Built on

T. D. Blanton, F. Romero-López and S. R. Sharpe, Implementing the three-particle quantization condition including higher partial waves , JHEP 03
Original
1901
Earlier work this paper cites.
M. T. Hansen and S. R. Sharpe, Lattice QCD and Three-particle Decays of Resonances , Ann. Rev. Nucl. Part. Sci. 69
Original
1901
Earlier work this paper cites.
J. Bulava and M. T. Hansen, Scattering amplitudes from finite-volume spectral functions , Phys. Rev. D 100
Original
1903
Earlier work this paper cites.
M. Hansen, A. Lupo and N. Tantalo, Extraction of spectral densities from lattice correlators , Phys. Rev. D 99
Original
1903
Earlier work this paper cites.
M. T. Hansen and A. Patella, Finite-volume effects in ( g − 2 ) μ HVP,LO (g-2)^{\text{HVP,LO}}_{\mu} , Phys. Rev. Lett. 123
Original
1904
Earlier work this paper cites.
M. Padmanath, Hadron Spectroscopy and Resonances: Review , PoS LATTICE2018
Original
1905
Earlier work this paper cites.
A. W. Jackura, S. M. Dawid, C. Fernández-Ramírez, V. Mathieu, M. Mikhasenko, A. Pilloni et al., Equivalence of three-particle scattering formalisms , Phys. Rev. D100
Original
1905
Earlier work this paper cites.
R. A. Briceño, M. T. Hansen, S. R. Sharpe and A. P. Szczepaniak, Unitarity of the infinite-volume three-particle scattering amplitude arising from a finite-volume formalism , Phys. Rev. D100
Original
1905
Earlier work this paper cites.
F. Romero-López, S. R. Sharpe, T. D. Blanton, R. A. Briceño and M. T. Hansen, Numerical exploration of three relativistic particles in a finite volume including two-particle resonances and bound states , JHEP 10
Original
1908
Earlier work this paper cites.
J. Bulava, Meson-Nucleon Scattering Amplitudes from Lattice QCD , AIP Conf. Proc. 2249
Original
1909
Earlier work this paper cites.
R. A. Briceño, M. T. Hansen and A. W. Jackura, Consistency checks for two-body finite-volume matrix elements: I. Conserved currents and bound states , Phys. Rev. D 100
Original
1909
Earlier work this paper cites.
R. A. Briceño, Z. Davoudi, M. T. Hansen, M. R. Schindler and A. Baroni, Long-range electroweak amplitudes of single hadrons from Euclidean finite-volume correlation functions , Phys. Rev. D 101
Original
1911
Earlier work this paper cites.
K. Osterwalder and R. Schrader, AXIOMS FOR EUCLIDEAN GREEN’S FUNCTIONS , Commun. Math. Phys. 31
1973
Earlier work this paper cites.
K. G. Wilson, “ Talk at the Abingdon Meeting on Lattice Gauge Theories .” 1981
1981
Earlier work this paper cites.
M. Bertero, P. Boccacci and E. R. Pike, On the recovery and resolution of exponential relaxation rates from experimental data: a singular-value analysis of the laplace transform inversion in the presence of noise , Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 383
1982
Earlier work this paper cites.
M. Lüscher, Volume Dependence of the Energy Spectrum in Massive Quantum Field Theories. 1. Stable Particle States , Commun. Math. Phys. 104
1986
Earlier work this paper cites.
M. Lüscher, Volume Dependence of the Energy Spectrum in Massive Quantum Field Theories. 2. Scattering States , Commun. Math. Phys. 105
1986
Earlier work this paper cites.
L. Maiani and M. Testa, Final state interactions from Euclidean correlation functions , Phys. Lett. B 245
1990
Earlier work this paper cites.
K. Rummukainen and S. A. Gottlieb, Resonance scattering phase shifts on a nonrest frame lattice , Nucl. Phys. B450
1995
Earlier work this paper cites.
L. Lellouch and M. Lüscher, Weak transition matrix elements from finite volume correlation functions , Commun. Math. Phys. 219
2001
Earlier work this paper cites.
C. Lin, G. Martinelli, C. T. Sachrajda and M. Testa, K – > > pi pi decays in a finite volume , Nucl. Phys. B 619
2001
Earlier work this paper cites.
G. Bailas, S. Hashimoto and T. Ishikawa, Reconstruction of smeared spectral function from Euclidean correlation functions , PTEP 2020
Original
2001
Earlier work this paper cites.
R. A. Briceño, M. T. Hansen and A. W. Jackura, Consistency checks for two-body finite-volume matrix elements: II. Perturbative systems , Phys. Rev. D 101
Original
2002
Earlier work this paper cites.
M. T. Hansen, F. Romero-López and S. R. Sharpe, Generalizing the relativistic quantization condition to include all three-pion isospin channels , JHEP 07
Original
2003
Earlier work this paper cites.

