We calculate partial widths of the gamma-gamma decay of the tensor q\bar q states a_2(1320), f_2(1270), f_2(1525), their radial excitations a_2(1660), f_2(1640), f_2(1800) as well as ^3F_2 q\bar q states. Calculations are performed in the framework of the same approach which was used before for the study of radiative decays f_0(980) -> gamma-gamma, a_0(980) -> gamma-gamma and phi(1020) -> gamma-f_0(980): the assumption made is that of q\bar q structure of f_0(980) and a_0(980) [A.V. Anisovich et al., Phys. Lett. B 456, 80 (1999); Eur. Phys. J. A 12, 103 (2001)]. The description of the decay partial widths for a_2(1320), f_2(1270), f_2(1525) and f_0(980), a_0(980) is reached with the approximately equal radial wave functions, thus giving a strong argument in favour of the fact that these scalar and tensor mesons are to be classified as members of the same P-wave q\bar q multiplet.

We present the results of the current analysis of the partial wave IJ^{PC}=00^{++} based on the available data for meson spectra (pi-pi, K\bar K, eta-eta, eta-eta', pi-pi-pi-pi). In the framework of the K-matrix approach, the analytical amplitude has been restored in the mass region 280 MeV< \sqrt s <1900 MeV. The following scalar-isoscalar states are seen: comparatively narrow resonances f_0(980), f_0(1300), f_0(1500), f_0(1750) and the broad state f_0(1200-1600). The positions of the amplitude poles (masses and total widths of the resonances) are determined as well as pole residues (partial widths to meson channels pi-pi, K\bar K, eta-eta, eta-eta', pi-pi-pi-pi). The fitted amplitude gives us the positions of the K-matrix poles (bare states) and the values of bare-state couplings to meson channels thus allowing the quark-antiquark nonet classification of bare states. On the basis of the obtained partial widths to the channels pi-pi, K\bar K, eta-eta, eta-eta', we estimate the quark/gluonium content of f_0(980), f_0(1300), f_0(1500), f_0(1750), f_0(1200-1600). For f_0(980), f_0(1300), f_0(1500) and f_0(1750),their partial widths testify the q\bar q origin of these mesons though being unable to provide precise evaluation of the possible admixture of the gluonium component in these resonances. The ratios of the decay coupling constants for the f_0(1200-1600) support the idea about gluonium nature of this broad state.

We study how the scalar mesons below 1 GeV are generated through the Oller-Oset-Pelaez version of the multichannel inverse amplitude method applied to the chiral perturbation theory. We find out that the f0(980) state is certainly generated as a bound state resonance below the K-Kbar threshold, while the a0(980) state, generated through the channel coupling between the pi-eta and K-Kbar channels, appears as a cusp at the K-Kbar threshold. The so-called sigma(500) and kappa(900) need not be interpreted as the conventional resonances.

Some aspects of a0-f0 mixing effects in the reaction ${\vec p} n\to da^0_0$ with perpendicular polarized proton beam are discussed. An angular--asymmetry parameter $A$ is defined to study those effects. It is shown that, for energies close to the production threshold, the angular--asymmetry parameter $A(\theta, \phi)$ is proportional to the a0-f0 mixing amplitude for arbitrary polar and azimuthal angles $\theta$ and $\phi$ of the outgoing $a_0$ meson. This statement is also valid for arbitrary energies, but then only at polar angles $\theta=0^0$ and $\theta=90^0$. The mass dependence of the differential cross section $d\sigma/dm_{\pi^0\eta}$ in the reaction $pn\to d\pi^0\eta$ in the presence of \mix mixing is also discussed.

A coupled channel model of the a0(980) and a0(1450) resonances has been constructed using the separable pion-eta and K-anti K interactions. We have shown that two S-matrix poles corresponding to the a0(980) meson have significantly different widths in the complex energy plane. The K-anti K to pion-eta branching ratio, predicted in our model near the a0(1450) mass, is in agreement with the result of the Crystal Barrel Collaboration. The K-anti K interaction in the S-wave isovector state is not sufficiently attractive to create a bound a0(980) meson.

An important role of the scalar isoscalar sigma-meson in the low-energy physics is discussed. The behavior of the sigma-meson in the hot and dense medium is studied. It is shown that in the vicinity of critical values of temperature(T) and chemical potential(m) the sigma-meson can become a sharp resonance. This effect can lead to a strong enhancement of the processes pi pi -> gamma gamma and pi pi-> pi pi near the two-pion threshold. Experimental observation of this phenomenon can be interpreted as a signal of approaching the domain where the chiral symmetry restoration and phase transition of the hadron matter into quark-gluon plasma take place.

We present the results of simultaneous analysis of the S-wave pi pi-spectra in the reactions pi^- p -> (pi^0 pi^0)_S n at p_{lab}=38 GeV/c (GAMS) and pi^- p -> (pi^+ pi^-)_S n at p_{lab}=18 GeV/c (E852 Collaboration) at moderate momenta transferred to the nucleon, |t| < 1.5 (GeV/c)^2. The t-distributions are described by the reggeized pi- and a_1-exchanges provided by the leading and daughter trajectories, while the M_{pi pi}-spectra are determined by a set of scalar-isoscalar resonances. With M_{pi pi}-distributions averaged over t-intervals, we have found several solutions given by different t-channel exchange mechanisms at |t| ~ (0.5-1.5) (GeV/c)^2, with resonance parameters close to each other. We conclude that despite a poor knowledge of the structure of the t-exchange, the characteristics of resonances such as masses and widths can be reliably determined using the processes under discussion. As to pole positions, we have found (1031 +/- 10) - i(35 +/- 6) MeV for f_0(980) and (1315 +/- 20) - i(150 +/- 30) MeV for f_0(1300).

Some aspects of a0-f0 mixing effects in the reaction ${\vec p} n\to da^0_0$ with perpendicular polarized proton beam are discussed. An angular--asymmetry parameter $A$ is defined to study those effects. It is shown that, for energies close to the production threshold, the angular--asymmetry parameter $A(\theta, \phi)$ is proportional to the a0-f0 mixing amplitude for arbitrary polar and azimuthal angles $\theta$ and $\phi$ of the outgoing $a_0$ meson. This statement is also valid for arbitrary energies, but then only at polar angles $\theta=0^0$ and $\theta=90^0$. The mass dependence of the differential cross section $d\sigma/dm_{\pi^0\eta}$ in the reaction $pn\to d\pi^0\eta$ in the presence of \mix mixing is also discussed.

