Scalar form factors of light mesons

Abstract

The scalar radius of the pion plays an important role in CHPT, because it is related to one of the basic effective coupling constants, viz. the one which controls the quark mass dependence of F_pi at one loop. In a recent paper, Yndurain derives a {\it robust lower bound} for this radius, which disagrees with earlier determinations. We show that such a bound does not exist: the "derivation" relies on an incorrect claim. Moreover, we discuss the physics of the form factors associated with the operators \ubar u, \dbar d and \sbar s and show that their structure in the vicinity of the K \Kbar threshold is quite different. Finally, we draw attention to the fact that the new data on the slope of the scalar K_l3 form factor confirm a recent, remarkably sharp theoretical prediction.