Scalar form factors of light mesons

The scalar radius of the pion plays an important role in χPT, because it is related to one of the basic effective coupling constants, viz. the one which controls the quark mass dependence of Fπ at one loop. In a recent Letter, Ynduráin derives a 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 u¯u, d¯d and s¯s and show that their structure in the vicinity of the KK¯ threshold is quite different. Finally, we draw attention to the fact that the new data on the slope of the scalar Kℓ3 form factor confirm a recent, remarkably sharp theoretical prediction.