We show that the F.E. Close and A. Kirk paper, Phys. Lett. B 515, 13 (2001) is a delusion for missing the effect of the overlapping resonances.

Based on gauge invariance, we show that the new threshold phenomenon is discovered in the \phi radiative decays \phi\to\gamma a0\to\gamma\pi0\eta and \phi\to\gamma f0\to\gamma\pi0\pi0. This enables to conclude that production of the lightest scalar mesons a0(980) and f0(980) in these decays is caused by the four-quark transitions, resulting in strong restrictions on the large Nc expansions of the decay amplitudes. The analysis shows that these constraints give new evidences in favor of the four-quark nature of a0(980) and f0(980) mesons.

First I review some previous work on the lightest scalars below 1.5 GeV, and how these scalars can be understood as unitarized nonet states. The bare scalars are strongly distorted by hadronic mass shifts, and the lightest I=0 state becomes a very broad resonance of mass and width of about 500 MeV. This is the sigma meson required by models based on linear realization of chiral symmetry. Recently the light sigma has clearly been observed in Ddecay to 3 pions by the E791 experiment at Fermilab and I discuss how this decay channel can be predicted in a Constituent Quark Meson Model, which incorporates heavy quark and chiral symmetries. At the end I discuss the likely possibility that there are in fact two light scalar nonets, such as one mainly meson-meson (or 4-quark) nonet and one qq bar nonet. I point out that an interesting approximate description of this could be modelled by starting with two coupled linear sigma models. After gauging the overall symmetry one of these could be looked upon as the "Higgs sector of strong interactions", and the lightest scalar nonet becomes the corresponding Higgs nonet.

We describe a four-parameter model for non-exotic meson-meson scattering, which accommodates all non-exotic mesons, hence also the light scalar mesons, as resonances and bound states characterised by complex singularities of the scattering amplitude as a function of the total invariant mass. The majority of the full $S$-matrix mesonic poles stem from an underlying confinement spectrum. However, the light scalar mesons K0*(830), a0(980), f0(400-1200), and f0(980) do not, but instead originate in 3P0-barrier semi-bound states. In the case of bound states, wave functions can be determined. For ccbar and bbbar, radiative transitions have been calculated. Here we compare the results to the data.

We discuss the classification of the light scalar mesons with mass below 2 GeV into q qbar nonets and glueballs. The information on production and decay of these states, in particular recent information on f_0(980), f_0(400-1200) (or sigma(600)) and f_0(1500) is considered. Although the data are not yet very precise the recent information is in favour of the previously developed scheme which includes f_0(980), a_0(980), K_0^*(1430), f_0(1500) into the lightest scalar nonet. The glueball in this approach appears as broad object around 1 GeV. Alternative schemes find the glueball at somewhat higher mass or suggest his mixing with q qbar states spread over a similar mass range. We do not see sufficient evidence yet for a light scalar nonet below 1 GeV around a sigma(600) resonance.

Applying the effective amplitude, which is evidently consistent with general constraints from chiral symmetry, the pipi spectra in the relevant processes are analyzed, leading to a strong evidence for existence of the light sigma meson. It is also pointed out that the pipi scattering process, which had been one of the main sources for PDG table for these many years, is, in principle, exceptionally difficult to investigate the property of sigma-meson.

Basing on the latest results of the PNPI (Gatchina) and QM&W College (London) groups, I discuss systematics of the IJ^{PC} q anti-q states in terms of trajectories on the (n,M^2) plane, where n is the radial quantum number and M is its mass. In the scalar sector, which is the most interesting because of the presence of extra states with respect to the q anti-q systematics, I discuss: 1) the results of the K-matrix analysis of the spectra pi-pi, pi-pi-pi-pi, K anti-K, eta-eta, eta-eta', pi-eta and characteristics of the resonances in the scalar sector, 2) q anti-q nonet classification of scalar bare states, 3) accumulation of widths of the q anti-q states by the glueball due to the overlapping of f_0 resonances at 1200-1700 MeV, 4) systematics of scalar q anti-q states, both bare states and resonances, on the (n,M^2) plots, 5) constraints on the quark-gluonium content of the resonances f_0(980), f_0(1300), f_0(1500), f_0(1750), and the broad state f_0(1420^{+150}_{-70}) from hadronic decays, 6) radiative decays of the P-wave q anti-q resonances: scalars f_0(980), a_0(980), and tensor mesons a_2(1320), f_2(1270), f_2(1525). The analysis proves that in the scalar sector we face two exotic mesons: the light sigma-meson, f_0(450), and the broad state f_0(1420^{+150}_{-70}), which is the descendant of the glueball.

Non-exotic scalar-meson resonances in S-wave meson-meson scattering are studied in the light of a unitarised Schroedinger model. The resulting poles in the scattering matrices, by analytical continuation into the complex-energy plane, are grouped into nonets of isoscalar, isodoublet, and isotriplet resonances. All singularities can be related to quark-antiquark confinement states, the light-quark nonet of which has ground states at 1.3 to 1.4 GeV and level spacings of some 300-400 MeV, except for a nonet of light scalar mesons below 1 GeV. All non-exotic S-wave resonances reported by experiment fit into this scheme.

The scalar-isoscalar, scalar-isotensor and vector-isovector pion-pion partial wave amplitudes are analyzed. Preliminary results indicate that only the scalar-isoscalar amplitude fitted to the "down-flat" data satisfies Roy's equations and consequently crossing symmetry.

We use our former results on pi+pi- S-wave obtained in a nearly assumption-free way from the 17.2 GeV/c data to predict the pi0pi0 S--wave. The predictions are compared with the recent results of the E852 experiment at 18.3 GeV/c. A good agreement is found for only one (the "down-flat") solution while the second one (the "up-flat") is excluded by the pi0pi0 data. Thus the long-standing "up-down" ambiguity has been finally resolved in favour of the S-wave intensity which stays large and nearly constant up to the KK-bar threshold. A joint analysis of both sets of data leads to considerable reduction of errors for this solution.

The assignments of the isoscalar scalar mesons f_0(980), f_0(1370), and f_0(1500) in terms of their \bar{q}q substructure is still a matter of heated dispute. Here we employ the weak and electromagnetic decays D_s^+ \to f_0 \pi^+ and f_0 \to \gamma\gamma, respectively, to identify the f_0(980) and f_0(1500) as mostly \bar{s}s, and the f_0(1370) as dominantly \bar{n}n, in agreement with previous work. The two-photon decays can be satisfactorily described with quark as well as with meson loops, though the latter ones provide a less model-dependent and more quantitative description.

