2020 article

Interpolating QCD(2) between the Instant and Front Forms of Relativistic Dynamics

PROCEEDINGS OF THE 15TH INTERNATIONAL CONFERENCE ON MESON-NUCLEON PHYSICS AND THE STRUCTURE OF THE NUCLEON, Vol. 2249.

By: B. Ma n & C. Ji n

co-author countries: United States of America 🇺🇸
Source: Web Of Science
Added: January 4, 2021

The two-dimensional quantum chromodynamics (QCD2) in the limit of infinite number of colors, known as ‘t Hooft model, was originally formulated in the Light Front Dynamics (LFD). The theory is exactly solvable, while still bearing some resemblance to the four-dimensional real world QCD in aspects such as confinement and mass g ap, as well as the spontaneous breaking of chiral symmetry. The work in the Instant Form Dynamics (IFD) was done in 1978 by Bars and Green. The quark- antiquark bound state equation was derived and solved in each of the two forms, i.e., ‘t Hooft equation and Bars-Green equations, respectively, and they give the same discrete meson mass spectrum independent of the quantization form as expected. Introducing an interpolation angle parameter δ, in this work, we link the two distinct forms of dynamics, IFD and LFD, by letting the space-time axes rotate from the ordinary equal-time form {t, x} to the light front{x+,x−}, as δ varies from 0 to π/4. We unify the ‘t Hooft and Bars-Green equations into one formula, and by numerically solving it we confirm the independence of the meson mass spectra on the interpolation angle δ. We note that the quark condensate is quantization angle independent. This indicates a non-trivial vacuum structure even in the light-front form.