Physical Review D
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 m𝜋 ≈ 400 MeV, is the first to determine the form factor of an unstable hadron within a first principles approach to QCD.
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
0000-0003-1109-1473 (Briceño), 0000-0003-4327-2121 (Dudek)
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.