Volume Dependence of Bound States with Angular Momentum

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, w...

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Bibliographic Details
Published inarXiv.org
Main Authors König, Sebastian, Lee, Dean, H -W Hammer
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 09.09.2011
Subjects
Angular momentum
Binding
Computer simulation
Dependence
Nuclei (nuclear physics)
Physics - High Energy Physics - Lattice
Physics - High Energy Physics - Phenomenology
Physics - Nuclear Theory
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1103.4468