Flatte-like distributions and the a_0(980)/f_0(980) mesons

We explore the features of Flatte-like parametrizations. In particular, we demonstrate that the large variation in the absolute values of the coupling constants to the pi-eta (or pi-pi) and KKbar channels for the a_0(980) and f_0(980) mesons that one can find in the literature can be explained by a specific scaling behaviour of the Flatte amplitude for energies near the KKbar threshold. We argue that the ratio of the coupling constants can be much better determined from a fit to experimental data.Comment: 12 pages, 12 figure

Analysis of the nature of the ϕ→γπη\phi\to\gamma\pi\eta and ϕ→γπ0π0\phi\to\gamma\pi^0\pi^0 decays

We study interference patterns in the $\phi\to(\gamma a_0+\pi^0\rho)\to\gamma\pi\eta$ and $\phi\to(\gamma f_0+\pi^0\rho)\to\gamma \pi^0\pi^0$ reactions. Taking into account the interference, we fit the experimental data and show that the background reaction does not distort the $\pi^0\eta$ spectrum in the decay $\phi\to\gamma\pi\eta$ everywhere over the energy region and does not distort the $\pi^0\pi^0$ spectrum in the decay $\phi\to\gamma\pi^0\pi^0$ in the wide region of the $\pi^0\pi^0$ system invariant mass, $m_{\pi\pi}>670$ MeV, or when the photon energy is less than 300 MeV. We discuss the details of the scalar meson production in the radiative decays and note that there are reasonable arguments in favor of the one-loop mechanism $\phi\to K^+K^-\to\gamma a_0$ and $\phi\to K^+K^-\to\gamma f_0$. We discuss also distinctions between the four-quark, molecular, and two-quark models and argue that the Novosibirsk data give evidence in favor of the four-quark nature of the scalar $a_0(980)$ and $f_0(980)$ mesons.Comment: 15 pages, 7 figures, title is changed, a few clarifying remarks are added, accepted for publication in Physical Review

The ππ\pi \pi S-Wave in the 1 to 2 GeV Region from a ππ\pi \pi, KˉK\bar{K}K and ρρ\rho \rho(ωω\omega \omega) Coupled Channel Model

A simple $\pi \pi$, $\bar{K}K$, and $\rho \rho$($\omega \omega$) fully coupled channel model is proposed to predict the isoscalar S-wave phase shifts and inelasticities for $\pi \pi$ scattering in the 1.0 to 2.0 GeV region. The S-matrix is required to exhibit poles corresponding to the established isoscalar J$^{\pi}$ = 0$^+$ resonances f$_0$(975), f$_0$(1400), and f$_0$(1710). A dominant feature of the experimental $\pi \pi$ inelasticity is the clear opening of the $\bar{K}K$ channel near 1 GeV, and the opening of another channel in the 1.4 - 1.5 GeV region. The success of our model in predicting this observed dramatic energy dependence indicates that the effect of multi-pion channels is adequately described by the $\pi \pi$ coupling to the $\bar{K}K$ channel, the $\rho \rho$(4$\pi$) and $\omega \omega$(6$\pi$) channels.Comment: 11 pages (Revtex 3.0), 4 figs. avail. upon request, RU946

Search for the scalar a0a_0 and f0f_0 mesons in the reactions e+e−→γπ0π0(η)e^+e^-\to\gamma\pi^0\pi^0(\eta)

It is shown that the reactions $e^+e^-\to\gamma\pi^0\pi^0(\eta)$ give a good chance for observing scalar $a_0$ and $f_0$ mesons. In the photon energy region less then 100 MeV the vector meson contributions $e^+e^-\to V^0\to\pi^0 V'^0\to\gamma\pi^0\pi^0(\eta)$ are negligible in comparison with the scalar mesons $e^+e^-\to\phi\to\gamma f_0(a_0)\to\gamma\pi^0\pi^0(\eta)$ for $BR(\phi\to\gamma f_0(a_0)\to\gamma\pi^0\pi^0(\eta))$ greater than $5\cdot10^{-6}(10^{-5})$. Using two-channel treatment of the $\pi\pi$ scattering the predictions for $BR(\phi\to\gamma (f_0+\sigma)\to\gamma\pi\pi)$ are derived. The four quark model, the model of $K\bar K$ molecule and the$s\bar s$ model of scalar $f_0$ and $a_0$ mesons are discussed.Comment: 31 pages, 10 ps files of figures, minor numerical changes, Appendix corrected, to be published in Phys.Rev.

