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Title: π π π γ * amplitude and the resonant ρ π γ * transition from lattice QCD

Abstract

We present a determination of the $P$-wave $$\pi\pi\to\pi\gamma^\star$$ 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-L\"uscher formalism. We determine the amplitude for a range of discrete values of the $$\pi\pi$$ energy and virtuality of the photon, and observe the expected dynamical enhancement due to the $$\rho$$ 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 $$\rho$$ pole extract the $$\rho\to\gamma^\star\pi$$ transition form factor. This calculation, at $$m_\pi\approx 400$$~MeV, is the first time a form factor of a hadron resonance has been calculated within a first-principles approach to QCD.

Authors:
 [1];  [2];  [1];  [3];  [4];  [3]
  1. Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
  2. Old Dominion Univ., Norfolk, VA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
  3. Old Dominion Univ., Norfolk, VA (United States)
  4. Univ. of Cambridge (United Kingdom)
Publication Date:
Research Org.:
Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)
OSTI Identifier:
1256680
Report Number(s):
JLAB-THY-16-2237; DOE/OR/23177-3785
Journal ID: ISSN 2470-0010; PRVDAQ
DOE Contract Number:
AC05-06OR23177; SC0006765; ST/L000385/1; RG74916
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review D; Journal Volume: 93; Journal Issue: 11
Country of Publication:
United States
Language:
English

Citation Formats

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. United States: N. p., 2016. Web. doi:10.1103/PhysRevD.93.114508.
Briceño, Raúl A., Dudek, Jozef J., Edwards, Robert G., Shultz, Christian J., Thomas, Christopher E., & Wilson, David J.. ππ→πγ* amplitude and the resonant ρ→πγ* transition from lattice QCD. United States. doi:10.1103/PhysRevD.93.114508.
Briceño, Raúl A., Dudek, Jozef J., Edwards, Robert G., Shultz, Christian J., Thomas, Christopher E., and Wilson, David J.. Wed . "ππ→πγ* amplitude and the resonant ρ→πγ* transition from lattice QCD". United States. doi:10.1103/PhysRevD.93.114508. https://www.osti.gov/servlets/purl/1256680.
@article{osti_1256680,
title = {ππ→πγ* amplitude and the resonant ρ→πγ* transition from lattice QCD},
author = {Briceño, Raúl A. and Dudek, Jozef J. and Edwards, Robert G. and Shultz, Christian J. and Thomas, Christopher E. and Wilson, David J.},
abstractNote = {We present a determination of the $P$-wave $\pi\pi\to\pi\gamma^\star$ 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-L\"uscher formalism. We determine the amplitude for a range of discrete values of the $\pi\pi$ energy and virtuality of the photon, and observe the expected dynamical enhancement due to the $\rho$ 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 $\rho$ pole extract the $\rho\to\gamma^\star\pi$ transition form factor. This calculation, at $m_\pi\approx 400$~MeV, is the first time a form factor of a hadron resonance has been calculated within a first-principles approach to QCD.},
doi = {10.1103/PhysRevD.93.114508},
journal = {Physical Review D},
number = 11,
volume = 93,
place = {United States},
year = {Wed Jun 01 00:00:00 EDT 2016},
month = {Wed Jun 01 00:00:00 EDT 2016}
}