Similar

W. Detmold and M. J. Savage, Electroweak matrix elements in the two nucleon sector from lattice QCD , Nucl. Phys. A 743
2004
Cited alongside, same era.
M. T. Hansen and A. Patella, Finite-volume and thermal effects in the leading-HVP contribution to muonic ( g − 2 ) (g-2) , JHEP 10
Original
2004
Cited alongside, same era.
S. He, X. Feng and C. Liu, Two particle states and the S-matrix elements in multi-channel scattering , JHEP 07
2005
Cited alongside, same era.
C. h. Kim, C. T. Sachrajda and S. R. Sharpe, Finite-volume effects for two-hadron states in moving frames , Nucl. Phys. B727
2005
Cited alongside, same era.
N. H. Christ, C. Kim and T. Yamazaki, Finite volume corrections to the two-particle decay of states with non-zero momentum , Phys. Rev. D72
2005
Cited alongside, same era.

Then

R. A. Briceño and Z. Davoudi, Three-particle scattering amplitudes from a finite volume formalism , Phys. Rev. D87
Original
2013
Later among the works it cites.
R. A. Briceño, Two-particle multichannel systems in a finite volume with arbitrary spin , Phys. Rev. D89
Original
2014
Later among the works it cites.
M. T. Hansen and S. R. Sharpe, Relativistic, model-independent, three-particle quantization condition , Phys. Rev. D90
Original
2014
Later among the works it cites.
A. Agadjanov, V. Bernard, U. G. Meißner and A. Rusetsky, A framework for the calculation of the Δ N γ ∗ \Delta N\gamma^{*} transition form factors on the lattice , Nucl. Phys. B886
Original
2014
Later among the works it cites.
M. T. Hansen and S. R. Sharpe, Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude , Phys. Rev. D92

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2020

Variations on the Maiani-Testa approach and the inverse problem

Bruno, Mattia, Hansen, Maxwell T.

Understand

We discuss a method to construct hadronic scattering and decay amplitudes from Euclidean correlators, by combining the approach of a regulated inverse Laplace transform with the work of Maiani and Testa.

Revisiting the original result, we observe that the key observation, i.e.
that only threshold scattering information can be extracted at large separations, can be understood by interpreting the correlator as a spectral function, $\rho(\omega)$, convoluted with the Euclidean kernel, $e^{- \omega t}$, which is sharply peaked at threshold.
We therefore consider a modification in which a smooth step function, equal to one above a target energy, is inserted in the spectral decomposition.

