scholarly journals Three-particle system in a finite volume: formalism, quantization condition, spectrum and energy shift

2020 ◽  
Vol 241 ◽  
pp. 02005
Author(s):  
Jin-Yi Pang
Keyword(s):  
Finite Volume ◽  
Bound States ◽  
Particle System ◽  
Energy Shift ◽  
Effective Field ◽  
Quantization Condition ◽  
High Current ◽  
Scattering States ◽  
Three Body ◽  
Hadronic Process

Lattice QCD calculations provide an ab initio access to hadronic process. These calculations are usu ally performed in a small cubic volume with periodic boundary conditions. The infinite volume extrapolations for three-body systems are indispensable to understand many systems of high current interest. We derive the three-body quantization condition in a finite volume using an effective field theory in the particle-dimer picture. Our work shows a powerful and transparent method to read off three-body physical observables from lattice simulations. In this paper, we review the formalism, quantization condition, spectrum analysis and energy shifts calculation both for 3-body bound states and scattering states.

scholarly journals Extracting observables from lattice data in the three-particle sector

2018 ◽  
Vol 175 ◽  
pp. 11006
Author(s):  
Akaki Rusetsky ◽  
Hans-Werner Hammer ◽  
Jin-Yi Pang
Keyword(s):  
Finite Volume ◽  
Energy Shift ◽  
Bound State ◽  
Effective Field ◽  
Quantization Condition ◽  
Unitary Limit ◽  
Lattice Data ◽  
Volume Energy ◽  
Three Body

The three-particle quantization condition is derived, using the particle-dimer picture in the non-relativistic effective field theory. The procedure for the extraction of various observables in the three-particle sector (the particle-dimer scattering amplitudes, breakup amplitudes, etc.) from the finite-volume lattice spectrum is discussed in detail. As an illustration of the general formalism, the expression for the finite-volume energy shift of the three-body bound-state in the unitary limit is re-derived. The role of the threebody force, which is essential for the renormalization, is highlighted, and the extension of the result beyond the unitary limit is studied. Comparison with other approaches, known in the literature, is carried out.

scholarly journals Spectrum of Three-Body Bound States in a Finite Volume

2015 ◽  
Vol 114 (9) ◽  
Author(s):  
Ulf-G. Meißner ◽  
Guillermo Ríos ◽  
Akaki Rusetsky
Keyword(s):  
Finite Volume ◽  
Bound States ◽  
Three Body

scholarly journals Relativistic N-particle energy shift in finite volume

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Fernando Romero-López ◽  
Akaki Rusetsky ◽  
Nikolas Schlage ◽  
Carsten Urbach
Keyword(s):  
Scattering Amplitudes ◽  
Finite Volume ◽  
Ground State ◽  
State Energy ◽  
Energy Shift ◽  
Particle Energy ◽  
Effective Field ◽  
Relativistic Scattering ◽  
Energy Constants ◽  
General Method

Abstract We present a general method for deriving the energy shift of an interacting system of N spinless particles in a finite volume. To this end, we use the nonrelativistic effective field theory (NREFT), and match the pertinent low-energy constants to the scattering amplitudes. Relativistic corrections are explicitly included up to a given order in the 1/L expansion. We apply this method to obtain the ground state of N particles, and the first excited state of two and three particles to order L−6 in terms of the threshold parameters of the two- and three-particle relativistic scattering amplitudes. We use these expressions to analyze the N-particle ground state energy shift in the complex φ4 theory.