We perform simultaneous calculations of the radiative decays of scalar mesons f_0(980)-> \gamma\gamma, a_0(980)-> \gamma\gamma, vector meson \phi(1020)-> \gamma f_0(980), \gamma a_0(980), \gamma \pi^0, \gamma \eta, \gamma \eta' and tensor mesons a_2(1320)-> \gamma\gamma, f_2(1270)-> \gamma\gamma, f_2(1525)-> \gamma\gamma assuming all these states to be dominantly the q\bar q ones. A good description of the considered radiative decays is reached by using almost the same radial wave functions for scalar and tensor mesons that supports the idea for the f_0(980), a_0(980) and a_2(1320), f_2(1270), f_2(1525) to belong to the same P -wave q\bar q multiplet.

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.

We investigate the cross section for the reaction $NN \to NNa_0$ near threshold and at medium energies. An effective Lagrangian approach with one-pion exchange is applied to analyze different contributions to the cross section for different isospin channels. The Reggeon exchange mechanism is also considered. The results are used to calculate the contribution of the $a_0$ meson to the cross sections and invariant $K \bar K$ mass distributions of the reactions $pp\to pn K^+\bar K^0$ and $pp\to pp K^+K^-$. It is found that the experimental observation of $a_0^+$ mesons in the reaction $pp\to pn K^+\bar K^0$ is much more promising than the observation of $a_0^0$ mesons in the reaction $pp\to pp K^+K^-$.

The model of the pure one-pion exchange mechanism, which gives a good description of the GAMS results on the alteration of the $S$-wave $\pi^0\pi^0$ mass spectrum in the $f_0(980)$ region in the reaction $\pi^-p\to\pi^0\pi^0n$ with increasing $-t$, is compared with the recent detailed data on the $m$ and $t$ distributions of the $\pi^-p\to\pi^0\pi^0n$ events obtained by the BNL-E852 Collaboration. It is shown that the predictions of this model are not confirmed by the BNL data. Therefore the observed phenomenon should be explained by the different exchange mechanism. It is most likely to be the $a_1$ exchange mechanism.

The measured rate for phi to gamma f0(980) appears to be larger than allowed on rather general grounds. We show that mixing between the f0(980) and a0(980), due to their dynamical interaction with the nearby KKbar thresholds, radically affects some existing predictions of their production in phi radiative decay. We predict that Gamma(phi to gamma f0)/Gamma(phi to gamma a_0) approx 3; that sum (b.r.(phi to gamma f0) + b.r. (phi to gamma a_0)) < 5 x 10^-4 with probable individual branching ratios 2 x 10^-4 and 0.7 x 10^-4 respectively.

I present a simple discussion of the masses and mixings of the light pseudoscalar and vector mesons based on a ``$q\bar{q}$'' description of the effective field theory. The analysis includes $\eta'$(958) from the beginning, and is largely concerned with structural questions. While the final results are mostly known, the method gives insight into the general form of the meson mass matrices and the different character of the mass splittings and mixings in the pseudoscalar and vector multiplets, and provides a coherent overall picture

A new phenomenological approach is suggested to determine the strangeness contents of light-flavour isoscalars. This approach is based on phenomenological laws of hadron production related to the spin, isospin, strangeness content and mass of the particles. The ``effective'' numbers of s and \bar{s} quarks in the isoscalar partners i_1 and i_2 are given by the nonstrange-strange mixing angle \phi: k(i_1)=2\sin^2\phi and k(i_2)=2\cos^2\phi. From the total production rates per hadronic Z decay of all light-flavour hadrons measured so far at LEP the values for k are found to be: k(\eta) \equiv 2-k(\eta^{\prime}) = 0.91 \pm 0.12, k(\phi) \equiv 2-k(\omega) = 1.94 \pm 0.09, k(f_2^{\prime}) \equiv 2-k(f_2) = 1.84 \pm 0.21 and k(f_0) = 0.09 \pm 0.13. Our results on the \eta--\eta^{\prime}, \omega--\phi and f_2--f_2^{\prime} isoscalar mixing are consistent with the present experimental evidence. Quite remarkably, our value for k(\eta) corresponds to the singlet-octet mixing angle \theta_P = -12.4^{\circ} \pm 3.5^{\circ}. The obtained strangeness content of the f_0(980) scalar/isoscalar is not consistent with the values supported by different model studies. However, taking the f_0(980) in our analysis with the mass of the bare state (K-matrix pole) f_0^{bare}(720 \pm 100), the mixing angle is found to be: |\phi_S^{bare}| = 73^{\circ} \pm 7^{\circ} \pm 24^{\circ}, in good agreement with the prediction of the K-matrix analysis.

The complementarity between Chiral Perturbation Theory and the Linear Sigma Model in the scalar channel is exploited to study $\pi^0\pi^0$ production in $\rho$ and $\omega$ radiative decays, where the effects of a low mass scalar resonance $\sigma(500)$ should manifest. The recently reported data on $\rho\to\pi^0\pi^0\gamma$ seem to require the contribution of a low mass and moderately narrow $\sigma(500)$. The properties of this controversial state could be fixed by improving the accuracy of these measurements. Data on $\omega\to\pi^0\pi^0\gamma$ can also be accommodated in our framework, but are much less sensitive to the $\sigma(500)$ properties.

Following the re-establishment of the \sigma(600) and the \kappa(900), the light scalar mesons a_0(980) and f_0(980) together with the \sigma(600) and the \kappa(900) are considered as the chiral scalar partner of pseudoscalar nonet in SU(3) chiral symmetry, and the high mass scalar mesons a_0(1450), K^*_0(1430), f_0(1370) and f_0(1710) turned out to be considered as the L=1 q\bar{q} scalar mesons. We assume that the high mass of the L=1 q\bar{q} scalar mesons is caused by the mixing with the light scalar mesons. For the structure of the light scalar mesons, we adopted the qq\bar{q}\bar{q} model in order to explain the "scalar meson puzzle". The inter-mixing between the light scalar nonet and the high mass L=1 q\bar{q} nonet and the intra-mixing among each nonet are analyzed by including the glueball into the high mass scalar nonet.

