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

Gauhar Abbas; B. Ananthanarayan

doi:10.1140/epja/i2009-10801-y

EPJ

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2023 Impact factor 2.6

Hadrons and Nuclei

Open Access

Eur. Phys. J. A (2009) 41: 7-11
https://doi.org/10.1140/epja/i2009-10801-y

Letter

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

Gauhar Abbas and B. Ananthanarayan^*

Centre for High Energy Physics, Indian Institute of Science, 560 012, Bangalore, India

^* e-mail: anant@cts.iisc.ernet.in

Received: 11 March 2009
Revised: 26 April 2009
Accepted: 6 May 2009
Published online: 24 May 2009

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.