A NEW GEOMETRICAL FRAMEWORK FOR THE DE BROGLIE–BOHM QUANTUM THEORY

2013 ◽  
Vol 10 (03) ◽  
pp. 1250096 ◽  
Author(s):  
D. J. HURLEY ◽  
M. A. VANDYCK
Keyword(s):  
Quantum Theory ◽  
Bound States ◽  
Particle System ◽  
Zeeman Effect ◽  
Free Particle ◽  
Physical Space ◽  
Quantization Condition ◽  
Curvilinear Coordinates ◽  
Dimensional Manifold ◽  
De Broglie Bohm

A geometrical framework for the de Broglie–Bohm quantum theory is presented, in which the trajectories of an N-particle system are interpretable as the integral curves of a particular vector field defined on a 3N-dimensional manifold [Formula: see text] constructed from physical space M. It is mathematically valid even when M is curved. If M is flat, the usual theory is recovered and automatically expressed in whatever curvilinear coordinates one may wish to choose. The general construction is illustrated by the case of a free particle moving on the surface of a sphere. (A modified Bohr quantization condition for angular momentum is obtained, with a first correction proportional to the curvature.) The Zeeman effect and some bound states on the sphere are also considered.

scholarly journals Energy shift of the three-particle system in a finite volume

2019 ◽  
Vol 99 (7) ◽  
Author(s):  
Jin-Yi Pang ◽  
Jia-Jun Wu ◽  
Hans-Werner Hammer ◽  
Ulf-G. Meißner ◽  
Akaki Rusetsky
Keyword(s):  
Finite Volume ◽  
Particle System ◽  
Energy Shift

scholarly journals Effective Interactions of Relativistic Composite Particles in Unified Nonlinear Spinor-Field Models. I

1985 ◽  
Vol 40 (1) ◽  
pp. 14-28
Author(s):  
H. Stumpf
Keyword(s):  
Spinor Field ◽  
Bound States ◽  
Composite Particle ◽  
Composite Particles ◽  
Statistical Interpretation ◽  
Particle Spectrum ◽  
Nonlinear Spinor ◽  
Effective Interactions ◽  
Scattering States ◽  
Diagonal Part

Unified nonlinear spinor field models are selfregularizing quantum field theories in which all observable (elementary and non-elementary) particles are assumed to be bound states of fermionic preon fields. Due to their large masses the preons themselves are confined. In preceding papers a functional energy representation, the statistical interpretation and the dynamical equations were derived. In this paper the dynamics of composite particles is discussed. The composite particles are defined to be eigensolutions of the diagonal part of the energy representation. Corresponding calculations are in preparation, but in the present paper a suitable composite particle spectrum is assumed. It consists of preon-antipreon boson states and threepreon- fermion states with corresponding antifermions and contains bound states as well as preon scattering states. The state functional is expanded in terms of these composite particle states with inclusion of preon scattering states. The transformation of the functional energy representation of the spinor field into composite particle functional operators produces a hierarchy of effective interactions at the composite particle level, the leading terms of which are identical with the functional energy representation of a phenomenological boson-fermion coupling theory. This representation is valid as long as the processes are assumed to be below the energetic threshold for preon production or preon break-up reactions, respectively. From this it can be concluded that below the threshold the effective interactions of composite particles in a unified spinor field model lead to phenomenological coupling theories which depend in their properties on the bound state spectrum of the self-regularizing spinor theory.

scholarly journals On the three-particle analog of the Lellouch-Lüscher formula

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Fabian Müller ◽  
Akaki Rusetsky
Keyword(s):  
Field Theory ◽  
Finite Volume ◽  
Effective Field Theory ◽  
Effective Field ◽  
Infinite Volume ◽  
Leading Order ◽  
Particle Decay ◽  
Particle Decays

Abstract Using non-relativistic effective field theory, we derive a three-particle analog of the Lellouch-Lüscher formula at the leading order. This formula relates the three-particle decay amplitudes in a finite volume with their infinite-volume counterparts and, hence, can be used to study the three-particle decays on the lattice. The generalization of the approach to higher orders is briefly discussed.

scholarly journals Numerical exploration of three relativistic particles in a finite volume including two-particle resonances and bound states

2019 ◽  
Vol 2019 (10) ◽  
Author(s):  
Fernando Romero-López ◽  
Stephen R. Sharpe ◽  
Tyler D. Blanton ◽  
Raúl A. Briceño ◽  
Maxwell T. Hansen
Keyword(s):  
Finite Volume ◽  
Bound States ◽  
Numerical Exploration ◽  
Relativistic Particles
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