1203.5398 (B. Ananthanarayan et al.)

Spacelike pion form factor from analytic continuation and the onset of
perturbative QCD    [PDF]

B. Ananthanarayan, Irinel Caprini, I. Sentitemsu Imsong

The factorization theorem for exclusive processes in perturbative QCD predicts the behaviour of the pion electromagnetic form factor $F(t)$ at asymptotic spacelike momenta $t(=-Q^2)<0$. We address the question of the onset energy using a suitable mathematical framework of analytic continuation, which uses as input the phase of the form factor below the first inelastic threshold, known with great precision through the Fermi-Watson theorem from $\pi\pi$ elastic scattering, and the modulus measured from threshold up to 3 GeV by the BaBar collaboration. The method leads to almost model-independent upper and lower bounds on the spacelike form factor. Further inclusion of the value of the charge radius and the experimental value at $-2.45 \gev^2$ measured at JLab considerably increases the strength of the bounds in the region $ Q^2 \lesssim 10 \gev^2$, excluding the onset of the asymptotic perturbative QCD regime for $Q^2< 7\gev^2$. We also compare the bounds with available experimental data and with several theoretical models proposed for the low and intermediate spacelike region.

View original: http://arxiv.org/abs/1203.5398