We consider the radiative transition $\phi \to f_0 \gamma$, which is a sensitive probe of the nature of the $f_0(980)$ particle. Using the QCD sum-rule technique, we estimate the branching ratio of such decay mode to be: ${\cal B}(\phi \to f_0 \gamma)=(2.7 \pm 1.1) ~ 10^{-4}$, in fair agreement with present experimental data. As for the structure of the $f_0$, the result suggests a sizeable $s {\bar s}$ component; however, this result does not exclude the possibility of further components and allows a more complex structure than indicated by the naive quark model.

It is demonstrated that f0-a0 mixing can lead to a comparatively large isospin violation in the reactions pN -> d a0, pd -> 3He/3H a0 and dd -> 4He a0 close to the corresponding production thresholds.

Recently the D$^+$ charm meson was observed to have a clear branching ratio into the low energy $\pi-\pi$ sigma resonance, while this channel was not detected in the D$_s^+$ decay. It is shown that this is consistent with the standard treatment of exclusive charm meson decays and a proposed glueball/sigma picture.

On the basis of a simultaneous description of the isoscalar s-wave of $\pi\pi$ scattering (from the threshold up to 1.9 GeV) and of $\pi\pi\to K\bar{K}$ process (from the threshold to $\sim$ 1.4 GeV) in the model-independent approach, it is shown that there exists the $f_0(665)$ state with properies of the $\sigma$-meson, the glueball nature of $f_0(1500)$ is indicated, and the $f_0(1370)$ is assigned mainly to $s{\bar s}$ state. The coupling constants of the observed states with $\pi\pi$ and $K\bar{K}$ systems and scattering lengths $a_0^0(\pi\pi)$ and $a_0^0(K\bar{K})$ are calculated. The existence of the $f_0(665)$ state and the obtained $\pi\pi$-scattering length ($a_0^0\approx 0.27 m_{\pi^+}^{-1}$) seem to suggest the linear realization of chiral symmetry.

The phenomenologically observed property of sigma(600) in our recent analyses of various pi pi-scattering and -production processes is reviewed and compared with the prediction of SU(2) linear sigma model. Furthermore, a possibility of the scalar sigma-nonet (sigma (600), kappa (900), f_0(980) and a_0(980)) forming with the pseudoscalar pi-nonet a linear representation of SU(3) chiral symmetry is investigated. The origin of repulsive background phase shift delta_BG, which is essential to lead us to the sigma-existence in our phase shift analysis, is shown to come from the repulsive lambda phi^4 interaction.

We examine the D_s -> f_0(980) pi amplitude through a constituent quark-meson model, incorporating heavy quark and chiral symmetries, finding a good agreement with the recent E791 data analysis of D_s -> 3pi via f_0(980). The f_0(980) resonance is considered at the moment of production as an s sbar state, later evolving to a superposition of mainly s sbar and K Kbar. The analysis is also extended to the more frequent process D_s -> phi pi.

By applying analyticity and single channel unitarity we derive a new formula which is very useful to analyze the role of the left-hand singularities in hadron form factors and in the determination of the resonance parameters. Chiral perturbation theory is used to estimate the left-hand cut effects in pi pi scattering processes. We find that in the IJ=11 channel the left-hand cut effect is negligible and in the IJ=20 channel the phase shift is dominated by the left-hand cut effect. In the IJ=00 channel the left-hand cut contribution to the phase shift is in the direction opposite to the experimental data and therefore it extrudes the necessity of the existence of the sigma resonance. Both the mass and the width of the sigma resonance are found to be around 550MeV.

Partial widths of the radiative decays $\phi(1020)\to\gamma f_0(980)$, $\gamma\eta$, $\gamma\eta'$, $\gamma\pi^0$ and $f_0(980)\to\gamma\gamma$ are calculated assuming all mesons under consideration to be $q\bar q$ states: $\phi(1020)$ is dominantly an $s\bar s$ state ($n\bar n$ component $\lesssim 1%$), $\eta$, $\eta'$ and $\pi^0$ are standard $q\bar q$ states, $\eta = n\bar n\cos\theta - s\bar s\sin\theta$ and $\eta'=n\bar n\sin\theta + s\bar s\cos\theta$ with $\theta\simeq 37^\circ$, and $f_0(980)$ is the $q\bar q$ meson with the flavour wave function $n\bar n\cos\phi + s\bar s \sin\phi$. Calculated partial widths for the decays $\phi\to\gamma \eta$, $\gamma\eta'$, $\gamma\pi^0$ are in a reasonable agreement with experiment. The measured value of the branching ratio $BR(\phi\to\gamma f_0(980))$ requires $25^\circ\le |\phi|\le 90^\circ$; for the decay $f_0(980)\to\gamma\gamma$ the agreement with data is reached at either $77^\circ\le\phi\le 93^\circ$ or $(-54^\circ)\le\phi\le (-38^\circ)$. Simultaneous analysis of the decays $\phi(1020)\to\gamma f_0(980)$ and $f_0(980)\to\gamma\gamma$ provides arguments in favour of the solution with negative mixing angle $\phi =-48^\circ\pm 6^\circ$.

We discuss how the lightest scalars, in particular the broad sigma resonance, can be understood as unitarized (qbar q) states within a unitarized quark model (UQM). The bare (qbar q) scalars are strongly distorted by hadronic mass shifts, and the (ubar u+ dbar d) state becomes a very broad resonance, with its pole at 470-i250 MeV. This is the sigma meson required by models for spontaneous breaking of chiral symmetry. We also discuss the less well known phenomenon that with a large coupling there can appear two physical resonance poles on the second sheet although only one bare quark-antiquark state is put in. The f_0(980) and f_0(1370) resonance poles can thus be two manifestations of the same (sbar s) quark state. Both of these are dominant in the E791 Dalitz plot of D_s-> 3pi, where (sbar s) intermediate states should be dominant. Recently this light sigma has clearly been observed in D-> sigma pi-> 3pi by the E791 experiment at Fermilab. We discuss how this decay channel can be predicted in a Constituent Quark Meson Model (CQM), which incorporates heavy quark and chiral symmetries.

Minkowski and Ochs have recently argued that the small two photon coupling of a conjectured $\sigma(600)$ is so small that it is likely to be a glueball. We ask whether this can be so or whether it is simply gauge invariance that produces the observed low mass suppression?

We exploit the W-emission process to study the measured weak decay of the D(s,+)(1.9686) meson into f(0)(980) and a positively charged pion. We conclude that the scalar f(0)(980) meson contains mostly strange-antistrange flavors, which is supported by different model studies.

