The $\pi \pi \to \pi {\gamma }^{\star }$ amplitude and the resonant $\rho \to \pi {\gamma }^{\star }$ 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-Lüscher 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 $\rho \to \pi {\gamma }^{\star }$ transition form factor. This calculation, at $m_{\pi }\approx 400$ MeV, is the first to determine the form factor of an unstable hadron within a first principles approach to QCD.

arXiv comment20 pages, 16 figures, 3 tables

References in corpus (69)

• The Chroma Software System for Lattice QCD
• Meson-Meson interaction in a non-perturbative chiral approach
• Solving Lattice QCD systems of equations using mixed precision solvers on GPUs
• Resonance Scattering Phase Shifts on a Non-Rest Frame Lattice
• A novel quark-field creation operator construction for hadronic physics in lattice QCD
• Finite-Volume Effects for Two-Hadron States in Moving Frames
• Non-perturbative Approach to effective chiral Lagrangians and Meson Interactions
• Physics Opportunities with the 12 GeV Upgrade at Jefferson Lab
• Weak transition matrix elements from finite-volume correlation functions
• Multiple-channel generalization of Lellouch-Luscher formula
• The inverse amplitude method in Chiral Perturbation Theory
• Excited and exotic charmonium spectroscopy from lattice QCD
• Toward the excited meson spectrum of dynamical QCD
• A relativistic, model-independent, three-particle quantization condition
• First results from 2+1 dynamical quark flavors on an anisotropic lattice: light-hadron spectroscopy and setting the strange-quark mass
• Meson-meson scattering within one loop Chiral Perturbation Theory and its unitarization
• Two-particle multichannel systems in a finite volume with arbitrary spin
• Moving Multi-Channel Systems in a Finite Volume with Application to Proton-Proton Fusion
• Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude
• Energy dependence of the ρ resonance in ππ elastic scattering from lattice QCD
• Coupled $\pi \pi ,K\overline{K}$ scattering in $P$-wave and the $\rho$ resonance from lattice QCD
• Towards a data-driven analysis of hadronic light-by-light scattering
• S and D-wave phase shifts in isospin-2 pi pi scattering from lattice QCD
• Nature of the f_0(600) from its N_c dependence at two loops in unitarized Chiral Perturbation Theory
• Three particles in a finite volume
• Toward the excited isoscalar meson spectrum from lattice QCD
• Three-particle scattering amplitudes from a finite volume formalism
• Finite Volume Corrections to the Two-Particle Decay of States with Non-Zero Momentum
• Resonance Parameters of the rho-Meson from Lattice QCD
• Isoscalar meson spectroscopy from lattice QCD
• Coupled channel analysis of the rho meson decay in lattice QCD
• Standard-model prediction for direct CP violation in $K\to \pi \pi$ decay
• $D_s$ mesons with $DK$ and $D^{\ast }K$ scattering near threshold
• Tuning for Three-flavors of Anisotropic Clover Fermions with Stout-link Smearing
• Resonances in coupled πK,ηK scattering from quantum chromodynamics
• Dispersive approach to hadronic light-by-light scattering
• Highly excited and exotic meson spectrum from dynamical lattice QCD
• Lattice QCD Calculation of the $\rho$ Meson Decay Width
• Resonances in coupled $\pi K,\eta K$ scattering from lattice QCD
• Lattice QCD and the Timelike Pion Form Factor
• Multichannel one-to-two transition amplitudes in a finite volume
• $\rho$ Meson Decay in 2+1 Flavor Lattice QCD
• Multichannel 0-to-2 and 1-to-2 transition amplitudes for arbitrary spin particles in a finite volume
• Resonance parameters of the rho-meson from asymmetrical lattices
• Predicting positive parity $B_s$ mesons from lattice QCD
• Timelike pion form factor in lattice QCD
• Helicity operators for mesons in flight on the lattice
• Excited spectroscopy of charmed mesons from lattice QCD
• Extracting the chiral anomaly from gamma pi --> pi pi
• The $K\to (\pi \pi {)}_{I=2}$ Decay Amplitude from Lattice QCD
• Lattice determination of the $K\to (\pi \pi {)}_{I=2}$ Decay Amplitude $A_2$
• Photocouplings at the Pole from Pion Photoproduction
• The nucleon to Delta electromagnetic transition form factors in lattice QCD
• The phase-shift of isospin-2 pi-pi scattering from lattice QCD
• A framework for the calculation of the $\Delta N{\gamma }^{\ast }$ transition form factors on the lattice
• K pi scattering and the K* decay width from lattice QCD
• Emerging understanding of the ΔI = 1/2 Rule from Lattice QCD
• The resonant ${\pi }^{+}\gamma \to {\pi }^{+}{\pi }^0$ amplitude from Quantum Chromodynamics
• Axial Nucleon and Nucleon to Delta form fractors and the Goldberger-Treiman Relations from Lattice QCD
• Matrix elements of unstable states
• Finite volume corrections to pi-pi scattering
• Perturbative results for two and three particle threshold energies in finite volume
• $K$ to $\pi \pi$ Decay amplitudes from Lattice QCD
• Nucleon to Delta transition form factors with $N_F=2+1$ domain wall fermions
• Cross sections for low-energy ${\pi }^{-}\gamma$ reactions
• Pole positions and residues from pion photoproduction using the Laurent+Pietarinen expansion method
• B to rho ell nu form factors in lattice QCD
• Baryon photo-decay amplitudes at the pole
• Axial Nucleon to Delta transition form factors on 2+1 flavor hybrid lattices

