Two-current transition amplitudes with two-body final states

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) ; 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) ; 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)

We derive the on-shell form of amplitudes containing two external currents with a single hadron in the initial state and two hadrons in the final state, denoted as 1+J2+J. This class of amplitude is relevant in precision tests of the Standard Model as well as for exploring the structure of excited states in the QCD spectrum. We present a model-independent description of the amplitudes where we sum to all orders in the strong interaction. From this analytic form we are able to extract transition and elastic resonance form factors consistent with previous work as well as a novel Compton-like amplitude coupling a single particle state to a resonance. The results also hold for reactions where the one-particle state is replaced with the vacuum, namely J2+J amplitudes. We also investigate constraints placed upon the formalism for the case of a conserved vector current in the form of the Ward-Takahashi identity. The formalism presented here is valid for currents of arbitrary Lorentz structure and quantum numbers with spinless hadrons where any number of two-particle intermediate channels may be open. When combined with the appropriate finite-volume framework, this work facilitates the extraction of physical observables from this class of amplitudes via lattice QCD calculations.

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  "abstracts": [
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      "source": "APS", 
      "value": "We derive the on-shell form of amplitudes containing two external currents with a single hadron in the initial state and two hadrons in the final state, denoted as <math><mrow><mn>1</mn><mo>+</mo><mi>J</mi><mo>\u2192</mo><mn>2</mn><mo>+</mo><mi>J</mi></mrow></math>. This class of amplitude is relevant in precision tests of the Standard Model as well as for exploring the structure of excited states in the QCD spectrum. We present a model-independent description of the amplitudes where we sum to all orders in the strong interaction. From this analytic form we are able to extract transition and elastic resonance form factors consistent with previous work as well as a novel Compton-like amplitude coupling a single particle state to a resonance. The results also hold for reactions where the one-particle state is replaced with the vacuum, namely <math><mi>J</mi><mo>\u2192</mo><mn>2</mn><mo>+</mo><mi>J</mi></math> amplitudes. We also investigate constraints placed upon the formalism for the case of a conserved vector current in the form of the Ward-Takahashi identity. The formalism presented here is valid for currents of arbitrary Lorentz structure and quantum numbers with spinless hadrons where any number of two-particle intermediate channels may be open. When combined with the appropriate finite-volume framework, this work facilitates the extraction of physical observables from this class of amplitudes via lattice QCD calculations."
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Published on:
21 June 2022
Publisher:
APS
Published in:
Physical Review D , Volume 105 (2022)
Issue 11
DOI:
https://doi.org/10.1103/PhysRevD.105.114510
arXiv:
2202.02284
Copyrights:
Published by the American Physical Society
Licence:
CC-BY-4.0

Fulltext files: