The I = 1 pion–pion scattering amplitude and timelike pion form factor from Nf = 2 + 1 lattice QCD

Andersen, Christian Walther; Bulava, John; Hörz, Ben; Morningstar, Colin

doi:10.1016/j.nuclphysb.2018.12.018

Cited by 128 publications

(183 citation statements)

References 195 publications

(279 reference statements)

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“…We also computed two other ratios with the same asymptotic value proposed by the authors of [16]. Similar to that work, we find R(t) produces the most precise plateaus of the three and is not reliant on the fit to Equation (2.15) for the extraction of Z n .…”

Section: A Determination Of the Finite Volume Energy Spectrumsupporting

confidence: 68%

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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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Section: A Determination Of the Finite Volume Energy Spectrumsupporting

confidence: 68%

“…Secondly, using the approach suggested by Meyer [20] (which is closely related to work by Lellouch and Lüscher [21]), the pion form factor, F π , can be determined in lattice QCD in the timelike region. For first lattice implementations of this method see [16,22].…”

Section: Introductionmentioning

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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“…• The determination of individual finite-volume energies and matrix elements becomes cumbersome in large spatial volumes. On one ensemble with m π L = 6.1 from a recent lattice QCD calculation of elastic pion-pion scattering [36], 43 energies are determined, while another recent ρπ scattering calculation [37] (performed at heavy quark masses so the ρ is stable) employs 141 energies across two volumes with m π L = 10.3 and 12.4. The increasingly dense finite-volume spectrum and the simultaneously decreasing magnitude of the desired finite volume effects makes the large volume limit of this formalism intractable.…”

Section: Introductionmentioning

confidence: 99%

Scattering amplitudes from finite-volume spectral functions

Bulava

Hansen

2019

Phys. Rev. D

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A novel proposal is outlined to determine scattering amplitudes from finite-volume spectral functions. The method requires extracting smeared spectral functions from finite-volume Euclidean correlation functions, with a particular complex smearing kernel of width which implements the standard i -prescription. In the L → ∞ limit these smeared spectral functions are therefore equivalent to Minkowskian correlators with a specific time ordering to which a modified LSZ reduction formalism can be applied. The approach is presented for general m → n scattering amplitudes (above arbitrary inelastic thresholds) for a single-species real scalar field, although generalization to arbitrary spins and multiple coupled channels is likely straightforward. Processes mediated by the single insertion of an external current are also considered. Numerical determination of the finitevolume smeared spectral function is discussed briefly and the interplay between the finite volume, Euclidean signature, and time-ordered i -prescription is illustrated perturbatively in a toy example.1 See recent proceedings of the yearly lattice conference for reviews on the current state-of-the-art for lattice QCD simulations [70].Furthermore, several novel algorithms [71-73] potentially enable significantly larger volumes than used at present. 2 The normalization of the unsmeared spectral function differs from the one used in Ref. [74] but is more appropriate for the smearing kernels considered in this work. In particular, for the complex kernels we introduce below the real part will continue to satisfy Eq. 3.Consider the endcap function defined in Eq. 5. We begin by reducing the rightmost field to isolate a two-particle in-state on the right endcap. Insert a complete set of two-particle in-states and examine the asymptotic contribution

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“…Varying the lattice size, through, e.g., elongated boxes [3,4], allows one to produce a number of phase-shifts at the eigenergies; additional phase-shifts can be determined by projecting the particles to moving frames [5]. This enabled lattice QCD calculations of the ρ meson phase-shifts in N f = 2 [6][7][8][9][10][11][12] and N f = 2 + 1 [13][14][15][16][17][18][19][20]. The isoscalar sector is particularly interesting because of the presence of the broad f 0 (500) "σ" resonance.…”

Section: Introductionmentioning

confidence: 99%

Pion scattering in the isospin I=2 channel from elongated lattices

et al. 2019

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Pion-pion elastic scattering in the isospin I = 2 channel is investigated in two-flavor dynamical lattice QCD. Six ensembles are used with lattices elongated in one of the spatial dimensions at two quark masses corresponding to a pion mass of 315 MeV and 226 MeV. The energy of the low-lying states below the inelastic threshold are extracted in each case using the standard variational method. The extracted finite-volume spectrum is fitted by the inverse amplitude method simultaneously for both quark masses and extrapolated thereafter to the physical point. The resulting phase-shifts and scattering length are compared with those from experiment, leading-order chiral perturbation theory and other lattice studies. Our calculations match the experimental results.

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The I = 1 pion–pion scattering amplitude and timelike pion form factor from Nf = 2 + 1 lattice QCD

Cited by 128 publications

References 195 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 amplitudes from finite-volume spectral functions

Pion scattering in the isospin I=2 channel from elongated lattices

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The I = 1 pion–pion scattering amplitude and timelike pion form factor from Nf = 2 + 1 lattice QCD

Cited by 128 publications

References 195 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 amplitudes from finite-volume spectral functions

Pion scattering in the isospin I=2 channel from elongated lattices

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The I = 1 pion–pion scattering amplitude and timelike pion form factor from Nf = 2 + 1 lattice QCD