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 scalar form factor and implications to low-energy theorems

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 -c plane where these are the scalar radius and the curvature parameters of the scalar K form factor, respectively, using analyticity and dispersion relation constraints, the knowledge of the form factor from the well-known Callan-Treiman point , as well as at , 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 . Such a variation in magnitude at the second Callan-Treiman point yields 0.12 fm² 〈r ² 0.21 fm²and 0.56 GeV^-4 c 1.47 GeV^-4and a strong correlation between them. A smaller value of shifts both bounds to lower values.