Volume Dependence of Bound States with Angular Momentum

Journal Article · Fri Sep 09 04:00:00 EDT 2011 · Physical Review Letters

DOI:https://doi.org/10.1103/PHYSREVLETT.107.112001· OSTI ID:21611760

Koenig, Sebastian; Hammer, H -W ^[1]; Lee, Dean ^[2]

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1. Helmholtz-Institut fuer Strahlen- und Kernphysik (Theorie) and Bethe Center for Theoretical Physics, Universitaet Bonn, 53115 Bonn (Germany)
2. Department of Physics, North Carolina State University, Raleigh, North Carolina 27695 (United States)

We derive general results for the mass shift of bound states with angular momentum l{>=}1 in a finite periodic volume. Our results have direct applications to lattice simulations of hadronic molecules as well as atomic nuclei. While the binding of S-wave bound states increases at finite volume, we show that the binding of P-wave bound states decreases. The mass shift for D-wave bound states as well as higher partial waves depends on the representation of the cubic rotation group. Nevertheless, the multiplet-averaged mass shift for any angular momentum l can be expressed in a simple form, and the sign of the shift alternates for even and odd l. We verify our analytical results with explicit numerical calculations. We also show numerically that similar volume corrections appear in three-body bound states.

• OSTI ID: 21611760
• Journal Information: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 11 Vol. 107; ISSN 0031-9007; ISSN PRLTAO
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ANGULAR MOMENTUM
BOUND STATE
COMPUTERIZED SIMULATION
CONSTRUCTIVE FIELD THEORY
D WAVES
ELEMENTARY PARTICLES
FIELD THEORIES
HADRONS
LATTICE FIELD THEORY
MANY-BODY PROBLEM
MASS
MOTION
P WAVES
PARTIAL WAVES
PERIODICITY
QUANTUM FIELD THEORY
ROTATION
S WAVES
SIMULATION
THREE-BODY PROBLEM
VARIATIONS