Ising Spectroscopy I: Mesons at T < T_c
Abstract
This paper is our progress report on the project "Ising spectroscopy", devoted to systematic study of the mass spectrum of particles in 2D Ising Field Theory in a magnetic field. Here we address the lowtemperature regime, and develop quantitative approach based on the idea (originally due to McCoy and Wu) of particles being the "mesons", consisting predominantly of two quarks confined by a longrange force. Systematic implementation of this idea leads to a version of the BetheSalpeter equation, which yields infinite sequence of meson masses. The BetheSalpeter spectrum becomes exact in the limit when the magnetic field is small, and we develop the corresponding weakcoupling expansions of the meson masses. The BetheSalpeter equation ignores the contributions from the multiquark components of the meson's states, but we discuss how it can be improved by treating these components perturbatively, and in particular by incorporating the radiative corrections to the quark mass and the coupling parameter (the "string tension"). The approach fails to properly treat the mesons above the stability threshold, where they are expected to become resonance states, but it is shown to yield very good approximation for the masses of all stable particles, at all real values of the IFT parameters in the lowtemperature regime. We briefly discuss how the BetheSalpeter approximation can be used to address the case of complex parameters, which was the main motivation of this work.
 Publication:

arXiv eprints
 Pub Date:
 December 2006
 arXiv:
 arXiv:hepth/0612304
 Bibcode:
 2006hep.th...12304F
 Keywords:

 High Energy Physics  Theory
 EPrint:
 43 pages with 8 figures