, Volume 41, Issue 1, pp 7-11,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 24 May 2009

Improved bounds on the radius and curvature of the K\( \pi\) scalar form factor and implications to low-energy theorems


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.