70}). The K-matrix technique used in the analysis makes it possible to evaluate the quark-gluonium content both for the states with switched-off decay channels (bare states, f^{bare}_0) and the real resonances. We observe significant change of the quark-gluonium composition in the evolution from bare states to real resonances, that is due to the mixing of states in the transitions f_0(m_1)-> real mesons-> f_0(m_2) responsible for the decay processes as well. For the f_0(980), the analysis confirmed the dominance of q\bar q component thus proving the n\bar n/s\bar s composition found in the study of the radiative decays. For the mesons f_0(1300), f_0(1500) and f_0(1750), the hadronic decays do not allow one to determine uniquely the n\bar n, s\bar s and gluonium components providing relative pecentage only. The analysis shows that the broad state f_0(1420 ^{+ 150}_{-70}) can mix with the flavour singlet q\bar q component only, that is consistent with gluonium origin of the broad resonance.Comment: 20 pages, LaTeX, 10 PostScript figures, epsfig.st

Another look at ππ\pi\pi scattering in the scalar channel

We set up a general framework to describe $\pi\pi$ scattering below 1 GeV based on chiral low-energy expansion with possible spin-0 and 1 resonances. Partial wave amplitudes are obtained with the $N/D$ method, which satisfy unitarity, analyticity and approximate crossing symmetry. Comparison with the phase shift data in the J=0 channel favors a scalar resonance near the $\rho$ mass.Comment: 17 pages, 5 figures, REVTe

\pi\pi, K\pi and \pi N potential scattering and a prediction of a narrow \sigma meson resonance

Low energy scattering and bound state properties of the \pi N, \pi\pi and K\pi systems are studied as coupled channel problems using inversion potentials of phase shift data. In a first step we apply the potential model to explain recent measurements of pionic hydrogen shift and width. Secondly, predictions of the model for pionium lifetime and shift confirm a well known and widely used effective range expression. Thirdly, as extension of this confirmation, we predict an unexpected medium effect of the pionium lifetime which shortens by several orders of magnitude. The \sigma meson shows a narrow resonance structure as a function of the medium modified mass with the implication of being essentially energy independent. Similarly, we see this medium resonance effect realized for the K\pi system. To support our findings we present also results for the \rho meson and the \Delta(1232) resonance.Comment: 42 pages, 17 PS figures, REFTeX, epsfig.sty needed, submitted to Phys. Re

UNDERSTANDING THE SCALAR MESON qqˉq\bar q NONET

It is shown that one can fit the available data on the a0(980), f0(980), f0(1300) and K*0(1430) mesons as a distorted 0++ qq bar nonet using very few (5-6) parameters and an improved version of the unitarized quark model. This includes all light two-pseudoscalar thresholds, constraints from Adler zeroes, flavour symmetric couplings, unitarity and physically acceptable analyticity. The parameters include a bare uu bar or dd bar mass, an over-all coupling constant, a cutoff and a strange quark mass of 100 MeV, which is in accord with expectations from the quark model. It is found that in particular for the a0(980) and f0(980) the KK bar component in the wave function is large, i.e., for a large fraction of the time the qq bar state is transformed into a virtual KK bar pair. This KK bar component, together with a similar component of eta' pi for the a0(980) , and eta eta, eta eta' and eta' eta' components for the f0(980), causes the substantial shift to a lower mass than what is naively expected from the qq bar component alone. Mass, width and mixing parameters, including sheet and pole positions, of the four resonances are given, with a detailed pedagogical discussion of their meaning.Comment: 35 pages in plain latex (ZPC in press), 10 figures obtainable from the author ([email protected]) with regular mail or as a large PS fil