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Register a new userCoupled $pipi, Koverline{K}$ scattering in $P$-wave and the $rho$ resonance from lattice QCD
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We determine elastic and coupled-channel amplitudes for isospin-1 meson-meson scattering in $P$-wave, by calculating correlation functions using lattice QCD with light quark masses such that $m_pi = 236$ MeV in a cubic volume of $sim (4 ,mathrm{fm})^3$. Variational analyses of large matrices of correlation functions computed using operator constructions resembling $pipi$, $Koverline{K}$ and $qbar{q}$, in several moving frames and several lattice irreducible representations, leads to discrete energy spectra from which scattering amplitudes are extracted. In the elastic $pipi$ scattering region we obtain a detailed energy-dependence for the phase-shift, corresponding to a $rho$ resonance, and we extend the analysis into the coupled-channel $Koverline{K}$ region for the first time, finding a small coupling between the channels.
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We calculate the parameters describing elastic $I=1$, $P$-wave $pipi$ scattering using lattice QCD with $2+1$ flavors of clover fermions. Our calculation is performed with a pion mass of $m_pi approx 320::{rm MeV}$ and a lattice size of $Lapprox 3.6$ fm. We construct the two-point correlation matrices with both quark-antiquark and two-hadron interpolating fields using a combination of smeared forward, sequential and stochastic propagators. The spectra in all relevant irreducible representations for total momenta $|vec{P}| leq sqrt{3} frac{2pi}{L}$ are extracted with two alternative methods: a variational analysis as well as multi-exponential matrix fits. We perform an analysis using Luschers formalism for the energies below the inelastic thresholds, and investigate several phase shift models, including possible nonresonant contributions. We find that our data are well described by the minimal Breit-Wigner form, with no statistically significant nonresonant component. In determining the $rho$ resonance mass and coupling we compare two different approaches: fitting the individually extracted phase shifts versus fitting the $t$-matrix model directly to the energy spectrum. We find that both methods give consistent results, and at a pion mass of $am_{pi}=0.18295(36)_{stat}$ obtain $g_{rhopipi} = 5.69(13)_{stat}(16)_{sys}$, $am_rho = 0.4609(16)_{stat}(14)_{sys}$, and $am_{rho}/am_{N} = 0.7476(38)_{stat}(23)_{sys} $, where the first uncertainty is statistical and the second is the systematic uncertainty due to the choice of fit ranges.
We present the first calculation of coupled-channel meson-meson scattering in the isospin $=1$, $G$-parity negative sector, with channels $pi eta$, $Koverline{K}$ and $pi eta$, in a first-principles approach to QCD. From the discrete spectrum of eigenstates in three volumes extracted from lattice QCD correlation functions we determine the energy dependence of the $S$-matrix, and find that the $S$-wave features a prominent cusp-like structure in $pi eta to pi eta$ close to $Koverline{K}$ threshold coupled with a rapid turn on of amplitudes leading to the $Koverline{K}$ final-state. This behavior is traced to an $a_0(980)$-like resonance, strongly coupled to both $pi eta$ and $Koverline{K}$, which is identified with a pole in the complex energy plane, appearing on only a single unphysical Riemann sheet. Consideration of $D$-wave scattering suggests a narrow tensor resonance at higher energy.
We present for the first time a determination of the energy dependence of the isoscalar $pipi$ elastic scattering phase-shift within a first-principles numerical lattice approach to QCD. Hadronic correlation functions are computed including all required quark propagation diagrams, and from these the discrete spectrum of states in the finite volume defined by the lattice boundary is extracted. From the volume dependence of the spectrum we obtain the $S$-wave phase-shift up to the $Koverline{K}$ threshold. Calculations are performed at two values of the $u,d$ quark mass corresponding to $m_pi = 236, 391$ MeV and the resulting amplitudes are described in terms of a $sigma$ meson which evolves from a bound-state below $pipi$ threshold at the heavier quark mass, to a broad resonance at the lighter quark mass.
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.
We present the first lattice QCD study of coupled isoscalar $pipi,Koverline{K},etaeta$ $S$- and $D$-wave scattering extracted from discrete finite-volume spectra computed on lattices which have a value of the quark mass corresponding to $m_pisim391$ MeV. In the $J^P=0^+$ sector we find analogues of the experimental $sigma$ and $f_0(980)$ states, where the $sigma$ appears as a stable bound-state below $pipi$ threshold, and, similar to what is seen in experiment, the $f_0(980)$ manifests itself as a dip in the $pipi$ cross section in the vicinity of the $Koverline{K}$ threshold. For $J^P=2^+$ we find two states resembling the $f_2(1270)$ and $f_2(1525)$, observed as narrow peaks, with the lighter state dominantly decaying to $pipi$ and the heavier state to $Koverline{K}$. The presence of all these states is determined rigorously by finding the pole singularity content of scattering amplitudes, and their couplings to decay channels are established using the residues of the poles.
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