Z+(4430) as a cusp in D*(2010)Dbar_1(2420)
The Z^+(4430) observed by Belle is explained naturally as a threshold cusp in the D*(2010)Dbar_1(2420) system.
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arXiv subjects
D. V. Bugg
Publications and source records attributed to D. V. Bugg.
Experimental disagreements with Extended Unitarity
In production processes, e.g. J/Psi -> omega-pi-pi or pbar-p -> 3pi, the sigma and fo(980) overlap in the same partial wave. The conjecture of Extended Unitarity (EU) states that the pi-pi pair should have the same phase variation as pi-pi elastic scattering. This is an extension of Watson's theorem beyond its original derivation, which stated only that the s-dependence of a single resonance should be universal. The prediction of EU is that the deep dip observed in pi-pi elastic scattering close to 1 GeV should also appear in production data. Four sets of data disagree with this prediction. All require different relative magnitudes of sigma and fo(980). That being so, a fresh conjecture is to rewrite the 2-body unitarity relation for production in terms of observed magnitudes. This leads to a prediction different to EU. Central production data from the AFS experiment fit naturally to this hypothesis.
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A Study in Depth of f0(1370)
Claims have been made that f0(1370) does not exist. The five primary sets of data requiring its existence are refitted. Major dispersive effects due to the opening of the 4pi threshold are included for the first time; the sigma -> 4pi amplitude plays a strong role. Crystal Barrel data on pbar-p -> 3pizero at rest require f0(1370) signals of at least 32 and 33 standard deviations in 1S0 and 3P1 annihilation respectively. Furthermore, they agree within 5 MeV for mass and width. Data on pbar-p -> eta-eta-pizero agree and require at least a 19 standard deviation contribution. This alone is sufficient to demonstrate the existence of f0(1370). BES II data for J/Psi -> phi-pi-pi contain a visible f0(1370) signal > 8 standard devations. In all cases, a resonant phase variation is required. The possibility of a second pole in the sigma amplitude due to the opening of the 4pi channel is excluded. Cern-Munich data for pi-pi elastic scattering are fitted well with the inclusion of some mixing between sigma, f0(1370) and f0(1500). The pi-pi widths for f2(1565), rho3(1690), rho3(1990) and f4(2040) are determined.
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f0(1370)
A summary is given of the main sets of data requiring the existence of f0(1370). Crystal Barrel data on pbar-p -> eta eta pizero contain a visible f0(1370) peak and require at least a 19 standard deviation contribution. This alone is sufficient to demonstrate its existence. More extensive data on pbar-p -> 3pizero at rest contain delicate interferences which determine the mass and width independently in 1S_0 and 3P_1 annihilation and agree within 5 MeV for both mass and width. The peak in 2pi is at 1282 +- 5 MeV, but the rapid increase in 4pi phase space with mass displaces the 4pi peak to 1360 MeV. BES II data for J/Psi -> phi-pi-πcontain a visible f0(1370) -> 2pi signal >8 sigma. In all cases, a resonant phase variation is required.
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The pi-pi mass spectrum in Y(4260) -> pi-pi-J/psi
Three ways of fitting the pi-pi mass spectrum in Y(4260) decays are studied. Data presented recently by Belle cannot be fitted by the pi-pi S-wave intensity for elastic scattering. They can be fitted by adding a rather arbitrary destructive interference with the sigma pole term. A better fit may be obtained with the decay sequence Y -> pi-H, H -> pi-J/psi, where H is a JPC=1-- c-cbar-q-qbar state peaking at 4.0 GeV with a width ~280 MeV. A third possibility, involving a triangle diagram due to Y(4260)-> DD_1(2420), D_1->D*(2007)-pi, DD*->pi-J/psi fails to fit the data. The first and second possibilities could be resolved by analysis of the Y(4260) Dalitz plot and pi-J/psi mass projection, not presently publicly available.
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Reply to Takamatsu's paper on the Kappa
The essential elements in my way of fitting the kappa reviewed. A number of incorrect claims made by Takamatsu are clarified and corrected.
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The mass of the sigma pole
BES data on the sigma pole are refitted taking into account new information on coupling of sigma to KK and eta-eta. The fit also includes Cern-Munich data on pi-pi elastic phases shifts and Ke4 data, and gives a pole position of 500 +- 30 - i(264 +- 30) MeV. However, there is a clear discrepancy with the sigma pole position recently predicted by Caprini et al. using the Roy equation. This discrepancy may be explained naturally by uncertainties arising from inelasticity in KK and eta-eta channels and mixing between sigma and f0(980). Adding freedom to accomodate these uncertainties gives an optimum compromise with a pole position of 472 +- 30 - i(271 +- 30) MeV.
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The nature of $σ$, $κ$, $a_0(980)$ and $f_0(980)$
Masses and widths of the four light scalar mesons $σ$, $κ$, $a_0$(980) and $f_0$(980) may be reproduced in a model where mesons scatter via a $q\bar{q}$ loop. A transition potential is used to couple mesons to $q\bar{q}$ at a radius of $\sim 0.57$ fm. Inside this radius, there is an infinite bare spectrum of confined $q\bar{q}$ states, for which a harmonic oscillator is chosen here. The coupled-channel system approximately reproduces the features of both light and heavy meson spectroscopy. The generation of $σ$, $κ$, $a_0(980)$ and $f_0(980)$ is a balance between attraction due to the $q\bar q$ loop and suppression of the amplitudes at the Adler zeros. Phase shifts increase more rapidly as the coupling constant to the mesons increases. This leads to resonant widths which decrease with increasing coupling constant - a characteristically non-perturbative effect.
