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

Journal Article · · Physical Review D
 [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)

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.

Research Organization:
Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Nuclear Physics (NP)
Grant/Contract Number:
AC05-06OR23177; SC0019229; SC0010300
OSTI ID:
1557352
Alternate ID(s):
OSTI ID: 1557629
Report Number(s):
JLAB-THY-18-2878; DOE/OR/-23177-4598; arXiv:1812.10504; PRVDAQ
Journal Information:
Physical Review D, Vol. 100, Issue 3; ISSN 2470-0010
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 24 works
Citation information provided by
Web of Science

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Hadrons and nuclei journal November 2019
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Consistency checks for two-body finite-volume matrix elements: I. Conserved currents and bound states text January 2019