skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

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

Abstract

Here we develop a Lorentz-covariant version of the previously derived formalism for relating finite-volume matrix elements to $$\textbf 2 + \mathcal J \to \textbf 2$$ transition amplitudes. Furthermore, we 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 $$\mathcal J$$ 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 $$\pi \pi + \mathcal J \to \pi \pi$$ amplitude in the $$\rho$$ channel, for which the single-pion form factor, $$F_\pi(Q^2)$$, as well as the scattering phase, $$\delta_{\pi\pi}$$, 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.

Authors:
 [1];  [2];  [3];  [4]
  1. Univ. of South Carolina, Columbia, SC (United States)
  2. Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Old Dominion Univ., Norfolk, VA (United States)
  3. European Organization for Nuclear Research (CERN), Geneva (Switzerland)
  4. Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); College of William and Mary, Williamsburg, VA (United States)
Publication Date:
Research Org.:
Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)
OSTI Identifier:
1557352
Alternate Identifier(s):
OSTI ID: 1557629
Report Number(s):
JLAB-THY-18-2878; DOE/OR/-23177-4598; arXiv:1812.10504
Journal ID: ISSN 2470-0010; PRVDAQ
Grant/Contract Number:  
AC05-06OR23177; SC0019229; SC0010300
Resource Type:
Published Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 100; Journal Issue: 3; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats

Baroni, Alessandro, Briceño, Raúl A., Hansen, Maxwell T., and Ortega-Gama, Felipe G. Form factors of two-hadron states from a covariant finite-volume formalism. United States: N. p., 2019. Web. doi:10.1103/PhysRevD.100.034511.
Baroni, Alessandro, Briceño, Raúl A., Hansen, Maxwell T., & Ortega-Gama, Felipe G. Form factors of two-hadron states from a covariant finite-volume formalism. United States. doi:10.1103/PhysRevD.100.034511.
Baroni, Alessandro, Briceño, Raúl A., Hansen, Maxwell T., and Ortega-Gama, Felipe G. Tue . "Form factors of two-hadron states from a covariant finite-volume formalism". United States. doi:10.1103/PhysRevD.100.034511.
@article{osti_1557352,
title = {Form factors of two-hadron states from a covariant finite-volume formalism},
author = {Baroni, Alessandro and Briceño, Raúl A. and Hansen, Maxwell T. and Ortega-Gama, Felipe G.},
abstractNote = {Here we develop a Lorentz-covariant version of the previously derived formalism for relating finite-volume matrix elements to $\textbf 2 + \mathcal J \to \textbf 2$ transition amplitudes. Furthermore, we 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 $\mathcal J$ 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 $\pi \pi + \mathcal J \to \pi \pi$ amplitude in the $\rho$ channel, for which the single-pion form factor, $F_\pi(Q^2)$, as well as the scattering phase, $\delta_{\pi\pi}$, 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.},
doi = {10.1103/PhysRevD.100.034511},
journal = {Physical Review D},
number = 3,
volume = 100,
place = {United States},
year = {2019},
month = {8}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1103/PhysRevD.100.034511

Save / Share:

Works referenced in this record:

Three-particle quantization condition in a finite volume: 2. General formalism and the analysis of data
journal, October 2017

  • Hammer, Hans-Werner; Pang, Jin-Yi; Rusetsky, Akaki
  • Journal of High Energy Physics, Vol. 2017, Issue 10, 31 p.
  • DOI: 10.1007/JHEP10(2017)115