Form factors of two-hadron states from a covariant finite-volume formalism

Alessandro Baroni; Raúl A. Briceño; Maxwell T. Hansen; Felipe G. Ortega-Gama

doi:10.1103/PhysRevD.100.034511

Form factors of two-hadron states from a covariant finite-volume formalism

Alessandro Baroni, Raúl A. Briceño, Maxwell T. Hansen, Felipe G. Ortega-Gama

Research output: Contribution to journal › Article › peer-review

31 Scopus citations

Abstract

In this work we develop a Lorentz-covariant version of the previously derived formalism for relating finite-volume matrix elements to 2+J→2 transition amplitudes. We also give various details relevant for the implementation of this formalism in a realistic numerical lattice QCD calculation. Particular focus is given to the role of single-particle form factors in disentangling finite-volume effects from the triangle diagram that arise when J couples to one of the two hadrons. This also leads to a new finite-volume function, denoted G, the numerical evaluation of which is described in detail. As an example we discuss the determination of the ππ+J→ππ amplitude in the ρ channel, for which the single-pion form factor, Fπ(Q2), as well as the scattering phase, δππ, are required to remove all power-law finite-volume effects. The formalism presented here holds for local currents with arbitrary Lorentz structure, and we give specific examples of insertions with up to two Lorentz indices.

Original language	English
Article number	034511
Journal	Physical Review D
Volume	100
Issue number	3
DOIs	https://doi.org/10.1103/PhysRevD.100.034511
State	Published - Aug 13 2019
Externally published	Yes

Funding

R. A. B. acknowledges support from U.S. Department of Energy Contract No. DE-AC05-06OR23177, under which Jefferson Science Associates, LLC, manages and operates Jefferson Lab, and the U.S. Department of Energy Early Career award Contract No. DE-SC0019229. A. B. acknowledges support from U.S. Department of Energy, Office of Science, Office of Nuclear Physics, under Award No. DE-SC0010300. The authors would like to thank A. Jackura, as well as J. Dudek, R. Edwards, D. Wilson, and the rest of the Hadron Spectrum Collaboration for useful discussions.

Funders	Funder number
U.S. Department of Energy	DE-SC0019229, DE-AC05-06OR23177
Nuclear Physics	DE-SC0010300
Office of Science

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abstract = "In this work we develop a Lorentz-covariant version of the previously derived formalism for relating finite-volume matrix elements to 2+J→2 transition amplitudes. We also give various details relevant for the implementation of this formalism in a realistic numerical lattice QCD calculation. Particular focus is given to the role of single-particle form factors in disentangling finite-volume effects from the triangle diagram that arise when J couples to one of the two hadrons. This also leads to a new finite-volume function, denoted G, the numerical evaluation of which is described in detail. As an example we discuss the determination of the ππ+J→ππ amplitude in the ρ channel, for which the single-pion form factor, Fπ(Q2), as well as the scattering phase, δππ, are required to remove all power-law finite-volume effects. The formalism presented here holds for local currents with arbitrary Lorentz structure, and we give specific examples of insertions with up to two Lorentz indices.",

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N2 - In this work we develop a Lorentz-covariant version of the previously derived formalism for relating finite-volume matrix elements to 2+J→2 transition amplitudes. We also give various details relevant for the implementation of this formalism in a realistic numerical lattice QCD calculation. Particular focus is given to the role of single-particle form factors in disentangling finite-volume effects from the triangle diagram that arise when J couples to one of the two hadrons. This also leads to a new finite-volume function, denoted G, the numerical evaluation of which is described in detail. As an example we discuss the determination of the ππ+J→ππ amplitude in the ρ channel, for which the single-pion form factor, Fπ(Q2), as well as the scattering phase, δππ, are required to remove all power-law finite-volume effects. The formalism presented here holds for local currents with arbitrary Lorentz structure, and we give specific examples of insertions with up to two Lorentz indices.

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Form factors of two-hadron states from a covariant finite-volume formalism

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