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

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.
 [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:
OSTI Identifier:
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
Research Org:
Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)
Sponsoring Org:
USDOE; USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)
Contributing Orgs:
Hadron Spectrum Collaboration
Country of Publication:
United States