For the first time a complete data set of the two-body decays of the f0(1370), f0(1500) and f0(1710) into all pseudoscalar mesons is available. The implications of these data for the flavour content for these three f0 states is studied. We find that they are in accord with the hypothesis that the scalar glueball of lattice QCD mixes with the qqbar nonet that also exists in its immediate vicinity. We show that this solution also is compatible with the relative production strengths of the f0(1370), f0(1500) and f0(1710) in pp central production, ppbar annihilations and J/psi radiative decays.

We first review the recent accumulating evidences of the existence of a scalar-isoscalar meson with the mass 500 to 800 MeV which may be identified with the sigma meson as the quantum fluctuation of the amplitude of the chiral order parameter. We indicate that phase shift analyses which respect chiral symmetry (ChS), analyticity and crossing symmetry of the scattering amplitude show the sigma meson pole in the $s$-channel as well as the $\rho$ meson pole in the $t$-channel in the pi-pi scattering in the $I=J=0$ channel. We emphasize that the existence of the $\sigma$ resonance does not contradict with the success of the chiral perturbation theory; phenomenological difficulties with the renormalizable linear sigma model do not necessarily deny the validity of the linear representation of \chis of QCD as given by the NJL-like models which not only admit the $\sigma$ resonance but also reproduce the coupling constants $L_i$ and $H_i$ appearing the nonlinear chiral lagrangian. We give some examples of the hadronic phenomena which are naturally accounted for with the $\sigma$ meson. We show that the the $\sigma$ meson as the amplitude fluctuation of the chiral order parameter may be more clearly identified than in free space in hot and/or dense matter, even in finite nuclei where partial restoration of ChS may be realized.

In the model-independent approach consisting in the immediate application to the analysis of experimental data of such general principles as analyticity and unitarity, a confirmation of the $\sigma$-meson at $\sim$ 665 MeV and an indication for the glueball nature of the $f_0(1500)$ state are obtained on the basis of a simultaneous description of the isoscalar s-wave channel of the $\pi\pi$ scattering (from the threshold up to 1.9 GeV) and of the $\pi\pi\to K\bar{K}$ process (from the threshold to $\sim$ 1.4 GeV where the 2-channel unitarity is valid). A parameterless description of the $\pi\pi$ background is first given by allowance for the left-hand branch-point in the proper uniformizing variable. It is shown that the large $\pi\pi$-background, usually obtained, combines, in reality, the influence of the left-hand branch-point and the contribution of a very wide resonance at $\sim$ 665 MeV. The coupling constants of the observed states with the $\pi\pi$ and $K\bar{K}$ systems and lengths of the $\pi\pi$ and $K\bar{K}$ scattering are obtained.

Interactions in three coupled channels: pi-pi, K-anti K and sigma-sigma have been investigated in a wide two-pion effective mass region from the pi-pi threshold up to 1600 MeV. Analytical structure of amplitudes in all channels has been studied. It was shown that its knowledge is necessary to understand spectrum of scalar mesons and their nature.

We first review the work of the Syracuse group, which uses an effective chiral Lagrangian approach, on meson-meson scattering. An illustration providing evidence for the existence of a strange scalar resonance of mass around 900 MeV is given. An attempt to fit this $\kappa (900)$ together with a similarly obtained $\sigma (560)$ and the well known $a_0(980)$ and $f_0(980)$ into a nonet pattern suggests that the underlying structure is closer to a dual quark-dual antiquark than to a quark-antiquark. A possible mechanism to explain a next higher-in mass scalar meson nonet is also discussed. This involves mixing between $q{\bar q}$ and $qq{\bar q} {\bar q}$ states.

The hypothesis of sigma meson pole dominance in the Delta I = 1/2 K -> pi pi amplitudes is tested by using the K_L-K_S mass difference.

Based on previous papers I discuss how I understand the lightest scalars using a general coupled channel model. This model includes all light two-pseudoscalar thresholds, constraints from Adler zeroes, flavour symmetric couplings, unitarity and physically acceptable analyticity. One finds that with a large coupling there can appear two physical resonance poles on the second sheet although only one bare quark-antiquark state is put in. The f0(980) and f0(1370) resonance poles are thus in this model two manifestations of the same strange-antistrange quark state. On the other hand, the isoscalar state containing u and d quarks becomes (when unitarized and strongly distorted by hadronic mass shifts) a very broad resonance, with its pole at 470-i250 MeV. This is the sigma meson required by models for spontaneous breaking of chiral symmetry.

This report summarizes the most important results presented at the recent conference held at the Yukawa Institute of Theoretical Physics in Kyoto, devoted to the recently confirmed light sigma resonance. Remarkably, all speakers at this meeting took the light sigma for granted and many mass and width estimations near 500 MeV were presented. We emphasize that if the light and broad sigma is accepted as a true resonance it explains many basic problems of low energy hadronic physics in a simple way, especially if the linear sigma model is used as an approximate effective low energy theory.

It is the purpose of the present manuscript to emphasize those aspects that make the scalar sector with vacuum quantum numbers rather unique. Chiral symmetry is the basic tool for our study together with a resummation of Chiral Perturbation Theory (CHPT) that stresses the role of unitarity but also allows one to include explicit resonance fields and to match with the CHPT expansion at low energies.

We investigate the reactions $\pi N \to a_0 N$ and $p p \to d a_0^+$ near threshold and at medium energies. An effective Lagragian approach and the Regge pole model are applied to analyze different contributions to the cross section of the reaction $\pi N \to a_0 N$. These results are used to calculate the differential and total cross sections of the reaction $p p \to d a_0^+$ within the framework of the two-step model in which two nucleons produce an $a_0$-meson via $\pi$ -meson exchange and fuse to a deuteron. The necessity of new measurements on $a_0$ production and branching fractions (of its decay to the $K\bar K$ and $\pi\eta$ channels) is emphasized for clarifying the $a_0$ structure. Detailed predictions for the reaction $pp \to d a_0^+$ are presented for the energy regime of the proton synchrotron COSY-J\"ulich.

I present the results of a recent calculation to determine the number of strange scalar resonances below 1.8 GeV based on the analytic properties of the experimental pi K scattering amplitude. Only one resonance was found in the data, and this is readily identifiable as the K_0^*(1430). We found no evidence to support the kappa(900).

