Quark mass dependence of the pion vector form factor

We examine the quark mass dependence of the pion vector form factor, particularly the curvature (mean quartic radius). We focus our study on the consequences of assuming that the coupling constant of the rho to pions is largely independent of the quark mass while the quark mass dependence of the rho--mass is given by recent lattice data. By employing the Omnes representation we can provide a very clean estimate for a certain combination of the curvature and the square radius, whose quark mass dependence could be determined from lattice computations. This study provides an independent access to the quark mass dependence of the rho-pi-pi coupling and in this way a non-trivial check of the systematics of chiral extrapolations. We also provide an improved value for the curvature for physical values for the quark masses, namely <r^4> = 0.73 +- 0.09 fm^4 or equivalently c_V=4.00\pm 0.50 GeV^{-4}.