Abstract
We present a formalism to describe two-$\pi^+$ and three-$\pi^+$ dynamics in finite volume, the formalism is based on combination of a variational approach and the Faddeev method. Both pair-wise and three-body interactions are included in the presentation. Impacts of finite lattice spacing and the cubic lattice symmetry are also discussed. To illustrate application of the formalism, the pair-wise contact interaction that resembles the leading order interaction terms in chiral effective theory is used to analyze recent lattice results.
Highlights
Understanding of few-hadron interactions is crucial in nuclear/hadron physics
Few-hadron dynamics provides a unique access to various fundamental parameters of quantum chromodynamics (QCD), for quarks and gluons only manifest themselves within hadrons due to color confinement
lattice QCD (LQCD) calculations are usually performed in a periodic box in the Euclidean space-time, and only discrete energy spectra are extracted from time dependent correlation functions
Summary
Understanding of few-hadron interactions is crucial in nuclear/hadron physics. Few-hadron dynamics provides a unique access to various fundamental parameters of quantum chromodynamics (QCD), for quarks and gluons only manifest themselves within hadrons due to color confinement. Mapping out infinite-volume few-body dynamics from finitevolume energy spectra is a key step toward understanding multihadron systems from LQCD calculations. [65,66], the quantization condition of fewbody systems may be presented in terms of finite-volume Green’s function and effective interaction between particles embodied by a potential. Solving for E yields the discrete energy spectrum of two interacting pions in finite volume at the continuum limit where the lattice space approaches zero. MULTI-πþ SYSTEMS IN A FINITE VOLUME where rij 1⁄4 xi − xj is relative coordinate between the ith and jth pions. As suggested in Refs. [64,65,66,67], the Faddeev amplitudes may be introduced by
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
