𝜋𝜋 → 𝜋𝛾* Amplitude and the Resonant 𝜌 → 𝜋𝛾* Transition from Lattice QCD

Authors

Raúl A. Briceño, Old Dominion UniversityFollow
Jozef J. Dudek, Old Dominion University
Robert G. Edwards
Christian J. Shultz, Old Dominion University
Christopher E. Thomas
David J. Wilson

Document Type

Article

Publication Date

2016

DOI

10.1103/PhysRevD.93.114508

Publication Title

Physical Review D

Volume

93

Issue

11

Pages

114508 (1-20)

Abstract

We present a determination of the P-wave 𝜋𝜋 → 𝜋𝛾⋆ transition amplitude from lattice quantum chromodynamics. Matrix elements of the vector current in a finite volume are extracted from three-point correlation functions, and from these we determine the infinite-volume amplitude using a generalization of the Lellouch-Lüscher formalism. We determine the amplitude for a range of discrete values of the 𝜋𝜋 energy and virtuality of the photon and observe the expected dynamical enhancement due to the ρ resonance. Describing the energy dependence of the amplitude, we are able to analytically continue into the complex energy plane and from the residue at the ρ pole extract the ρ → 𝜋𝛾⋆ transition form factor. This calculation, at m_𝜋 ≈ 400  MeV, is the first to determine the form factor of an unstable hadron within a first principles approach to QCD.

Comments

© 2016 American Physical Society

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An Erratum to this article was published on April 27, 2022.

Original Publication Citation

Briceño, R.A., Dudek, J.J., Edwards, R.G., Shultz, C.J., Thomas, C.E. & Wilson, D.J. (2016) 𝜋𝜋 → 𝜋𝛾* amplitude and the resonant 𝜌 → 𝜋𝛾* transition from lattice QCD Physical Review D. 93(11), 1-20, Article 114508. https://doi.org/10.1103/PhysRevD.93.114508

ORCID

0000-0003-1109-1473 (Briceño), 0000-0003-4327-2121 (Dudek)

Repository Citation

Briceño, Raúl A.; Dudek, Jozef J.; Edwards, Robert G.; Shultz, Christian J.; Thomas, Christopher E.; and Wilson, David J., "𝜋𝜋 → 𝜋𝛾* Amplitude and the Resonant 𝜌 → 𝜋𝛾* Transition from Lattice QCD" (2016). Physics Faculty Publications. 624.
https://digitalcommons.odu.edu/physics_fac_pubs/624