On lightest baryon and its excitations in large-N 1+1-dimensional QCD

Abstract: We study baryons in multicolour 1+1D QCD via Rajeev's gauge-invariant reformulation as a non-linear classical theory of a bilocal meson field constrained to lie on a Grassmannian. It is known to reproduce 't Hooft's meson spectrum via small oscillations around the vacuum, while baryons arise as topological solitons. The lightest baryon has zero mass per colour in the chiral limit; we find its form factor. It moves at the speed of light through a family of massless states. To model excitations of this baryon, we linearize equations for motion in the tangent space to the Grassmannian, parameterized by a bilocal field U. A redundancy in U is removed and an approximation is made in lieu of a consistency condition on U. The baryon spectrum is given by an eigenvalue problem for a hermitian singular integral operator on such tangent vectors. Excited baryons are like bound states of the lightest one with a meson. Using a rank-1 ansatz for U in a variational formulation, we estimate the mass and form factor of the first excitation.