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Register a new userThe $kappa$ resonance in s wave $pi K$ scatterings
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A new unitarization approach incorporated with chiral symmetry is established and applied to study the $pi K$ elastic scatterings. We demonstrate that the $kappa$ resonance exists, if the scattering length parameter in the I=1/2, J=0 channel does not deviate much from its value predicted by chiral perturbation theory. The mass and width of the $kappa$ resonance is found to be $M_kappa=594pm 79MeV$, $Gamma_kappa=724pm 332MeV$, obtained by fitting the LASS data up to 1430MeV. Better determination to the pole parameters is possible if the chiral predictions on scattering lengths are taken into account.
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A new approach to the analysis of three body decays is presented. Model-independent results are obtained for the swave $Kpi$ amplitude as a function of $Kpi$ invariant mass. These are compared with results from $Kmpip$ elastic scattering, and the prediction of the Watson theorem, that the phase behavour be the same below $Keta^{prime}$ threshold, is tested. Contributions from $I=half$ and $I={3over 2}$ are not resolved in this study. If $I=half$ dominates, however, the Watson theorem does not describe these data well.}
Within the quasi-two-body decay model, we study the localized $CP$ violation and branching fraction of the four-body decay $bar{B}^0rightarrow [K^-pi^+]_{S/V}[pi^+pi^-]_{V/S} rightarrow K^-pi^+pi^-pi^+$ when $K^-pi^+$ and $pi^-pi^+$ pair invariant masses are $0.35<m_{K^-pi^+}<2.04 , mathrm{GeV}$ and $0<m_{pi^-pi^+}<1.06, mathrm{GeV}$, with the pairs being dominated by the $bar{K}^*_0(700)^0$, $bar{K}^*(892)^0$, $bar{K}^*(1410)^0$, $bar{K}^*_0(1430)$ and $bar{K}^*(1680)^0$, and $f_0(500)$, $rho^0(770)$ , $omega(782)$ and $f_0(980)$ resonances, respectively. When dealing with the dynamical functions of these resonances, $f_0(500)$, $rho^0(770)$, $f_0(980)$ and $bar{K}^*_0(1430)$ are modeled with the Bugg model, Gounaris-Sakurai function, Flatt$acute{mathrm{e}}$ formalism and LASS lineshape, respectively, while others are described by the relativistic Breit-Wigner function. Adopting the end point divergence parameters $rho_Ain[0,0.5]$ and $phi_Ain[0,2pi]$, our predicted results are $mathcal{A_{CP}}(bar{B}^0rightarrow K^-pi^+pi^+pi^-)in[-0.383,0.421]$ and $mathcal{B}(bar{B}^0rightarrow K^-pi^+pi^+pi^-)in[7.36,199.69]times10^{-8}$ based on the hypothetical $qbar{q}$ structures for the scalar mesons in the QCD factorization approach. Meanwhile, we calculate the $CP$ violating asymmetries and branching fractions of the two-body decays $bar{B}^0rightarrow SV(VS)$ and all the individual four-body decays $bar{B}^0rightarrow SV(VS) rightarrow K^-pi^+pi^-pi^+$, respectively. Our theoretical results for the two-body decays $bar{B}^0rightarrow bar{K}^*(892)^0$$f_0(980)$, $bar{B}^0rightarrow bar{K}^*_0(1430)^0$$omega(782)$, $bar{B}^0rightarrow bar{K}^*(892)^0f_0(980)$, $bar{B}^0rightarrowbar{K}^*_0(1430)^0rho$,
We briefly review the recent results obtained by Fermilab experiment E791 on the Dalitz plot analysis of the decay D+ -> K- pi+ pi+, where indication for a light Kpi scalar resonance, the kappa, was found. We also present preliminary studies providing further information on the phase behavior of the scalar components at low mass, supporting the previous indication for the kappa.
Low-energy partial-wave $pi N$ scattering data is reexamined with the help of the production representation of partial-wave $S$ matrix, where branch cuts and poles are thoroughly under consideration. The left-hand cut contribution to the phase shift is determined, with controlled systematic error estimates, by using the results of $mathcal{O}(p^3)$ chiral perturbative amplitudes obtained in the extended-on-mass-shell scheme. In $S_{11}$ and $P_{11}$ channels, severe discrepancies are observed between the phase shift data and the sum of all known contributions. Statistically satisfactory fits to the data can only be achieved by adding extra poles in the two channels. We find that a $S_{11}$ resonance pole locates at $sqrt{z_{r}}=(0.895pm0.081)-(0.164pm0.023)i$ GeV, on the complex $s$-plane. On the other hand, a $P_{11}$ virtual pole, as an accompanying partner of the nucleon bound-state pole, locates at $sqrt{z_{v}}=(0.966pm0.018)$ GeV, slightly above the nucleon pole on the real axis below threshold. Physical origin of the two newly established poles is explored to the best of our knowledge. It is emphasized that the $mathcal{O}(p^3)$ calculation greatly improves the fit quality comparing with the previous $mathcal{O}(p^2)$ one.
The COMPASS collaboration has collected the currently largest data set on diffractively produced $pi^-pi^-pi^+$ final states using a negative pion beam of 190 GeV/c momentum impinging on a stationary proton target. This data set allows for a systematic partial-wave analysis in 100 bins of three-pion mass, $0.5 < m_{3pi} < 2.5$ GeV/c$^2$ , and in 11 bins of the reduced four-momentum transfer squared, $0.1 < t < 1.0$ (GeV/c)$^2$ . This two-dimensional analysis offers sensitivity to genuine one-step resonance production, i.e. the production of a state followed by its decay, as well as to more complex dynamical effects in nonresonant $3pi$ production. In this paper, we present detailed studies on selected $3pi$ partial waves with $J^{PC} = 0^{-+}$, $1^{++}$, $2^{-+}$, $2^{++}$, and $4^{++}$. In these waves, we observe the well-known ground-state mesons as well as a new narrow axial-vector meson $a_1(1420)$ decaying into $f_0(980) pi$. In addition, we present the results of a novel method to extract the amplitude of the $pi^-pi^+$ subsystem with $I^{G}J^{PC} = 0^+ 0^{++}$ in various partial waves from the $pi^-pi^-pi^+$ data. Evidence is found for correlation of the $f_0(980)$ and $f_0(1500)$ appearing as intermediate $pi^- pi^+$ isobars in the decay of the known $pi(1800)$ and $pi_2(1880)$.
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