Letter

The European Physical Journal A

, Volume 41, Issue 1, pp 7-11

Open Access This content is freely available online to anyone, anywhere at any time.

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

  • Gauhar AbbasAffiliated withCentre for High Energy Physics, Indian Institute of Science
  • , B. AnanthanarayanAffiliated withCentre for High Energy Physics, Indian Institute of Science Email author 

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.

PACS

11.55.Fv Dispersion relations 12.39.Fe Chiral Lagrangians