Symmetrization selection rules for the decay of four-quark states to two J=0 mesons are analysed in a non - field theoretic context with isospin symmetry. The OZI allowed decay of an isoscalar J^PC = (1,3,...)^{-+} exotic state to eta' eta or f_0' f_0 is only allowed for four-quark components of the state containing one s sbar pair, providing a filter for strangeness content in these states. Decays of four-quark a_0 states are narrower than otherwise expected. If the experimentally observed 1^{-+} enhancement in eta pi is resonant, it is qualitatively in agreement with being a four-quark state.

In the I=0 sector there are more scalar mesons than can fit in one $q{\bar q}$ nonet. Consequently, many have claimed that there is in fact more than one multiplet, perhaps both $q{\bar q}$ and $qq{\bar {qq}}$. Such proposals require the existence of at least two strange isodoublets (and their antiparticles). The current PDG Tables list just one state, the $K^*_0(1430)$, while fits to data with Breit-Wigner forms and variable backgrounds can accommodate a $\kappa(900)$ too. Whether a state exists in the spectrum of hadrons is not a matter of ability to fit data along the real energy axis, but is completely specified by the number of poles in the complex energy plane. Here we perform a model-independent analytic continuation of $\pi K$ scattering results below 2 GeV to determine the number and position of resonance poles. We find that there {\bf is} a $K^*_0(1430)$, but {\bf no} $\kappa(900)$.

The a_0(980), a_0(1450) and K_0(1430) decay constants are determined using a form of QCD sum rules known to produce a very accurate determination of the rho decay constant. The ratio of a_0(980) to K_0(1430) decay constants is shown to be ~0.6, ruling out both the ``loosely-bound-K\bar{K}-molecule'' and Gribov minion scenarios for the a_0(980). Solutions for the isovector scalar spectral function obtained in the literature from sum rule analyses employing a more restrictive single-resonance-plus-continuum form of the input spectral ansatz, are also investigated. These solutions, which suggest, in contrast to the present results, negligible coupling of the a_0(980) to the isovector scalar density are shown to produce a poor quality match between the OPE and hadronic sides of the sum rules employed here, and hence to be strongly disfavored relative to the present solution.

We explore how chiral-symmetry constraints on weak-interaction matrix elements suggest the existence of an intermediate state sigma in several different weak-interaction processes. Particular attention is directed toward recent evidence for a sigma within three-body nonleptonic weak decays.

We continue our studies of a relativistic quark model that features chiral symmetry, covariance, and confinement. In this work we apply our model to the study of scalar-isoscalar mesons. Several of the parameters of the model have been determined in our earlier work, so that only two new parameters are needed for our analysis. We find a good fit to the spectrum of the f0 mesons, if we add a glueball with energy of about 1700 MeV. In this model we are rather close to "ideal mixing," with the f0(980) having the largest s mixture of 10%. The f0(1370) is the nodeless s state, while the f0(1500) is a n = (u + d)/ state with a single node. [The presence of that node accounts for the small width of the f0(1500).] The next state is a n state with two nodes at 1843 MeV. Thus, we identify the f0(1770) as the state with the largest glueball component. It was found that the vacuum polarization functions that describe coupling to the two-meson and other continuum meson channels play an important role in achieving a good fit to the experimentally determined spectrum. In this work we use a Gaussian regulator in all our calculations of meson decay amplitudes. In the first part of our study we multiply the Gaussian regulator by a P2-dependent factor that was chosen so as to modify the threshold behavior of our polarization functions. With that factor in place, we can study the spectrum of f0 states without introducing the imaginary parts of the polarization functions that describe decay to the two-meson continuum. When we do introduce the imaginary parts, we use the vacuum polarization functions with unmodified threshold behavior. The use of the P2-dependent factor helps to clarify the nature of the f0(400-1200), which is seen, in part, to have its origin as a rather complex thresholdeffect associated with the rapid increase of the amplitudes for decay to the and K channels. [For a full understanding of the f0(400-1200) one needs to also consider the role of t-channel exchange.] The model used in this work is based upon weak quarkonium-glueball coupling. However, the four-pion decay of the f0(1370) and the f0(1500) suggests that these states may be strongly mixed with the glueball, which may have a large four-pion decay width. It is also possible that mixing of these states with the f0(980) may be important for understanding the four-pion decay widths. We provide a short discussion of quarkonium-glueball mixing in a schematic model. There is not enough information presently available to treat that problem in an unambiguous manner.

It is presented a critical consideration of all unusual properties of the scalar a_0(980) and f_0(980)-mesons in the four-quark, two-quark and molecular models. The arguments are adduced that the four-quark model is more preferable. It is discussed the complex of experiments that could finally resolve this issue.

We explore the Delta-I= 1/2 rule and epsilon'/epsilon in K -> pi pi transitions using a Dyson-Schwinger equation model. Exploiting the feature that QCD penguin operators direct K^0_S transitions through 0^{++} intermediate states, we find an explanation of the enhancement of I=0 K -> pi pi transitions in the contribution of a light sigma-meson. This mechanism also affects epsilon'/epsilon.

Scalar-isoscalar mesons are studied using an unitary model in three channels: pi-pi, K-anti K and an effective 2pi-2pi. All the solutions, fitted to the pi-pi and K-anti K data, exhibit a wide f0(500), a narrow f0(980) and two relatively narrow resonances, lying on different sheets between 1300 MeV and 1500 MeV. These latter states are similar to the f0(1370) and f0(1500) seen in experiments at CERN. Branching ratios are compared with available data. We have started investigations of some crossing symmetry and chiral constraints imposed near the pi-pi threshold on the scalar-isoscalar, scalar-isotensor and P-wave pi-pi amplitudes.

In this talk, an overview of the status of the light scalar mesons in the context of the non linear chiral Lagrangian of references [1-3] is presented. The evidence for the existence of a scalar nonet below 1 GeV is reviewed, and it is shown that by introducing a scalar nonet an indirect way of probing the quark substructure of these scalars through the scalar mixing angle can be obtained. It is then reviewed that consistency of this non-linear chiral Lagrangian framework with the experimental data on pi pi and pi K scattering, as well as the decay eta' to eta pi pi, results in a range for the mixing angle which indicates that the quark substructure of these light scalars are closer to a four quark picture.

Recent work suggests the existence of a non-conventional lowest-lying scalar nonet containing the a0(980). Then the a0(1450) and also the K0*(1430) are likely candidates to belong to a conventional p-wave $q \bar q$ nonet. However a comparison of their properties with those expected on this basis reveals a number of puzzling features. It is pointed out that these puzzles can be resolved in a natural and robust way by assuming a ``bare'' conventional p-wave scalar $q \bar q$ nonet to mix with a lighter four quark $qq \bar q \bar q$ scalar nonet to form new ``physical'' states. The essential mechanism is driven by the fact that the isospinor is lighter than the isovector in the unmixed $qq \bar q \bar q$ multiplet.

