Abstract
Rigorous bounds on K l 3 spectral functions with up to two substractions are used in order to test the hypothesis m u = 0 Results strongly support an earlier proof, based on a no-subtraction assumption, which shows that the non-renormalization theorem is badly violated if m u= 0. Also, a relation between the K l3 ± scalar form factor and the quark mass ratio m u / m s is obtained in the soft pion limit. Predictions from this relation are then discussed and compared with other estimates based on the baryon and meson spectra and the η→3 π decay.
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