Take the tour ×  Do all nonabelian gauge theories produce short
range force?  share|improve this question QCD forces only look
"short range" because they're so powerful at long distances that
they're confining. That's why only color-neutral objects may
exist in isolation and the residual forces acting on such color-
neutral objects (like nucleons) decreases quickly with the
distance. –  Luboš Motl Jan 27 '12 at 15:43 add comment  2
Answers  No, pure (unbroken) SU(2) Yang Mills for example is
massless, i.e. long range  share|improve this answer add comment
One can use the running of the coupling constant as a proxy for
confinement. The $\beta$-function for $SU(N)$ to first order
gives (see http://en.wikipedia.org/wiki/Asymptotic_freedom#Calcu
lating_asymptotic_freedom): $$\beta_1(\alpha) = { \alpha^2 \over
\pi} \left( -{11N \over 6} + {n_f \over 3} \right).$$ So for
$N=3$ confinement (i.e. short range force) occurs with fewer
than 16 species of fermions, but for $N=2$ it has to be fewer
than 11.  share|improve