, Volume 41, Issue 1, pp 7-11,
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Improved bounds on the radius and curvature of the K $ \pi$ scalar form factor and implications to low-energy theorems

Abstract

We obtain stringent bounds in the 〈r 2 $ \rangle_{S}^{{K\pi}}$ -c plane where these are the scalar radius and the curvature parameters of the scalar K $ \pi$ form factor, respectively, using analyticity and dispersion relation constraints, the knowledge of the form factor from the well-known Callan-Treiman point $\mathrm{\ensuremath m_K^2-m_\pi^2}$ , as well as at $\mathrm{\ensuremath m_\pi^2-m_K^2}$ , which we call the second Callan-Treiman point. The central values of these parameters from a recent determination are accomodated in the allowed region provided the higher loop corrections to the value of the form factor at the second Callan-Treiman point reduce the one-loop result by about 3% with $\mathrm{\ensuremath F_K/F_\pi=1.21}$ . Such a variation in magnitude at the second Callan-Treiman point yields 0.12 fm2 $ \lesssim$ r 2 $ \rangle_{S}^{{K\pi}}$ $ \lesssim$ 0.21 fm2and 0.56 GeV-4 $ \lesssim$ c $ \lesssim$ 1.47 GeV-4and a strong correlation between them. A smaller value of $\mathrm{\ensuremath F_K/F_\pi}$ shifts both bounds to lower values.

J. Bijnens