The light sigma-particle is, regardless of the strong criticism, reviving recently due to the works done from various sides. I review essential points of the controversies (especially related to our works) and of their answer: Conventionally a large concentration of the iso-scalar S-wave 2 pi events below 1 GeV (being, correctly, due to the sigma-production), which is observed in most of production processes, is interpreted as a mere background from the viewpoint of, so called, universality argument. However, I show, by resorting to a simple field theoretical model, that the argument is not correct and the production process has ``its own value'' independent of the scattering process. Thus it is suggested that the present index ``f_0(400-1200) or sigma'' in PDG'98 is to be changed as ``sigma(400-800)'' in the PDG 2000.

Recently we obtained the evidence for the existence of sigma(600) meson, which had been sought but missing for a long time, by reanalyzing the I=0 S-wave pi pi scattering phase shift. The sigma-existence was also suggested through the analyses of pi pi production processes, pp central collision pp to pp pi^0 pi^0 and J/psi to omega pi pi decay. The observed properties through these works of sigma meson satisfy the mass and width relation of SU(2) linear sigma model. The physical origin of the repulsive background phase shift delta_{BG}, which was essential to lead to the sigma-existence in our phase shift analysis, is also due to the "compensating lambda phi^4-interaction" in linear sigma model. Furthermore in this talk the experimental property of the delta_{BG} is shown to be describable quantitatively in the framework of linear sigma model including rho-meson contribution.

We first discuss the theoretical and phenomenological significance of the sigma meson ($\sigma$) in QCD. It is indicated that if the collective modes with the mass 500-600 MeV exists in the $I=J=0$ channel, various empirical facts in hadron physics can be naturally accounted for, which otherwise would remain mysterious. We propose several experiments to produce and detect the $\sigma$ in nuclei using nuclear and electro-magnetic projectiles. The recent CHAOS data which show a spectral enhancement near the 2 $m_{\pi}$ threshold in the $\sigma$ channel from the reactions A$(\pi, 2\pi)$A' where A and A' denotes nuclei is interpreted as a possible evidence of a partial restoration of chiral symmetry in nuclei.

Recently, by reanalyzing the phase shift data of I=0 pipi$ and of I=1/2 Kpi scatterings, we showed the evidences for existence of light scalar mesons, sigma(600) and kappa(900), respectively, which had been sought but missing for a long time. The sigma(600) and kappa(900) together with the established resonances, a_0(980) and f_0(980), are shown to be consistently classified as the members of a single scalar sigma-nonet, appearing in the SU(3) linear sigma model. Especially the mass value of the iso-singlet flavor-octet member satisfies, together with those of kappa(900) and a_0(980), the Gell-Mann Okubo mass formula. The repulsive background phase shift delta_{BG}, which was essential to lead the sigma/kappa-existence in our phase shift analyses, is also shown to be quantitatively describable in the framework of linear sigma model. Thus, the origin of delta_{BG} is reduced to the ``compensating lambda phi^4-interaction," necessary from the viewpoint of chiral symmetry.

The riddle of the sigma is recast in a way that tries to differentiate fact from fiction as a basis for future/further discussion. By doing this, it is hoped that the role of the sigma as dominating the ubiquitous $\pi\pi$ interactions below 1 GeV and its relation to the QCD vacuum can be clarified.

From recent analysis of the $\pi\pi$ scattering amplitude, it has been claimed that there exists a broad and light $\sigma$ meson. However, if this meson really exists, it must also appear in other observables such as the pion scalar form factor. With the use of unitarity and dispersion relations together with chiral perturbation theory, this form factor is analyzed in the complex energy plane. The result agrees well with the empirical information in the elastic region and reveals a resonance pole at $\sqrt{s}=445-i235$ MeV. This gives further strong evidence for the existence of the $\sigma$ meson.

Properties of scalar--isoscalar mesons in a mass range from pi-pi threshold up to 1800 MeV are analysed using an unitary model with separable interactions in three decay channels: pi-pi, K-anti K and an effective 2pi-2pi. Different solutions are obtained by fitting pi-pi and K-anti K data. Analytical structure of the meson-meson multichannel amplitudes is studied with a special emphasis on the important role played by the S-matrix zeroes. The dependence of the positions of S-matrix singularities on the interchannel coupling strength is investigated. Poles, located in the complex energy plane not too far from the physical region, are interpreted as scalar resonances: a wide f0(500), a narrow f0(980) and a relatively narrow f0(1400). In all our solutions two resonances, lying on different sheets, in the energy region between 1300 MeV and 1500 MeV are found. These states may be compared with the resonances f0(1370) and f0(1500) seen in the experiments at CERN. Total, elastic and inelastic channel cross sections, branching ratios and coupling constants are evaluated and compared with available data.

A partial wave analysis of the centrally produced KK and pipi systems shows that the fJ(1710) has J = 0. In addition, a study of central meson production as a function of the difference in transverse momentum (dPT) of the exchanged particles shows that undisputed qqbar mesons are suppressed at small dPT whereas the glueball candidates are enhanced and that the production cross section for different resonances depends strongly on the azimuthal angle between the two outgoing protons.

The lightest scalar and pseudoscalar nonets are discussed within the framework of the broken U3$\times$U3 linear sigma model, and it is shown that already at the tree level this model works remarkably well predicting scalar masses and couplings not far from present experimental values, when all parameters are fixed from the pseudoscalar masses and decay constants. It is argued that this strongly suggests that the light and very broad $\sigma$ resonance exists near 500 MeV.

Two photon decay widths of the $J^P = O^+$ scalar mesons $a_{0} (980)$, $f_{0}(980)$, $f_{0}(1370)$ and $\chi_{c0}$ are calculated in a covariant model which is characterized by the quark - antiquark structure. Previously such models were used to calculate current form factors. Here a different application is tried. A simple version of the model uses adjusted nonrelativistic model parameters with small quark masses. The results seem to prefer nonideal mixing of $f_0(980)$ and $f_0(1370)$. The calculated decay rate of $\chi_{c0}$ agrees with the experimental results.

