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

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.

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Ground state energy shift ofnpions andmkaons in a finite volume

Physical Review D ◽

10.1103/physrevd.79.054506 ◽

2009 ◽

Vol 79 (5) ◽

Cited By ~ 8

Author(s):

Brian Smigielski ◽

Joseph Wasem

Keyword(s):

Finite Volume ◽

Ground State Energy ◽

Ground State ◽

State Energy ◽

Energy Shift

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Three-particle system in a finite volume

Hadron Spectroscopy and Structure ◽

10.1142/9789811219313_0083 ◽

2020 ◽

Author(s):

Jin-Yi Pang

Keyword(s):

Finite Volume ◽

Particle System

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Relativistic N-particle energy shift in finite volume

Journal of High Energy Physics ◽

10.1007/jhep02(2021)060 ◽

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.

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Extracting observables from lattice data in the three-particle sector

EPJ Web of Conferences ◽

10.1051/epjconf/201817511006 ◽

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.

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NONCOMMUTATIVE NONRELATIVISTIC FERMIONS

Modern Physics Letters A ◽

10.1142/s0217732307023018 ◽

2007 ◽

Vol 22 (35) ◽

pp. 2669-2674 ◽

Cited By ~ 1

Author(s):

A. JAHAN ◽

M. NASSERI ◽

M. JAFARI

Keyword(s):

Particle System ◽

Electron Gas ◽

Energy Shift ◽

Second Order ◽

Reference Temperature ◽

Nonrelativistic Electron ◽

First Order ◽

Order Energy ◽

Temperature Reference ◽

Correlation Term

Spatial noncommutativity removes the degeneracy of nonrelativistic electron gas. In particular one can interpret the noncommutativity parameter appearing in the second-order correlation term, as a new temperature reference. We investigate the effect of the noncommutativity of space on a many-particle system composed of locally interacting nonrelativistic fermions. We calculate the first-order energy shift of the system up to the second order in noncommutativity parameter and as a result the noncommutativity of space eliminates the degeneracy of the model. Thus, as the case of electron gas, one may interpret the noncommutativity parameter as a new reference temperature.

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