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.
Article PDF
Avoid common mistakes on your manuscript.
References
FlaviaNet Working Group on Kaon Decays (M. Antonelli), arXiv:0801.1817 [hep-ph].
J. Gasser, H. Leutwyler, Nucl. Phys. B 250, 517 (1985).
P. Post, K. Schilcher, Eur. Phys. J. C 25, 427 (2002) (arXiv:hep-ph/0112352).
J. Bijnens, P. Talavera, Nucl. Phys. B 669, 341 (2003) (arXiv:hep-ph/0303103).
M. Jamin, J.A. Oller, A. Pich, JHEP 0402, 047 (2004) (arXiv:hep-ph/0401080).
C.G. Callan, S.B. Treiman, Phys. Rev. Lett. 16, 153 (1966).
R.F. Dashen, M. Weinstein, Phys. Rev. Lett. 22, 1337 (1969).
J. Bijnens, K. Ghorbani, arXiv:0711.0148 [hep-ph].
A. Kastner, H. Neufeld, Eur. Phys. J. C 57, 541 (2008) (arXiv:0805.2222 [hep-ph]).
V. Cirigliano, G. Ecker, M. Eidemuller, R. Kaiser, A. Pich, J. Portoles, JHEP 0504, 006 (2005) (arXiv:hep-ph/ 0503108).
V. Bernard, M. Oertel, E. Passemar, J. Stern, arXiv: 0903.1654 [hep-ph].
R. Oheme, Phys. Rev. Lett. 16, 215 (1966).
C. Bourrely, I. Caprini, Nucl. Phys. B 722, 149 (2005) (arXiv:hep-ph/0504016).
C. Bourrely, B. Machet, E. de Rafael, Nucl. Phys. B 189, 157 (1981).
I. Caprini, Eur. Phys. J. C 13, 471 (2000) (arXiv:hep-ph/9907227).
B. Ananthanarayan, S. Ramanan, Eur. Phys. J. C 54, 461 (2008) (arXiv:0801.2023 [hep-ph]).
HPQCD Collaboration and MILC Collaboration and UKQCD Collaboration (C. Aubin), Phys. Rev. D 70, 031504 (2004) (arXiv:hep-lat/0405022).
QCDSF Collaboration and UKQCD Collaboration (M. Gockeler, R. Horsley, A.C. Irving, D. Pleiter, P.E.L. Rakow, G. Schierholz, H. Stuben), Phys. Lett. B 639, 307 (2006) (arXiv:hep-ph/0409312).
European Twisted Mass Collaboration (B. Blossier), JHEP 0804, 020 (2008) (arXiv:0709.4574 [hep-lat]).
V. Bernard, M. Oertel, E. Passemar, J. Stern, JHEP 0801, 015 (2008) (arXiv:0707.4194 [hep-ph]).
Author information
Authors and Affiliations
Corresponding author
Additional information
J. Bijnens
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Abbas, G., Ananthanarayan, B. Improved bounds on the radius and curvature of the K\( \pi\) scalar form factor and implications to low-energy theorems. Eur. Phys. J. A 41, 7–11 (2009). https://doi.org/10.1140/epja/i2009-10801-y
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epja/i2009-10801-y