Form factors of two-hadron states from a covariant finite-volume formalism

Abstract

In this work we develop a Lorentz-covariant version of the previously derived formalism for relating finite-volume matrix elements to $\text{2}+\mathcal{J}\to \text{2}$ transition amplitudes. We also give various details relevant for the implementation of this formalism in a realistic numerical lattice QCD calculation. Particular focus is given to the role of single-particle form factors in disentangling finite-volume effects from the triangle diagram that arise when $\mathcal{J}$ couples to one of the two hadrons. This also leads to a new finite-volume function, denoted $G$, the numerical evaluation of which is described in detail. As an example we discuss the determination of the $\pi \pi +\mathcal{J}\to \pi \pi$ amplitude in the $\rho$ channel, for which the single-pion form factor, $F_{\pi }(Q^2)$, as well as the scattering phase, ${\delta }_{\pi \pi }$, are required to remove all power-law finite-volume effects. The formalism presented here holds for local currents with arbitrary Lorentz structure, and we give specific examples of insertions with up to two Lorentz indices.

arXiv comment42 pages, 11 figures, JLAB-THY-18-2878, CERN-TH-2018-263

References in corpus (73)

• Hadronic molecules
• The hidden-charm pentaquark and tetraquark states
• Heavy-Quark QCD Exotica
• Parton Physics on Euclidean Lattice
• Resonance Scattering Phase Shifts on a Non-Rest Frame Lattice
• Finite-Volume Effects for Two-Hadron States in Moving Frames
• Weak transition matrix elements from finite-volume correlation functions
• Scattering processes and resonances from lattice QCD
• Multiple-channel generalization of Lellouch-Luscher formula
• A relativistic, model-independent, three-particle quantization condition
• 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
• Energy dependence of the ρ resonance in ππ elastic scattering from lattice QCD
• Aharonov-Bohm effect and nucleon-nucleon phase shifts on the lattice
• Coupled $\pi \pi ,K\overline{K}$ scattering in $P$-wave and the $\rho$ resonance from lattice QCD
• Isoscalar $\pi \pi$ scattering and the $\sigma$ meson resonance from QCD
• Three-particle scattering amplitudes from a finite volume formalism
• A method to measure the antikaon-nucleon scattering length in lattice QCD
• Two Particle States and the $S$-matrix Elements in Multi-channel Scattering
• Relating the finite-volume spectrum and the two-and-three-particle $S$ matrix for relativistic systems of identical scalar particles
• Finite Volume Corrections to the Two-Particle Decay of States with Non-Zero Momentum
• Three particle quantization condition in a finite volume: 2. general formalism and the analysis of data
• Standard-model prediction for direct CP violation in $K\to \pi \pi$ decay
• Resonances in coupled πK,ηK scattering from quantum chromodynamics
• A Discussion on Triangle Singularities in the ${\Lambda }_b\to J/\psi K^{-}p$ Reaction
• An overview of $XYZ$ new particles
• Three-body Unitarity in the Finite Volume
• The coupled-channel scattering on a torus
• Scalar mesons in a finite volume
• Scattering phase shifts for two particles of different mass and non-zero total momentum in lattice QCD
• Resonances in coupled $\pi K,\eta K$ scattering from lattice QCD
• An $a_0$ resonance in strongly coupled $\pi \eta$, $K\overline{K}$ scattering from lattice QCD
• Coupled-Channel $D\pi$, $D\eta$ and $D_s\bar{K}$ Scattering from Lattice QCD
• Rummukainen-Gottlieb's formula on two-particle system with different mass
• Lattice QCD and the Timelike Pion Form Factor
• Multichannel one-to-two transition amplitudes in a finite volume
• Isoscalar $\pi \pi ,K\overline{K},\eta \eta$ scattering and the $\sigma ,f_0,f_2$ mesons from QCD
• Multichannel 0-to-2 and 1-to-2 transition amplitudes for arbitrary spin particles in a finite volume
• $I=1$ and $I=2$ $\pi -\pi$ scattering phase shifts from $N_{\mathrm{f}}=2+1$ lattice QCD
• Three-particle systems with resonant subprocesses in a finite volume
• Timelike pion form factor in lattice QCD
• Helicity operators for mesons in flight on the lattice
• $P$-wave $\pi \pi$ scattering and the $\rho$ resonance from lattice QCD
• Effects of finite volume on the $K_L$-$K_S$ mass difference
• The $K\to (\pi \pi {)}_{I=2}$ Decay Amplitude from Lattice QCD
• Electroweak Matrix Elements in the Two-Nucleon Sector from Lattice QCD
• Proton-proton fusion and tritium $\beta$-decay from lattice quantum chromodynamics
• Two Particle States in an Asymmetric Box and the Elastic Scattering Phases
• $\rho$ and $K^{\ast }$ resonances on the lattice at nearly physical quark masses and $N_f=2$
• The $\pi \pi \to \pi {\gamma }^{\star }$ amplitude and the resonant $\rho \to \pi {\gamma }^{\star }$ transition from lattice QCD
• Two Particle States in a Box and the $s$-Matrix in Multi-Channel Scattering
• Relativistic, model-independent, multichannel $2\to 2$ transition amplitudes in a finite volume
• Lattice determination of the $K\to (\pi \pi {)}_{I=2}$ Decay Amplitude $A_2$
• The elastic $I=3/2$ $p$-wave nucleon-pion scattering amplitude and the $\Delta (1232)$ resonance from $N_{\mathrm{f}}=2+1$ lattice QCD
• Issues and Opportunities in Exotic Hadrons
• A framework for the calculation of the $\Delta N{\gamma }^{\ast }$ transition form factors on the lattice
• Heavy physics contributions to neutrinoless double beta decay from QCD
• The resonant ${\pi }^{+}\gamma \to {\pi }^{+}{\pi }^0$ amplitude from Quantum Chromodynamics
• Emerging understanding of the ΔI = 1/2 Rule from Lattice QCD
• Generalized Lüscher Formula in Multi-channel Baryon-Meson Scattering
• Matrix elements of unstable states
• Double-$\beta$ Decay Matrix Elements from Lattice Quantum Chromodynamics
• Determination of $s$- and $p$-wave $I=1/2$ $K\pi$ scattering amplitudes in $N_{\mathrm{f}}=2+1$ lattice QCD
• Two-Baryon Systems with Twisted Boundary Conditions
• $K$ to $\pi \pi$ Decay amplitudes from Lattice QCD
• Nuclear modification of scalar, axial and tensor charges from lattice QCD
• The $\pi \gamma \to \pi \pi$ transition and the $\rho$ radiative decay width from lattice QCD
• Dynamically-coupled partial-waves in $\rho \pi$ isospin-2 scattering from lattice QCD
• Finite-volume effects due to spatially non-local operators
• First lattice QCD study of the gluonic structure of light nuclei
• Finite-volume matrix elements in multi-boson states
• Off-forward gluonic structure of vector mesons
• Gluonic Transversity from Lattice QCD

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• Consistency checks for two-body finite-volume matrix elements: I. Conserved currents and bound states
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