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 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 Three-body systems in pionless effective field theory

2016 ◽  
Vol 25 (05) ◽  
pp. 1641002 ◽  
Author(s):  
Jared Vanasse
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Bound State ◽  
Effective Field ◽  
Nuclear Systems ◽  
History Of ◽  
Three Body ◽  
Theory Formula

Investigations of three-body nuclear systems using pionless effective field theory ([Formula: see text]) are reviewed. The history of [Formula: see text] in [Formula: see text] and [Formula: see text] scattering is briefly discussed and emphasis put on the use of strict perturbative techniques. In addition renormalization issues appearing in [Formula: see text] scattering are also presented. Bound state calculations are addressed and new perturbative techniques for describing them are highlighted. Three-body breakup observables in [Formula: see text] scattering are also considered and the utility of [Formula: see text] for addressing them.

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.

scholarly journals Hypernuclei in halo/cluster effective field theory

2016 ◽  
Vol 25 (05) ◽  
pp. 1641005 ◽  
Author(s):  
Shung-Ichi Ando
Keyword(s):  
Field Theory ◽  
Limit Cycle ◽  
Effective Field Theory ◽  
Bound States ◽  
Scattering Length ◽  
Bound State ◽  
High Energy ◽  
Effective Field ◽  
Unitary Limit ◽  
Energy Mechanism

The light double [Formula: see text] hypernuclei, [Formula: see text] and [Formula: see text], are studied as three-body [Formula: see text] and [Formula: see text] cluster systems in halo/cluster effective field theory at leading order. We find that the [Formula: see text] system in spin-0 channel does not exhibit a limit cycle whereas the [Formula: see text] system in spin-1 channel and the [Formula: see text] system in spin-0 channel do. The limit cycle is associated with the formation of bound states, known as Efimov states, in the unitary limit. For the [Formula: see text] system in the spin-0 channel we estimate the scattering length [Formula: see text] for [Formula: see text]-wave [Formula: see text] hyperon–hypertriton scattering as [Formula: see text][Formula: see text]fm. We also discuss that studying the cutoff dependences in the [Formula: see text] and [Formula: see text] systems, the bound state of [Formula: see text] is not an Efimov state but formed due to a high energy mechanism whereas that of [Formula: see text] may be regarded as an Efimov state.

scholarly journals Three-body spectrum in a finite volume: The role of cubic symmetry

2018 ◽  
Vol 97 (11) ◽  
Author(s):  
M. Döring ◽  
H.-W. Hammer ◽  
M. Mai ◽  
J.-Y. Pang ◽  
A. Rusetsky ◽  
...  
Keyword(s):  
Finite Volume ◽  
Cubic Symmetry ◽  
Three Body

THE BOUNDARY CONDITION MODEL APPROACH TO BORROMEAN NUCLEI

2007 ◽  
Vol 22 (20) ◽  
pp. 1469-1479
Author(s):  
CORNEL HATEGAN ◽  
REMUS AMILCAR IONESCU ◽  
HERMANN H. WOLTER
Keyword(s):  
Boundary Condition ◽  
Bound State ◽  
Weakly Bound ◽  
Condition Model ◽  
Boundary Condition Model ◽  
Resonant States ◽  
Scattering Lengths ◽  
Three Body ◽  
Model Approach

Three-body systems are studied in the framework of the Boundary Condition Model, in which the relevant interactions are expressed in terms of the scattering lengths of the two-body subsystems. We demonstrate explicitly the role of resonant states in the two-body subsystems and of multiple scattering between the constituents in producing a weakly bound three-body system, i.e. a Borromean nucleus. We obtain qualitative relations between the spatial extension of the three-body bound state, its energy, and the scattering lengths in the subsystems. The results are compared with experimental data for the Borromean nucleus 11 Li and 14 Be .

scholarly journals Finite-volume energy shift of the three-pion ground state

2021 ◽  
Vol 103 (5) ◽  
Author(s):  
Fabian Müller ◽  
Tiansu Yu ◽  
Akaki Rusetsky
Keyword(s):  
Finite Volume ◽  
Ground State ◽  
Energy Shift ◽  
Volume Energy

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.

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