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 >_S^{K pi}-c plane where these are the scalar radius and the curvature parameters of the scalar pi K form factor respectively using analyticity and dispersion relation constraints, the knowledge of the form factor from the well-known Callan-Treiman point m_K^2-m_pi^2, as well as at 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 F_K/F_pi=1.21. Such a variation in magnitude at the second Callan-Treiman point yields 0.12 fm^2 \lesssim < r^2>_S^{K pi} \lesssim 0.21 fm^2 and 0.56 GeV^{-4} \lesssim c \lesssim 1.47 GeV^{-4} and a strong correlation between them. A smaller value of F_K/F_pi shifts both bounds to lower values.

arXiv comment4 pages using EPJ style files, accepted for publication in European Physical Journal A

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Cited by in corpus (6)

• Chiral Extrapolation of the Strangeness Changing K pi Form Factor
• Theory of unitarity bounds and low energy form factors
• Stringent constraints on the scalar K pi form factor from analyticity, unitarity and low-energy theorems
• Implications of unitarity and analyticity for the Dπform factors
• Improving the phenomenology of K_{l3} form factors with analyticity and unitarity
• Constraining Form Factors with the Method of Unitarity Bounds