Evidence for an explicitly exotic state with isospin 2 and spin-parity 2^+ near the $\rho\rho$ threshold and nontrivial complementary indications of the unusual quark composition of the $f_0(980)$ and $a_0(980)$ states obtained from the reactions of two-photon formation of neutral meson resonances are discussed, together with puzzling phenomena in the channels $\gamma\gamma\to\rho^0\phi$ and $\gamma\gamma\to\rho^0\rho^0$ at high energies.

First radial excitations of the isoscalar and isovector scalar mesons f_0(400-1200), f_0(980) and a_0(980) are investigated in the framework of a nonlocal version of a chiral quark model of the Nambu--Jona-Lasinio type. It is shown that f_0(1370), f_J(1710) and a_0(1450) are the first radially excited states of f_0(400-1200), f_0(980) and a_0(980) which are ground states of the scalar meson nonet. The mesons' masses and strong decay widths are calculated. The scalar resonance f_0(1500) is supposed to be a glueball. The status of K_0^*(1430) is discussed.

It is presented a critical consideration of all unusual properties of the scalar $a_0(980)$ and $f_0(980)$-mesons in the four-quark, two-quark and molecular models. The arguments are adduced that the four-quark model is more preferable. It is discussed the complex of experiments that could finally resolve this issue.

We calculate partial widths for the decays a_0(980)\to\gamma\gamma and f_0(980)\to\gamma\gamma under the assumption that a_0(980) and f_0(980) are members of the basic 1^3P_0 q\bar q nonet. The results are in a reasonable agreement with data thus giving an argument for a q\bar q origin of these mesons. We also calculate the \gamma\gamma partial widths for the other scalar mesons, members of the 2^3P_0 q\bar q nonet.

We work out the Linear Sigma Model (LSM) predictions for the 2 gamma decay rates of the a_0(980),f_0(980) mesons under the assumption that they are respectively the I=1 and I=0 members of the bar q q scalar nonet. Agreement with experimental data is achieved provided we include the contribution of a \kappa meson with mass approx. 900 MeV, and a scalar mixing angle (sigma -f_0 mixing in the {|NS>,|S>} basis) varphi_s approx. -14^\circ, as predicted by the model.

We study the eta' to eta pi pi decay within an effective chiral Lagrangian approach in which the lowest lying scalar meson candidates sigma(560) and kappa(900) together with the f0(980) and a0(980) are combined into a possible nonet. We show that there exists a unique choice of the free parameters of this model which, in addition to fitting the pi pi and pi K scattering amplitudes, well describes the experimental measurements for the partial decay width of eta' to eta pi pi and the energy dependence of this decay. As a by-product, we estimate the a0(980) width to be 70 MeV, in agreement with a new experimental analysis.

The four-quark equations are found in the framework of the dispersion relation technique. The approximate solutions of these equations using the method based on the extraction of leading singularities of the amplitudes are obtained. The four-quark amplitudes of cryptoexotic mesons including the quarks of three flavours (u, d, s) are calculated. The mass values of low-lying cryptoexotic mesons are calculated.

It is shown that the list of unusual mesons planned for a careful study with the photon facility at JLAB can be extended by the exotic states $X^\pm(1600)$ with $I^G(J^{PC})=2^+(2^{++})$ which should be looked for in the $\rho^\pm\rho ^0$ decay channels in the reactions $\gamma N\to\rho^\pm\rho^0N$ and $\gamma N \to\rho^\pm\rho^0\Delta$. The full classification of the $\rho^\pm\rho^0$ states by their quantum numbers is presented. A simple model for the spin structure of the $\gamma p\to f_2(1270)p$, $\gamma p\to a^0_2(1320)p$ and $\gamma N\to X^\pm(N, \Delta)$ reaction amplitudes is formulated and the tentative estimates of the corresponding cross sections at the incident photon energy $E_\gamma\approx6$ GeV are obtained: $\sigma(\gamma p\to f_2(1270)p) \approx0.12$ $\mu$b, $\sigma(\gamma p\to a^0_2(1320)p)\approx0.25$ $\mu$b, $\sigma(\gamma N\to X^\pm N\to\rho^\pm\rho^0N)\approx0.018$ $\mu$b and $\sigma (\gamma p\to X^-\Delta^{++}\to\rho^-\rho^0\Delta^{++})\approx0.031$ $\mu$b. The problem of the $X^\pm$ signal extraction from the natural background due to the other $\pi^\pm\pi^0\pi^+\pi^-$ production channels is discussed. In particular the estimates are presented for the $\gamma p\to h_1(1170)\pi^+n$, $\gamma p\to\rho'^{+}n\to\pi^+\pi^0\pi^+\pi^-n$, and $\gamma p\to\omega\rho^0 p$ reaction cross sections. Our main conclusion is that the search for the exotic$X^\pm(2^+(2^{++}))$ states is quite feasible at JLAB facility. The expected yield of the $\gamma N\to X^\pm N\to\rho^\pm\rho^0N$ events in a 30-day run at the 100% detection efficiency approximates $2.8\times10^6$ events.

We generalize Schwinger's original mass formula to the case of an additional isosinglet which mixes with the nonet mesons, by considering the corresponding 3\times 3 mass matrix in the most general case. We then make further generalization to either (i) an arbitrary number of additional isosinglets mixing with nonet mesons, or (ii) an arbitrary number of mesons with common J^{PC} mixing with an additional isosinglet. In the former case, we present an explicit relation, while in the latter case, we show by numerical example that the new mass formula is only weakly affected by the inclusion of additional mesons, and hence holds with good accuracy for each of the 3\times 3 mass sub-matrices.

The scalar mesons in the 1 GeV region constitute the Higgs sector of the strong interactions. They are responsible for the masses of all light flavour hadrons. However, the composition of these scalar states is far from clear, despite decades of experimental effort. The two photon couplings of the $f_{0}$'s are a guide to their structure. Two photon results from Mark II, Crystal Ball and CELLO prompt a new Amplitude Analysis of $\gamma\gamma\to\pi^+\pi^-$, $\pi^0\pi^0$ cross-sections. Despite their currently limited angular coverage and lack of polarized photons, we use a methodology that provides the nearest one can presently achieve to a model-independent partial wave separation. We find two distinct classes of solutions. Both have very similar two photon couplings for the $f_0(980)$ and $f_0(400-1200)$. Hopefully these definitive results will be a spur to dynamical calculations that will bring us a better understanding of these important states.

We prove that recent data demonstrates unequivocally that the scalar meson $f_0(980)$ is mostly composed of $s\bar{s}$ quarks and that the coupling of $f_0$ to photons and mesons is in agreement with the linear sigma model.