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We present a determination of the mass, width and coupling of the strange resonances appearing in pion-kaon scattering below 1.8 GeV, namely the much debated $K^*_0(800)$ or $kappa$, the scalar $K^*_0(1430)$, the $K^*(892)$ and $K^*(1410)$ vectors, the spin-two $K^*_2(1430)$ as well as the spin-three $K^*_3(1780)$. The parameters of each resonance are determined using a direct analytic continuation of the pion-kaon partial waves by means of Pade approximants, thus avoiding any particular model description of their pole positions and residues, while taking into account the analytic requirements imposed by dispersion relations.
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Coupled-channel $pi K$ and $eta K$ scattering amplitudes are determined by studying the finite-volume energy spectra obtained from dynamical lattice QCD calculations. Using a large basis of interpolating operators, including both those resembling a $qbar{q}$ construction and those resembling a pair of mesons with relative momentum, a reliable excited-state spectrum can be obtained. Working at ${m_pi=391,mathrm{MeV}}$, we find a gradual increase in the $J^P=0^+$ $pi K$ phase-shift which may be identified with a broad scalar resonance that couples strongly to $pi K$ and weakly to $eta K$. The low-energy behavior of this amplitude suggests a virtual bound-state that may be related to the $kappa$ resonance. A bound state with $J^P=1^-$ is found very close to the $pi K$ threshold energy, whose coupling to the $pi K$ channel is compatible with that of the experimental $K^star(892)$. Evidence is found for a narrow resonance in $J^P=2^+$. Isospin--3/2 $pi K$ scattering is also studied and non-resonant phase-shifts spanning the whole elastic scattering region are obtained.
In this article we study resonances and surface waves in $pi^+$--p scattering. We focus on the sequence whose spin-parity values are given by $J^p = {3/2}^+,{7/2}^+, {11/2}^+, {15/2}^+,{19/2}^+$. A widely-held belief takes for granted that this sequence can be connected by a moving pole in the complex angular momentum (CAM) plane, which gives rise to a linear trajectory of the form $J = alpha_0+alpha m^2$, $alphasim 1/(mathrm{GeV})^2$, which is the standard expression of the Regge pole trajectory. But the phenomenology shows that only the first few resonances lie on a trajectory of this type. For higher $J^p$ this rule is violated and is substituted by the relation $Jsim kR$, where $k$ is the pion--nucleon c.m.s.-momentum, and $Rsim 1$ fm. In this article we prove: (a) Starting from a non-relativistic model of the proton, regarded as composed by three quarks confined by harmonic potentials, we prove that the first three members of this $pi^+$-p resonance sequence can be associated with a vibrational spectrum of the proton generated by an algebra $Sp(3,R)$. Accordingly, these first three members of the sequence can be described by Regge poles and lie on a standard linear trajectory. (b) At higher energies the amplitudes are dominated by diffractive scattering, and the creeping waves play a dominant role. They can be described by a second class of poles, which can be called Sommerfelds poles, and lie on a line nearly parallel to the imaginary axis of the CAM-plane. (c) The Sommerfeld pole which is closest to the real axis of the CAM-plane is dominant at large angles, and describes in a proper way the backward diffractive peak in both the following cases: at fixed $k$, as a function of the scattering angle, and at fixed scattering angle $theta=pi$, as a function of $k$. (d) The evolution of this pole, as a function of $k$, is given in first approximation by $Jsimeq kR$.
The low-energy S-wave component of the decay $D^+ to K^- pi^+ pi^+$ is studied by means of a chiral SU(3)XSU(3) effective theory. As far as the primary vertex is concerned, we allow for the possibility of either direct production of three pseudoscalar mesons or a meson and a scalar resonance. Special attention is paid to final state interactions associated with elastic meson-meson scattering. The corresponding two-body amplitude is unitarized by ressumming s-channel diagrams and can be expressed in terms of the usal phase shifts $delta$. This procedure preserves the chiral properties of the amplitude at low-energies. Final state interactions also involve another phase $omega$, which describes intermediate two-meson propagation and is theoretically unambiguous. This phase is absent in the K-matrix approximation. Partial contributions to the decay amplitude involve a real term, another one with phase $delta$ and several others with phases $delta+omega$. Our main result is a simple and almost model independent chiral generalization of the usual Breit-Wigner expression, suited to be used in analyses of production data involving scalar resonances.
After having announced the statistically significant observation (5.6~$sigma$) of the new exotic $pi K$ atom, the DIRAC experiment at the CERN proton synchrotron presents the measurement of the corresponding atom lifetime, based on the full $pi K$ data sample: $tau = (5.5^{+5.0}_{-2.8}) cdot 10^{-15}s$. By means of a precise relation ($<1%$) between atom lifetime and scattering length, the following value for the S-wave isospin-odd $pi K$ scattering length $a_0^{-}~=~frac{1}{3}(a_{1/2}-a_{3/2})$ has been derived: $left|a_0^-right| = (0.072^{+0.031}_{-0.020}) M_{pi}^{-1}$.
We extend our study of the $Kpi$ system to moving frames and present an exploratory extraction of the masses and widths for the $K^*$ resonances by simulating $Kpi$ scattering in p-wave with $I=1/2$ on the lattice. Using $Kpi$ systems with non-vanishing total momenta allows the extraction of phase shifts at several values of $Kpi$ relative momenta. A Breit-Wigner fit of the phase renders a $K^*(892)$ resonance mass and $K^*to K pi $ coupling compatible with the experimental numbers. We also determine the $K^*(1410)$ mass assuming the experimental $K^*(1410)$ width. We contrast the resonant $I=1/2$ channel with the repulsive non-resonant $I=3/2$ channel, where the phase is found to be negative and small, in agreement with experiment.
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