On-shell representations of two-body transition amplitudes: Single external current

Raúl A. Briceño (Thomas Jefferson National Accelerator Facility, 12000 Jefferson Avenue, Newport News, Virginia 23606, USA; Department of Physics, Old Dominion University, Norfolk, Virginia 23529, USA) ; Andrew W. Jackura (Thomas Jefferson National Accelerator Facility, 12000 Jefferson Avenue, Newport News, Virginia 23606, USA; Department of Physics, Old Dominion University, Norfolk, Virginia 23529, USA) ; Felipe G. Ortega-Gama (Thomas Jefferson National Accelerator Facility, 12000 Jefferson Avenue, Newport News, Virginia 23606, USA; Department of Physics, William & Mary, Williamsburg, Virginia 23187, USA) ; Keegan H. Sherman (Thomas Jefferson National Accelerator Facility, 12000 Jefferson Avenue, Newport News, Virginia 23606, USA; Department of Physics, Old Dominion University, Norfolk, Virginia 23529, USA)

This work explores scattering amplitudes that couple two-particle systems via a single external current insertion, 2+J2. Such amplitudes can provide structural information about the excited QCD spectrum. We derive an exact analytic representation for these reactions. From these amplitudes, we show how to rigorously define resonance and bound-state form factors. Furthermore, we explore the consequences of the narrow-width limit of the amplitudes as well as the role of the Ward-Takahashi identity for conserved vector currents. These results hold for any number of two-body channels with no intrinsic spin, and a current with arbitrary Lorentz structure and quantum numbers. This work and the existing finite-volume formalism provide a complete framework for determining this class of amplitudes from lattice QCD.

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      "value": "This work explores scattering amplitudes that couple two-particle systems via a single external current insertion, <math><mn>2</mn><mo>+</mo><mi>J</mi><mo>\u2192</mo><mn>2</mn></math>. Such amplitudes can provide structural information about the excited QCD spectrum. We derive an exact analytic representation for these reactions. From these amplitudes, we show how to rigorously define resonance and bound-state form factors. Furthermore, we explore the consequences of the narrow-width limit of the amplitudes as well as the role of the Ward-Takahashi identity for conserved vector currents. These results hold for any number of two-body channels with no intrinsic spin, and a current with arbitrary Lorentz structure and quantum numbers. This work and the existing finite-volume formalism provide a complete framework for determining this class of amplitudes from lattice QCD."
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Published on:
22 June 2021
Publisher:
APS
Published in:
Physical Review D , Volume 103 (2021)
Issue 11
DOI:
https://doi.org/10.1103/PhysRevD.103.114512
arXiv:
2012.13338
Copyrights:
Published by the American Physical Society
Licence:
CC-BY-4.0

Fulltext files: