Estimating the two-particle K-matrix for multiple partial waves and decay channels from finite-volume energies

Morningstar, Colin; Bulava, John; Singha, Bijit; Brett, Ruairí; Fallica, Jacob; Hanlon, Andrew D.; Hörz, Ben

doi:10.1016/j.nuclphysb.2017.09.014

Cited by 76 publications

(106 citation statements)

References 60 publications

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“…Our code uses the library QDP++ from USQCD [53] and the deflated SAP+GCR solver from the openQCD package [54]. For cross-checks of the analysis the package TwoHadronsInBox [55] was used.…”

Section: Gauge Field Configurations and Distillation Schemesmentioning

confidence: 99%

Rho resonance, timelike pion form factor, and implications for lattice studies of the hadronic vacuum polarization

et al. 2020

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We study isospin-1 P-wave ππ scattering in lattice QCD with two flavours of O(a) improved Wilson fermions. For pion masses ranging from m π = 265 MeV to m π = 437 MeV, we determine the energy spectrum in the centre-of-mass frame and in three moving frames. We obtain the scattering phase shifts using Lüscher's finite-volume quantisation condition. Fitting the dependence of the phase shifts on the scattering momentum to a Breit-Wigner form allows us to determine the resonance parameters m ρ and g ρππ . By combining the scattering phase shifts with the decay matrix element of the vector current, we calculate the timelike pion form factor, F π , and compare the results to the Gounaris-Sakurai representation of the form factor in terms of the resonance parameters. In addition, we fit our data for the form factor to the functional form suggested by the Omnès representation, which allows for the extraction of the charge radius of the pion. As a further application, we discuss the long-distance behaviour of the vector correlator, which is dominated by the two-pion channel. We reconstruct the long-distance part in two ways: one based on the finite-volume energies and matrix elements and the other based on F π . It is shown that this part can be accurately constrained using the reconstructions, which has important consequences for lattice calculations of the hadronic vacuum polarisation contribution to the muon anomalous magnetic moment. * felix.erben@ed.ac.uk

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“…Our code uses the library QDP++ from USQCD [53] and the deflated SAP+GCR solver from the openQCD package [54]. For cross-checks of the analysis the package TwoHadronsInBox [55] was used.…”

Section: Gauge Field Configurations and Distillation Schemesmentioning

confidence: 99%

Rho resonance, timelike pion form factor, and implications for lattice studies of the hadronic vacuum polarization

et al. 2020

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“…[5], but it is very difficult to implement. A much simpler method, known as the determinant residual method, is advocated in Ref.…”

Section: Fittingmentioning

confidence: 99%

“…A much simpler method, known as the determinant residual method, is advocated in Ref. [5]. In this method, we introduce the quantization determinant itself as a residual in the correlated χ 2 to be minimized.…”

Section: Fittingmentioning

confidence: 99%

“…This talk reports on work completed in Ref. [5] to provide explicit formulas, software, and new fitting implementations for carrying out two-particle scattering studies using energies obtained from lattice QCD. In our first tests, we incorporate the L = 3 and L = 5 partial waves in the decay of the ρ-meson to two pions and find their contributions to be negligible in the elastic energy region.…”

Section: Introductionmentioning

confidence: 99%

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Scattering from finite-volume energies including higher partial waves and multiple decay channels

et al. 2018

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Abstract. A new implementation of estimating the two-to-two K-matrix from finitevolume 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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“…This method was first proposed in Ref. [10], and a complete description can be found, e.g., in the recent work [11].…”

Section: Introductionmentioning

confidence: 99%

Vector particle scattering on the lattice

2018

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Estimating the two-particle K-matrix for multiple partial waves and decay channels from finite-volume energies

Cited by 76 publications

References 60 publications

Rho resonance, timelike pion form factor, and implications for lattice studies of the hadronic vacuum polarization

Rho resonance, timelike pion form factor, and implications for lattice studies of the hadronic vacuum polarization

Scattering from finite-volume energies including higher partial waves and multiple decay channels

Vector particle scattering on the lattice

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