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 $\rho -\gamma$ 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 $\omg π^0$ improves significantly the fit quality below the $\varphi$ 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 $\mathcal{O}(s^2)$ and with the phase shift data on ${\delta }_1^1(s)$ from threshold to somewhat above the $\varphi$ mass. The $\omg$ sector is also examined in relation with recent data from CMD--2.

26 pages, 4 eps figs

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• Muon g-2 estimates : Can one trust Effective Lagrangians and global fits ?
• A Global Treatment Of VMD Physics Up To The $\varphi$: I. $e^{+}{e}^{-}$ Annihilations, Anomalies And Vector Meson Partial Widths
• Anomalous $\eta /{\eta }^{\prime }$ Decays: The Triangle and Box Anomalies