3 research outputs found
Solving the Bars-Green equation for moving mesons in two-dimensional QCD
The two-dimensional QCD in the large limit, generally referred to as the
't Hooft model, is numerically investigated in the axial gauge in a
comprehensive manner. The corresponding Bethe-Salpeter equation for a bound
pair, originally derived by Bars and Green in 1978, was first
numerically tackled by Li and collaborators in late 1980s, yet only for the
{\it stationary} mesons. In this paper, we make further progress by numerically
solving the Bars-Green equation for {\it moving} mesons, ranging from the
chiral pion to charmonium. By choosing several different quark masses, we
computed the corresponding quark condensates, meson spectra and their decay
constants for a variety of meson momenta, and found satisfactory agreement with
their counterparts obtained using light-cone gauge, thus numerically verified
the gauge and Poincar\'{e} invariance of the 't Hooft model. Moreover, we have
explicitly confirmed that, as the meson gets more and more boosted, the large
component of the Bars-Green wave function indeed approaches the corresponding
't Hooft light-cone wave function, while the small component of the wave
function rapidly fades away.Comment: v2, 25 pages, 12 figures, and 1 table; Some figures updated,
references added, typo corrrected; to appear in JHE