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Register a new userAn $a_0$ resonance in strongly coupled $pi eta$, $Koverline{K}$ scattering from lattice QCD
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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.
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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.
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.
In this project, we will compute the form factors relevant for $B to K^*(to K pi)ell^+ell^-$ decays. To map the finite-volume matrix elements computed on the lattice to the infinite-volume $B to K pi$ matrix elements, the $K pi$ scattering amplitude needs to be determined using Luschers method. Here we present preliminary results from our calculations with $2+1$ flavors of dynamical clover fermions. We extract the $P$-wave scattering phase shifts and determine the $K^*$ resonance mass and the $K^* K pi$ coupling for two different ensembles with pion masses of $317(2)$ and $178(2)$ MeV.
A calculation of the ratio of leptonic decay constants f_{K^+}/f_{pi^+} makes possible a precise determination of the ratio of CKM matrix elements |V_{us}|/|V_{ud}| in the Standard Model, and places a stringent constraint on the scale of new physics that would lead to deviations from unitarity in the first row of the CKM matrix. We compute f_{K^+}/f_{pi^+} numerically in unquenched lattice QCD using gauge-field ensembles recently generated that include four flavors of dynamical quarks: up, down, strange, and charm. We analyze data at four lattice spacings a ~ 0.06, 0.09, 0.12, and 0.15 fm with simulated pion masses down to the physical value 135 MeV. We obtain f_{K^+}/f_{pi^+} = 1.1947(26)(37), where the errors are statistical and total systematic, respectively. This is our first physics result from our N_f = 2+1+1 ensembles, and the first calculation of f_{K^+}/f_{pi^+} from lattice-QCD simulations at the physical point. Our result is the most precise lattice-QCD determination of f_{K^+}/f_{pi^+}, with an error comparable to the current world average. When combined with experimental measurements of the leptonic branching fractions, it leads to a precise determination of |V_{us}|/|V_{ud}| = 0.2309(9)(4) where the errors are theoretical and experimental, respectively.
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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