The Pion Form Factor Within the Hidden Local Symmetry Model

Abstract

We 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 $ρ-γ$ VMD coupling and an account of several coupled channels. The corresponding function $F_π(s)$ 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 $\omg π^0$ improves significantly the fit quality below the $ϕ$ 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 $F_π(s)$ at $s=0$ up to ${\cal O} (s^2)$ and with the phase shift data on $δ_1^1(s)$ from threshold to somewhat above the $ϕ$ mass. The $\omg$ sector is also examined in relation with recent data from CMD--2.

26 pages, 4 eps figs