Built on

T. D. Blanton, F. Romero-López and S. R. Sharpe, Implementing the three-particle quantization condition including higher partial waves , JHEP 03
Original
1901
Earlier work this paper cites.
M. T. Hansen and S. R. Sharpe, Lattice QCD and Three-particle Decays of Resonances , Ann. Rev. Nucl. Part. Sci. 69
Original
1901
Earlier work this paper cites.
J. Bulava and M. T. Hansen, Scattering amplitudes from finite-volume spectral functions , Phys. Rev. D 100
Original
1903
Earlier work this paper cites.
M. Hansen, A. Lupo and N. Tantalo, Extraction of spectral densities from lattice correlators , Phys. Rev. D 99
Original
1903
Earlier work this paper cites.
M. T. Hansen and A. Patella, Finite-volume effects in ( g − 2 ) μ HVP,LO (g-2)^{\text{HVP,LO}}_{\mu} , Phys. Rev. Lett. 123
Original
1904
Earlier work this paper cites.
M. Padmanath, Hadron Spectroscopy and Resonances: Review , PoS LATTICE2018
Original
1905
Earlier work this paper cites.
A. W. Jackura, S. M. Dawid, C. Fernández-Ramírez, V. Mathieu, M. Mikhasenko, A. Pilloni et al., Equivalence of three-particle scattering formalisms , Phys. Rev. D100
Original
1905
Earlier work this paper cites.
R. A. Briceño, M. T. Hansen, S. R. Sharpe and A. P. Szczepaniak, Unitarity of the infinite-volume three-particle scattering amplitude arising from a finite-volume formalism , Phys. Rev. D100
Original
1905
Earlier work this paper cites.
F. Romero-López, S. R. Sharpe, T. D. Blanton, R. A. Briceño and M. T. Hansen, Numerical exploration of three relativistic particles in a finite volume including two-particle resonances and bound states , JHEP 10
Original
1908
Earlier work this paper cites.
J. Bulava, Meson-Nucleon Scattering Amplitudes from Lattice QCD , AIP Conf. Proc. 2249
Original
1909
Earlier work this paper cites.
R. A. Briceño, M. T. Hansen and A. W. Jackura, Consistency checks for two-body finite-volume matrix elements: I. Conserved currents and bound states , Phys. Rev. D 100
Original
1909
Earlier work this paper cites.
R. A. Briceño, Z. Davoudi, M. T. Hansen, M. R. Schindler and A. Baroni, Long-range electroweak amplitudes of single hadrons from Euclidean finite-volume correlation functions , Phys. Rev. D 101
Original
1911
Earlier work this paper cites.
K. Osterwalder and R. Schrader, AXIOMS FOR EUCLIDEAN GREEN’S FUNCTIONS , Commun. Math. Phys. 31
1973
Earlier work this paper cites.
K. G. Wilson, “ Talk at the Abingdon Meeting on Lattice Gauge Theories .” 1981
1981
Earlier work this paper cites.
M. Bertero, P. Boccacci and E. R. Pike, On the recovery and resolution of exponential relaxation rates from experimental data: a singular-value analysis of the laplace transform inversion in the presence of noise , Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 383
1982
Earlier work this paper cites.
M. Lüscher, Volume Dependence of the Energy Spectrum in Massive Quantum Field Theories. 1. Stable Particle States , Commun. Math. Phys. 104
1986
Earlier work this paper cites.
M. Lüscher, Volume Dependence of the Energy Spectrum in Massive Quantum Field Theories. 2. Scattering States , Commun. Math. Phys. 105
1986
Earlier work this paper cites.
L. Maiani and M. Testa, Final state interactions from Euclidean correlation functions , Phys. Lett. B 245
1990
Earlier work this paper cites.
K. Rummukainen and S. A. Gottlieb, Resonance scattering phase shifts on a nonrest frame lattice , Nucl. Phys. B450
1995
Earlier work this paper cites.
L. Lellouch and M. Lüscher, Weak transition matrix elements from finite volume correlation functions , Commun. Math. Phys. 219
2001
Earlier work this paper cites.
C. Lin, G. Martinelli, C. T. Sachrajda and M. Testa, K – > > pi pi decays in a finite volume , Nucl. Phys. B 619
2001
Earlier work this paper cites.
G. Bailas, S. Hashimoto and T. Ishikawa, Reconstruction of smeared spectral function from Euclidean correlation functions , PTEP 2020
Original
2001
Earlier work this paper cites.
R. A. Briceño, M. T. Hansen and A. W. Jackura, Consistency checks for two-body finite-volume matrix elements: II. Perturbative systems , Phys. Rev. D 101
Original
2002
Earlier work this paper cites.
M. T. Hansen, F. Romero-López and S. R. Sharpe, Generalizing the relativistic quantization condition to include all three-pion isospin channels , JHEP 07
Original
2003
Earlier work this paper cites.

Similar

W. Detmold and M. J. Savage, Electroweak matrix elements in the two nucleon sector from lattice QCD , Nucl. Phys. A 743
2004
Cited alongside, same era.
M. T. Hansen and A. Patella, Finite-volume and thermal effects in the leading-HVP contribution to muonic ( g − 2 ) (g-2) , JHEP 10
Original
2004
Cited alongside, same era.
S. He, X. Feng and C. Liu, Two particle states and the S-matrix elements in multi-channel scattering , JHEP 07
2005
Cited alongside, same era.
C. h. Kim, C. T. Sachrajda and S. R. Sharpe, Finite-volume effects for two-hadron states in moving frames , Nucl. Phys. B727
2005
Cited alongside, same era.
N. H. Christ, C. Kim and T. Yamazaki, Finite volume corrections to the two-particle decay of states with non-zero momentum , Phys. Rev. D72
2005
Cited alongside, same era.