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

On the precision of chiral-dispersive calculations of ππ\pi\pi scattering

We calculate the combination $2a_0^{(0)}-5a_0^{(2)}$ (the Olsson sum rule) and the scattering lengths and effective ranges $a_1$, $a_2^{(I)}$ and $b_1$, $b_2^{(I)}$ dispersively (with the Froissart--Gribov representation) using, at low energy, the phase shifts for $\pi\pi$ scattering obtained by Colangelo, Gasser and Leutwyler (CGL) from the Roy equations and chiral perturbation theory, plus experiment and Regge behaviour at high energy, or directly, using the CGL parameters for $a$s and $b$s. We find mismatch, both among the CGL phases themselves and with the results obtained from the pion form factor. This reaches the level of several (2 to 5) standard deviations, and is essentially independent of the details of the intermediate energy region ($0.82\leq E\leq 1.42$ GeV) and, in some cases, of the high energy behaviour assumed. We discuss possible reasons for this mismatch, in particular in connection with an alternate set of phase shifts.Comment: Version to appear in Phys. Rev. D. Graphs and sum rule added. Plain TeX fil

Darkness visible: reflections on underground ecology

1 Soil science and ecology have developed independently, making it difficult for ecologists to contribute to urgent current debates on the destruction of the global soil resource and its key role in the global carbon cycle. Soils are believed to be exceptionally biodiverse parts of ecosystems, a view confirmed by recent data from the UK Soil Biodiversity Programme at Sourhope, Scotland, where high diversity was a characteristic of small organisms, but not of larger ones. Explaining this difference requires knowledge that we currently lack about the basic biology and biogeography of micro-organisms. 2 It seems inherently plausible that the high levels of biological diversity in soil play some part in determining the ability of soils to undertake ecosystem-level processes, such as carbon and mineral cycling. However, we lack conceptual models to address this issue, and debate about the role of biodiversity in ecosystem processes has centred around the concept of functional redundancy, and has consequently been largely semantic. More precise construction of our experimental questions is needed to advance understanding. 3 These issues are well illustrated by the fungi that form arbuscular mycorrhizas, the Glomeromycota. This ancient symbiosis of plants and fungi is responsible for phosphate uptake in most land plants, and the phylum is generally held to be species-poor and non-specific, with most members readily colonizing any plant species. Molecular techniques have shown both those assumptions to be unsafe, raising questions about what factors have promoted diversification in these fungi. One source of this genetic diversity may be functional diversity. 4 Specificity of the mycorrhizal interaction between plants and fungi would have important ecosystem consequences. One example would be in the control of invasiveness in introduced plant species: surprisingly, naturalized plant species in Britain are disproportionately from mycorrhizal families, suggesting that these fungi may play a role in assisting invasion. 5 What emerges from an attempt to relate biodiversity and ecosystem processes in soil is our extraordinary ignorance about the organisms involved. There are fundamental questions that are now answerable with new techniques and sufficient will, such as how biodiverse are natural soils? Do microbes have biogeography? Are there rare or even endangered microbes

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

Rescattering and chiral dynamics in B\to \rho\pi decay

We examine the role of B^0(\bar B^0) \to \sigma \pi^0 \to \pi^+\pi^- \pi^0 decay in the Dalitz plot analysis of B^0 (\bar B^0) \to \rho\pi \to \pi^+\pi^-\pi^0 decays, employed to extract the CKM parameter \alpha. The \sigma \pi channel is significant because it can break the relationship between the penguin contributions in B\to\rho^0\pi^0, B\to\rho^+\pi^-, and B\to\rho^-\pi^+ decays consequent to an assumption of isospin symmetry. Its presence thus mimics the effect of isospin violation. The \sigma\pi^0 state is of definite CP, however; we demonstrate that the B\to\rho\pi analysis can be generalized to include this channel without difficulty. The \sigma or f_0(400-1200) ``meson'' is a broad I=J=0 enhancement driven by strong \pi\pi rescattering; a suitable scalar form factor is constrained by the chiral dynamics of low-energy hadron-hadron interactions - it is rather different from the relativistic Breit-Wigner form adopted in earlier B\to\sigma\pi and D\to\sigma\pi analyses. We show that the use of this scalar form factor leads to an improved theoretical understanding of the measured ratio Br(\bar B^0 \to \rho^\mp \pi^\pm) / Br(B^-\to \rho^0 \pi^-).Comment: 26 pages, 8 figs, published version. typos fixed, minor change