Confinement in the 3-dimensional Gross-Neveu model
A. P. C. Malbouisson, J. M. C. Malbouisson, A. E. Santana, J. C. da Silva
Abstract
We consider the
N
-components 3-dimensional massive Gross-Neveu model compactified in one spatial direction, the system being constrained to a slab of thickness
L
. We derive a closed formula for the effective renormalized
L
-dependent coupling constant in the large-N limit, using bag-model boundary conditions. For values of the fixed coupling constant in absence of boundaries
λ≥
λ
c
≃19.16
, we obtain ultra-violet asymptotic freedom (for
L→0
) and confinement for a length
L
(c)
such that
2.07
m
−1
<
L
(c)
≲2.82
m
−1
,
m
being the fermionic mass. Taking for
m
an average of the masses of the quarks composing the proton, we obtain a confining legth
L
(c)
p
which is comparable with an estimated proton diameter.