1,783 research outputs found
Phase transition in matrix model with logarithmic action: Toy-model for gluons in baryons
We study the competing effects of gluon self-coupling and their interactions
with quarks in a baryon, using the very simple setting of a hermitian 1-matrix
model with action tr A^4 - log det(nu + A^2). The logarithmic term comes from
integrating out N quarks. The model is a caricature of 2d QCD coupled to
adjoint scalars, which are the transversely polarized gluons in a dimensional
reduction. nu is a dimensionless ratio of quark mass to coupling constant. The
model interpolates between gluons in the vacuum (nu=infinity), gluons weakly
coupled to heavy quarks (large nu) and strongly coupled to light quarks in a
baryon (nu to 0). It's solution in the large-N limit exhibits a phase
transition from a weakly coupled 1-cut phase to a strongly coupled 2-cut phase
as nu is decreased below nu_c = 0.27. Free energy and correlation functions are
discontinuous in their third and second derivatives at nu_c. The transition to
a two-cut phase forces eigenvalues of A away from zero, making glue-ring
correlations grow as nu is decreased. In particular, they are enhanced in a
baryon compared to the vacuum. This investigation is motivated by a desire to
understand why half the proton's momentum is contributed by gluons.Comment: 20 pages, 7 figure
On lightest baryon and its excitations in large-N 1+1-dimensional QCD
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.Comment: 26 pages, 3 figures, shorter published version, added remarks on
parit
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