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Register a new userScattering from finite-volume energies including higher partial waves and multiple decay channels
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A new implementation of estimating the two-to-two $K$-matrix from finite-volume energies based on the Luescher formalism is described. The method includes higher partial waves and multiple decay channels, and the fitting procedure properly includes all covariances and statistical uncertainties. The method is also simpler than previously used procedures. Formulas and software for handling total spins up to $S=2$ and orbital angular momenta up to $L=6$ are presented.
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An implementation of estimating the two-to-two $K$-matrix from finite-volume energies based on the Luscher formalism and involving a Hermitian matrix known as the box matrix is described. The method includes higher partial waves and multiple decay channels. Two fitting procedures for estimating the $K$-matrix parameters, which properly incorporate all statistical covariances, are discussed. Formulas and software for handling total spins up to $S=2$ and orbital angular momenta up to $L=6$ are obtained for total momenta in several directions. First tests involving $rho$-meson decay to two pions include the $L=3$ and $L=5$ partial waves, and the contributions from these higher waves are found to be negligible in the elastic energy range.
We study two- and three-meson systems composed either of pions or kaons at maximal isospin using Monte Carlo simulations of lattice QCD. Utilizing the stochastic LapH method, we are able to determine hundreds of two- and three-particle energy levels, in nine different momentum frames, with high precision. We fit these levels using the relativistic finite-volume formalism based on a generic effective field theory in order to determine the parameters of the two- and three-particle K-matrices. We find that the statistical precision of our spectra is sufficient to probe not only the dominant $s$-wave interactions, but also those in $d$ waves. In particular, we determine for the first time a term in the three-particle K-matrix that contains two-particle $d$ waves. We use three $N_f=2+1$ CLS ensembles with pion masses of $200$, $280$, and $340;$MeV. This allows us to study the chiral dependence of the scattering observables, and compare to the expectations of chiral perturbation theory.
We determine scattering phase shifts for S,P,D, and F partial wave channels in two-nucleon systems using lattice QCD methods. We use a generalization of Luschers finite volume method to determine infinite volume phase shifts from a set of finite volume ground- and excited-state energy levels on two volumes, V=(3.4 fm)^3 and V=(4.5 fm)^3. The calculations are performed in the SU(3)-flavor limit, corresponding to a pion mass of approximately 800 MeV. From the energy dependence of the phase shifts we are able to extract scattering parameters corresponding to an effective range expansion.
The presence of long-range interactions violates a condition necessary to relate the energy of two particles in a finite volume to their S-matrix elements in the manner of Luscher. While in infinite volume, QED contributions to low-energy charged particle scattering must be resummed to all orders in perturbation theory (the Coulomb ladder diagrams), in a finite volume the momentum operator is gapped, allowing for a perturbative treatment. The leading QED corrections to the two-particle finite-volume energy quantization condition below the inelastic threshold, as well as approximate formulas for energy eigenvalues, are obtained. In particular, we focus on two spinless hadrons in the A1+ irreducible representation of the cubic group, and truncate the strong interactions to the s-wave. These results are necessary for the analysis of Lattice QCD+QED calculations of charged-hadron interactions, and can be straightforwardly generalized to other representations of the cubic group, to hadrons with spin, and to include higher partial waves.
Luschers method is routinely used to determine meson-meson, meson-baryon and baryon-baryon s-wave scattering amplitudes below inelastic thresholds from Lattice QCD calculations - presently at unphysical light-quark masses. In this work we review the formalism and develop the requisite expressions to extract phase-shifts describing meson-meson scattering in partial-waves with angular-momentum l<=6 and l=9. The implications of the underlying cubic symmetry, and strategies for extracting the phase-shifts from Lattice QCD calculations, are presented, along with a discussion of the signal-to-noise problem that afflicts the higher partial-waves.
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