Cited by in corpus (58)

• Hadronic molecules
• The $XYZ$ states: experimental and theoretical status and perspectives
• Scattering processes and resonances from lattice QCD
• 50 Years of Quantum Chromodynamics
• Isoscalar $\pi \pi$ scattering and the $\sigma$ meson resonance from QCD
• Isoscalar $\pi \pi ,K\overline{K},\eta \eta$ scattering and the $\sigma ,f_0,f_2$ mesons from QCD
• The $I=1$ pion-pion scattering amplitude and timelike pion form factor from $N_{\mathrm{f}}=2+1$ lattice QCD
• $P$-wave $\pi \pi$ scattering and the $\rho$ resonance from lattice QCD
• Numerical study of the relativistic three-body quantization condition in the isotropic approximation
• Lattice calculation of the pion transition form factor ${\pi }^0\to {\gamma }^{\ast }{\gamma }^{\ast }$
• The elastic $I=3/2$ $p$-wave nucleon-pion scattering amplitude and the $\Delta (1232)$ resonance from $N_{\mathrm{f}}=2+1$ lattice QCD
• Towards grounding nuclear physics in QCD
• Estimating the two-particle $K$-matrix for multiple partial waves and decay channels from finite-volume energies
• Precision Studies of QCD in the Low Energy Domain of the EIC
• Hadrons and Nuclei
• Challenges in Semileptonic B Decays
• Nuclear matrix elements from lattice QCD for electroweak and beyond-Standard-Model processes
• Scattering amplitudes from finite-volume spectral functions
• The energy-dependent ${\pi }^{+}{\pi }^{+}{\pi }^{+}$ scattering amplitude from QCD
• Determination of $s$- and $p$-wave $I=1/2$ $K\pi$ scattering amplitudes in $N_{\mathrm{f}}=2+1$ lattice QCD
• The quark-mass dependence of elastic $\pi K$ scattering from QCD
• Radiative resonance couplings in $\gamma \pi \to \pi \pi$
• The Role of Lattice QCD in Searches for Violations of Fundamental Symmetries and Signals for New Physics
• Lattice QCD and Neutrino-Nucleus Scattering
• The $\pi \gamma \to \pi \pi$ transition and the $\rho$ radiative decay width from lattice QCD
• Two- and three-body interactions in ${\phi }^4$ theory from lattice simulations
• Form factors of two-hadron states from a covariant finite-volume formalism
• Long-range electroweak amplitudes of single hadrons from Euclidean finite-volume correlation functions
• Two-loop analysis of the pion-mass dependence of the $\rho$ meson
• The $B\to K^{\ast }$ form factors on the lattice
• P-wave nucleon-pion scattering amplitude in the $\Delta (1232)$ channel from lattice QCD
• Constraining $1+\mathcal{J}\to 2$ coupled-channel amplitudes in finite-volume
• Consistency checks for two-body finite-volume matrix elements: I. Conserved currents and bound states
• The $\gamma \pi \to \pi \pi$ anomaly from lattice QCD and dispersion relations
• Opportunities for lattice QCD in quark and lepton flavor physics
• On the three-particle analog of the Lellouch-Lüscher formula
• Consistency checks for two-body finite-volume matrix elements: II. Perturbative systems
• $1^{-+}$ Hybrid in $J/\psi$ Radiative Decays from Lattice QCD
• Finite-volume formalism in the $2\stackrel{H_I+H_I}{\to }2$ transition: an application to the lattice QCD calculation of double beta decays
• Elastic Form Factors of Nucleon Excitations in Lattice QCD
• Radiative decay of the resonant $K^{\ast }$ and the $\gamma K\to K\pi$ amplitude from lattice QCD
• On-shell representations of two-body transition amplitudes: single external current
• Excited $J^{--}$ meson resonances at the SU(3) flavor point from lattice QCD
• Dispersive analysis of the Primakoff reaction $\gamma K\to K\pi$
• The semileptonic decays ${\eta }^{(\prime )}\to {\pi }^0{\ell }^{+}{\ell }^{-}$ and ${\eta }^{\prime }\to \eta {\ell }^{+}{\ell }^{-}$ in the standard model
• $B\to \rho \ell \bar{\nu }$ resonance form factors from $B\to \pi \pi \ell \bar{\nu }$ in lattice QCD
• Restrained Dark $U(1{)}_d$ at Low Energies
• Two-current transition amplitudes with two-body final states
• Exploring Baryon Resonances with Transition Generalized Parton Distributions: Status and Perspectives
• Rho-pion transition form factors in the $k_T$ factorization formulism revisited
• Physical-mass calculation of $\rho (770)$ and $K^{\ast }(892)$ resonance parameters via $\pi \pi$ and $K\pi$ scattering amplitudes from lattice QCD
• Timelike form factor for the anomalous process ${\gamma }^{\ast }\pi \to \pi \pi$
• Meson-Nucleon Scattering Amplitudes from Lattice QCD
• Prospects for ${\gamma }^{\star }{\gamma }^{\star }\to \pi \pi$ via lattice QCD
• Phenomenological model for the $\gamma \gamma \to {\pi }^{+}{\pi }^{-}{\pi }^0$ reaction
• Transition form-factor of $\gamma \to 3\pi$ in nonlocal quark model
• Lattice methods and effective field theory
• Recent progress on hadron spectroscopy from lattice QCD