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

Abstract

Using the framework of non-relativistic effective field theory, the finite-volume ground-state energy shift is calculated up-to-and-including $O(L^{-6})$ for the system of three pions in the channel with the total isospin $I=1$. The relativistic corrections are included perturbatively, up to the same order in the inverse of the box size $L$. The obtained explicit expression, together with the known result for the system with maximal isospin $I=3$, can be used for the extraction of two independent effective three-body couplings from the measured ground-state spectrum of three pions.

12 pages

References in corpus (14)

• A relativistic, model-independent, three-particle quantization condition
• Three particle quantization condition in a finite volume: 2. general formalism and the analysis of data
• Three-body Unitarity in the Finite Volume
• Three-particle quantization condition in a finite volume: 1. The role of the three-particle force
• n-Boson Energies at Finite Volume and Three-Boson Interactions
• Implementing the three-particle quantization condition including higher partial waves
• Three-boson problem at low energy and Implications for dilute Bose-Einstein condensates
• Efimov physics in a finite volume
• The triton in a finite volume
• Alternative derivation of the relativistic three-particle quantization condition
• Equivalence of relativistic three-particle quantization conditions
• The Energy of n Identical Bosons in a Finite Volume at O(L^{-7})
• Lattice QCD study of the s-wave $\pi \pi$ scattering lengths in the I=0 and 2 channels
• Few-body bound states and resonances in finite volume

Cited by in corpus (2)

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