Related papers: Finite-volume quantization condition from the $N/D…
In this article we complete our formalism relating the finite-volume energy spectrum of a scalar quantum field theory to the three-to-three scattering amplitude, ${\cal M}_3$. In previous work we found a quantization condition relating the…
We present the formalism for connecting a second-order electroweak $2\xrightarrow[]{H_I+H_I}2$ transition amplitudes in the finite volume (with two hadrons in the initial and final states) to the physical amplitudes in the infinite volume.…
We derive the finite-volume correction to the binding energy of an N-particle quantum bound state in a cubic periodic volume. Our results are applicable to bound states with arbitrary composition and total angular momentum, and in any…
An approach for relating the nucleon resonances extracted from $\pi N$ reaction data to lattice QCD calculations has been developed by using the finite-volume Hamiltonian method. Within models of $\pi N$ reactions, bare states are…
In this talk we discuss finite-volume computations of two-body hadronic decays below the inelastic threshold (e.g. $K\to\pi\pi$ decays). In particular we show how the relation between finite-volume matrix elements and physical amplitudes,…
We propose a systematic method to block-diagonalize the finite volume effective Hamiltonian for two-particle systems with arbitrary spin in both the rest and moving frame. The framework is convenient and efficient for addressing the…
This is a combined write-up for two talks which were given consecutively and which described different aspects of the same topic. We present a generalization of L\"uscher's relation between the finite-volume spectrum and S-matrix to three…
Recent results from lattice QCD on baryon resonances and meson-baryon, baryon-baryon scattering are presented. Such scattering processes and resonances can be determined in lattice QCD by first obtaining the finite-volume energy spectrum of…
We develop a comprehensive framework for extracting the pole position and properties of the doubly-charmed tetraquark $T_{\rm cc}^+(3875)$ from lattice QCD data using the relativistic three-particle formalism. This approach incorporates the…
Lattice QCD calculations of scattering phaseshifts and resonance parameters in the two-body sector are becoming precision studies. Early calculations employed L\"uscher's formula for extracting these quantities at lowest order. As the…
We give an update on our derivation of a quantization condition relating the finite-volume spectrum of three particles in a cubic box to infinite-volume scattering quantities. We have discovered and fixed technical problems in the…
Most strong-interaction resonances have decay channels involving three or more particles, including many of the recently discovered $X$, $Y$ and $Z$ resonances. In order to study such resonances from first principles using lattice QCD, one…
I review recent progress in calculating scattering amplitudes and resonance properties involving three particles using results from lattice QCD. The necessary input is the finite-volume spectrum, and the outputs -- via solutions of integral…
We explore variational approach to the finite-volume $N$-body problem. The general formalism for N non-relativistic spinless particles interacting with periodic pair-wise potentials yields N-body secular equations. The solutions depend on…
Within a formulation of $\pi\pi$ scattering, we investigate the use of the finite-volume Hamiltonian approach to resolving scattering observables from lattice QCD spectra. We consider spectra in the centre-of-mass and moving frames for both…
We derive the three-body quantization condition in a finite volume using an effective field theory in the particle-dimer picture. Moreover, we consider the extraction of physical observables from the lattice spectrum using the quantization…
Lattice QCD already offers the possibility of extracting three-hadron scattering quantities from first principles. In the last few years, significant progress has been achieved in developing and applying the finite-volume three-body…
We present a method to couple finite-volume QCD to infinite-volume QED by an appropriate twist-averaging procedure. We demonstrate the prescription numerically for the leading-order hadronic contribution to the anomalous magnetic moment of…
We present a nonperturbative Hamiltonian framework (NPHF) to address the general $N$-body problem. This framework rigorously connects finite-volume spectra from lattice QCD to scattering observables from experiment. To demonstrate its…
The ab-initio understanding of hadronic three-body systems above threshold, such as exotic resonances or the baryon spectrum, requires the mapping of the finite-volume eigenvalue spectrum, produced in lattice QCD calculations, to the…