ππ→πγ* amplitude and the resonant ρ→πγ* transition from lattice QCD

Briceño, Raúl A.; Dudek, Jozef J.; Edwards, Robert G.; Shultz, Christian J.; Thomas, Christopher E.; Wilson, David J.

doi:10.1103/PhysRevD.93.114508

Title: $π π \to π γ^{}$ amplitude and the resonant $ρ \to π γ^{}$ transition from lattice QCD

Journal Article · Wed Jun 01 00:00:00 EDT 2016 · Physical Review D

DOI:https://doi.org/10.1103/PhysRevD.93.114508· OSTI ID:1256680

Briceño, Raúl A. ^[1]; Dudek, Jozef J. ^[2]; Edwards, Robert G. ^[1]; Shultz, Christian J. ^[3]; Thomas, Christopher E. ^[4]; Wilson, David J. ^[3]

Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Old Dominion Univ., Norfolk, VA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Old Dominion Univ., Norfolk, VA (United States)
Univ. of Cambridge (United Kingdom)

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.

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Research Organization:: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP)

Contributing Organization:: Hadron Spectrum Collaboration

DOE Contract Number:: AC05-06OR23177; SC0006765; ST/L000385/1; RG74916

OSTI ID:: 1256680

Report Number(s):: JLAB-THY-16-2237; DOE/OR/23177-3785; PRVDAQ

Journal Information:: Physical Review D, Vol. 93, Issue 11; ISSN 2470-0010

Country of Publication:: United States

Language:: English

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