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Volume dependence of bound states with angular momentum
Sebastian König1, Dean Lee, H-W Hammer
1Helmholtz-Institut für Strahlen- und Kernphysik (Theorie) and Bethe Center for Theoretical Physics, Universität Bonn, 53115 Bonn, Germany.
Physical Review Letters
|October 27, 2011
Summary
Finite volume effects alter the binding of hadronic molecules and atomic nuclei. While S-wave states bind more strongly, P-wave states become less bound, with alternating shifts for higher angular momentum states.
Area of Science:
- Nuclear Physics
- Quantum Chromodynamics
- Hadron Spectroscopy
Background:
- Understanding the behavior of bound states in finite volumes is crucial for interpreting lattice quantum chromodynamics (LCC) simulations.
- Previous studies have primarily focused on S-wave interactions, leaving higher partial waves less explored in finite-volume contexts.
Purpose of the Study:
- To derive general analytical results for the mass shifts of bound states with angular momentum (ℓ) ≥ 1 in a finite periodic volume.
- To investigate the impact of finite volume on different partial waves, including P-wave, D-wave, and higher states.
- To provide a unified framework for understanding volume corrections across various angular momenta.
Main Methods:
- Derivation of general analytical formulas for mass shifts in finite periodic volumes.
- Application of group theory, specifically the representation of the cubic rotation group, for higher partial waves.
- Numerical verification of analytical predictions through explicit calculations.
- Extension of the analysis to three-body bound states.
Main Results:
- The mass shift for S-wave bound states increases in a finite volume, indicating stronger binding.
- The binding of P-wave bound states decreases in a finite volume.
- Mass shifts for D-wave and higher partial waves depend on the cubic rotation group representation.
- A simple, alternating form for the multiplet-averaged mass shift is found for any angular momentum (ℓ).
- Numerical calculations confirm the analytical findings and reveal similar volume corrections in three-body systems.
Conclusions:
- Finite volume effects significantly influence the binding energies of hadronic molecules and atomic nuclei.
- The derived formulas provide a universal description of volume corrections for various partial waves.
- The alternating sign of the mass shift for even and odd angular momenta offers a key prediction.
- The results are directly applicable to refining lattice simulations in nuclear and particle physics.
