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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…

High Energy Physics - Lattice · Physics 2014-09-25 Maxwell T. Hansen , Stephen R. Sharpe

Using non-relativistic effective Lagrangians in the particle-dimer picture, we rederive the expression for the energy shift of a loosely bound three-particle bound state of identical bosons in the unitary limit. The effective field theory…

High Energy Physics - Lattice · Physics 2017-10-25 H. -W. Hammer , J. -Y. Pang , A. Rusetsky

We extend the relativistic field theoretic finite-volume formalism to $N \pi \pi$ scattering states at maximal isospin, $I=5/2$. As in previous work using the relativistic field theory approach, we work to all orders in a generic low-energy…

High Energy Physics - Lattice · Physics 2025-10-07 Maxwell T. Hansen , Fernando Romero-López , Stephen R. Sharpe

We present a simplified derivation of the relativistic three-particle quantization condition for identical, spinless particles described by a generic relativistic field theory satisfying a $\mathbb Z_2$ symmetry. The simplification is…

High Energy Physics - Lattice · Physics 2020-10-07 Tyler D. Blanton , Stephen R. Sharpe

We describe in detail the implementation of the relativistic three-neutron finite-volume quantization condition derived in Ref. [1]. In particular, we show how the complications due to Wigner rotations acting on spins are included, and…

High Energy Physics - Lattice · Physics 2026-02-17 Wilder Schaaf , Stephen R. Sharpe

A three-particle quantization condition on the lattice is written down in a manifestly relativistic-invariant form by using a generalization of the non-relativistic effective field theory (NREFT) approach. Inclusion of the higher partial…

High Energy Physics - Lattice · Physics 2022-03-09 Fabian Müller , Jin-Yi Pang , Akaki Rusetsky , Jia-Jun Wu

Recently, formalism has been derived for studying electroweak transition amplitudes for three-body systems both in infinite and finite volumes. The formalism provides exact relations that the infinite-volume amplitudes must satisfy, as well…

High Energy Physics - Lattice · Physics 2024-05-24 Raul A. Briceño , Andrew Jackura , Dimitra A. Pefkou , Fernando Romero-López

Working in relativistic quantum field theory, we derive the quantization condition satisfied by coupled two- and three-particle systems of identical scalar particles confined to a cubic spatial volume with periodicity $L$. This gives the…

High Energy Physics - Lattice · Physics 2017-05-02 Raúl A. Briceño , Maxwell T. Hansen , Stephen R. Sharpe

We report progress on extending the relativistic model-independent quantization condition for three particles, derived previously by two of us, to a broader class of theories, as well as progress on checking the formalism. In particular, we…

High Energy Physics - Lattice · Physics 2016-10-03 Raul A. Briceno , Maxwell T. Hansen , Stephen R. Sharpe

Studying of the relativistic three-body bound state in a three-dimensional (3D) approach is a necessary first step in a process to eventually perform scattering calculations at GeV energies, where partial-wave expansions are not useful. To…

Nuclear Theory · Physics 2016-04-20 M. R. Hadizadeh , Ch. Elster , W. N. Polyzou

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…

High Energy Physics - Lattice · Physics 2016-01-06 Maxwell T. Hansen , Stephen R. Sharpe

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…

High Energy Physics - Lattice · Physics 2013-11-20 Maxwell T. Hansen , Stephen R. Sharpe

We present the status of our formalism for extracting three-particle scattering observables from lattice QCD (LQCD). The method relies on relating the discrete finite-volume spectrum of a quantum field theory with its scattering amplitudes.…

High Energy Physics - Lattice · Physics 2017-04-05 Raúl A. Briceño , Maxwell T. Hansen , Stephen R. Sharpe

Recently, the formalism needed to relate the finite-volume spectrum of systems of nondegenerate spinless particles has been derived. In this work we discuss a range of issues that arise when implementing this formalism in practice, provide…

High Energy Physics - Lattice · Physics 2022-03-02 Tyler D. Blanton , Fernando Romero-López , Stephen R. Sharpe

We present a generalization of Luescher's relation between the finite-volume spectrum and scattering amplitudes to the case of three particles. We consider a relativistic scalar field theory in which the couplings are arbitrary aside from a…

High Energy Physics - Lattice · Physics 2014-12-24 Maxwell T. Hansen , Stephen R. Sharpe

An explicit expression for the finite-volume energy shift of shallow three-body bound states for non-identical particles is obtained in the unitary limit. The inclusion of the higher partial waves is considered. To this end, the method of…

High Energy Physics - Lattice · Physics 2018-07-18 Yu Meng , Chuan Liu , Ulf-G. Meißner , A. Rusetsky

In a previous publication, two of us derived a relation between the scattering amplitude of three identical bosons, $\mathcal M_3$, and a real function referred to as the {divergence-free} K matrix and denoted $\mathcal K_{\text{df},3}$.…

High Energy Physics - Lattice · Physics 2019-09-25 Raúl A. Briceño , Maxwell T. Hansen , Stephen R. Sharpe , Adam P. Szczepaniak

We show that a recently derived alternative form of the relativistic three-particle quantization condition for identical particles can be rewritten in terms of the R matrix introduced to give a unitary representation of the infinite-volume…

High Energy Physics - Lattice · Physics 2020-10-07 Tyler D. Blanton , Stephen R. Sharpe

We calculate the energy of the state closest to threshold for two and three identical, spinless particles confined to a cubic spatial volume with periodic boundary conditions and with zero total momentum in the finite-volume frame. The…

High Energy Physics - Lattice · Physics 2016-01-27 Maxwell T. Hansen , Stephen R. Sharpe

In this paper we discuss the use of wavelet bases to solve the relativistic three-body problem. Wavelet bases can be used to transform momentum-space scattering integral equations into an approximate system of linear equations with a sparse…

Nuclear Theory · Physics 2009-11-11 Fatih Bulut , W. N. Polyzou