The Pion Form Factor Within the Hidden Local Symmetry Model

26 pages, 4 eps figsWe analyze a pion form factor formulation which fulfills the Analyticity requirement within the Hidden Local Symmetry (HLS) Model. We show that it implies an $s$--dependent dressing of the $\rho-\gamma$ VMD coupling and an account of several coupled channels. The corresponding function $F_\pi(s)$ provides nice fits of the pion form factor data from $s=-0.25$ to $s=1$ GeV$^2$. It is shown that the coupling to $K \bar{K}$ has little effects, while $\omg \pi^0$ improves significantly the fit quality below the $\phi$ mass. All parameters, except for the subtraction polynomial coefficients are fixed from the rest of the HLS phenomenology. The fits show consistency with the expected behaviour of $F_\pi(s)$ at $s=0$ up to ${\cal O} (s^2)$ and with the phase shift data on $\delta_1^1(s)$ from threshold to somewhat above the $\phi$ mass. The $\omg$ sector is also examined in relation with recent data from CMD--2