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Decays of sigma, kappa, a0(980) and fo(980)
Ratios of coupling constants for these decays are compared with q-qbar predictions and Jaffe's 4-quark model. In both models, the predicted ratio g^2(kappa -> K-pi)/ g^2(sigma -> pi-pi) is much too small. Also, for q-qbar, the predicted ratio g^2(kappa -> K-eta ')/g^2(kappa -> K-pi) is much larger than observed. Both models fail for g^2(fo -> KK)/g^2(a0 -> KK). This ratio requires that fo has a dominant KK component. It arises naturally because the fo pole lies very close to the KK threshold, giving its wave function a long KK tail.
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Reconclining phi radiative decays with other data for a0(980), fo(980), pi-pi -> KK and pi-pi -> eta-eta
Data for phi -> gamma (eta-pizero) are analysed using the KK loop model and compared with parameters of a0(980) derived from Crystal Barrel data. The eta-pi mass spectrum agrees closely and the absolute normalisation lies just within errors. However, BES parameters for fo(980) predict a normalisation for phi -> gamma (pizero-pizero) at least a factor 2 lower than is observed. This discrepancy may be eliminated by including constructive interference between fo(980) and sigma. The magnitude required for sigma -> KK is consistent with data on pi-pi -> KK. A dispersion relation analysis by Buttiker, Descotes-Genon and Moussallam of pi-pi -> KK leads to a similar conclusion. Data on pi-pi -> eta-eta also require decays of sigma to eta-eta. Four sets of pi-pi -> KK data all require a small but definite fo(1370) signal.
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A glueball component in fo(1790)
The omega-phi threshold peak observed by BES in J/Psi -> gamma(omega-phi) may be interpreted quantitatively in terms of a glueball component in fo(1790).
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Sigma, Kappa, fo(980) and a0(980)
Both sigma and kappa are well established from E791 data on D->3pi and Ds->Kpipi and BES II data on J/Psi -> omega pi pi and KKpipi. These fits are accurately consistent with pipi and Kpi elastic scattering when one allows for the Adler zero which arises from Chiral Symmetry Breaking. The phase variation with mass is consistent between elastic scattering and production data. Possible interpretations of sigma, kappa, fo(980) and ao(980) are explored. The experimental ratio g^2(fo(980)->KK)/g^2(ao(980)->KK) = 2.7+-0.5 suggests strongly that fo(980) has a large KK component in its wave function. This is a natural consequence of its pole lying very close to the KK threshold.
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The kappa in E791 data for D->K-pi-pi
A combined fit is made to E791 data on D->K-pi-pi, LASS data on K-pi elastic scattering, and BES II data on J/Psi->K*(890)-K-pi.In all cases, the K-pi S-wave is fitted well with a kappa resonance and Ko(1430); the kappa requires an s-dependent width with an Adler zero near threshold. The pole position of the kappa is at M - iGamma/2 = (750 +30 -55) - i(342 +- 60) MeV. The E791 collaboration fitted their data using a form factor for the production process D->kappa-pi. It is shown that this form factor is not needed. The data require point-like production with an RMS radius <0.38 fm with 95 percent confidence.
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Sigma, Kappa and fo(980) in E791 and BES II data
Both sigma and kappa are well established from E791 data on D->3pi and D->K-pi-pi$ and BES II data on J/Psi->omega-pi-pi and KKpipi. Fits to these data are accurately consistent with pi-pi and Kpi elastic scattering when one allows for the Adler zero which arises from Chiral Symmetry Breaking. The phase variation with mass is also consistent between elastic scattering and production data.
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The Kappa in J/Psi -> Kpplus-piminus-Kminus-piplus
BES II data for J/Psi->K*(890)Kpi reveal a strong kappa peak in the Kpi S-wave near threshold. Both magnitude and phase are determined in slices of Kpi mass by interferences with strong Ko(1430), K1(1270) and K1(1400) signals. The phase variation with mass agrees within errors with LASS data for Kpi elastic scattering. A combined fit is presented to both BES and LASS data. The fit uses a Breit-Wigner amplitude with an s-dependent width containing an Adler zero. The kappa pole is at 760+-20(stat)+-40(syst) - i(420+-45+-60syst) MeV. The S-wave I=0 scattering length a_0 = 0.23+-0.04 (in units of m(pi)) is close to the prediction 0.19+-0.02 of Chiral Perturbation Theory.
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The X(3872) and the 3941 MeV peak in omega+J/Psi
Belle data for the pi-pi mass spectrum in X(3872) -> pi-pi + JPsi are well fitted by rho + J/Psi with JPC = 1++, but are poorly fitted by the pi-pi S-wave. Formulae for partial wave amplitudes are given for all likely JPC and decay modes of the 3941 MeV peak in omega + J/Psi. Angular correlations involving up to five angles may allow a spin-parity determination, even with quite low statistics. Special attention is given to the case where X(3872) is a cusp or quasi-bound state with the same quantum numbers as the 3941 MeV peak.
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Four Sorts of Mesons
This report reviews the extensive spectrum of light non-strange qbar-q states up to a mass of 2400 MeV from Crystal Barrel and PS172 data on pbar-p -> Resonance -> A + B in 17 final states. For I=0, C=+1, the spectrum is complete and very secure. Glueball candidates fo(1500), fo(2100), f_2(1950) and eta(2190) are reviewed and also hybrid candidates eta_2(1870) and pi_2(1880). A fourth category of anomalously light 0+ mesons is made of sigma(540), kappa(750), a_0(980) and f_0(980).
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