Abstract
We extend previous work concerning rest-frame partial-wave mixing in Hamiltonian effective field theory to both elongated and moving systems, where two particles are in a periodic elongated cube or have nonzero total momentum, respectively. We also consider the combination of the two systems when directions of the elongation and the moving momentum are aligned. This extension should also be applicable in any Hamiltonian formalism. As a demonstration, we analyze lattice QCD results for the spectrum of an isospin-2 $\ensuremath{\pi}\ensuremath{\pi}$ scattering system and determine the $s$, $d$, and $g$ partial-wave scattering information. The inclusion of lattice simulation results from moving frames significantly improves the uncertainty in the scattering information.
Highlights
Lattice simulations of relativistic quantum-field theories are performed in a Euclidean four-dimensional finite volume
We extend previous work concerning rest-frame partial-wave mixing in Hamiltonian effective field theory to both elongated and moving systems, where two particles are in a periodic elongated cube or have nonzero total momentum, respectively
A Hamiltonian which respects the constraints of chiral effective field theory is fit to the finite-volume energy spectrum of lattice field theory and the infinitevolume scattering observables are obtained from the constrained Hamiltonian
Summary
Lattice simulations of relativistic quantum-field theories are performed in a Euclidean four-dimensional finite volume. A recent work [12] established a formalism for disentangling partial-wave mixing and maximally reducing the dimension of the Hamiltonian matrix in the finite volume via an optimal set of rest-frame basis states. To realize the extension in a Hamiltonian formalism, one needs a Hamiltonian making contact with both the infinite-volume scattering observables parametrized in the rest frame and the finite-volume spectrum in the moving frame. The symmetry in a moving frame is quite compatible with a cube elongated in the same direction as the nonzero total momentum This case will be termed the elongated moving system, and disentangling partial-wave mixing in the elongated moving system is the main concern of this work.
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.
