Analysis and interpretation of new low-energy $\pi\pi$ scattering data

S. Descotes; N.H. Fuchs; L. Girlanda; J. Stern

doi:doi:10.1007/s10052-002-0965-3

EPJ

a
b
c
d
e
ap
st
h
plus
ds
pv
ti
qt
am
n

2023 Impact factor 4.2

Particles and Fields

Eur. Phys. J. C 24, 469-483 (2002)
DOI: 10.1007/s10052-002-0965-3

Analysis and interpretation of new low-energy $\pi\pi$ scattering data

S. Descotes¹, N.H. Fuchs², L. Girlanda³ and J. Stern⁴

¹ Department of Physics and Astronomy, University of Southampton, Southampton SO17 1BJ, UK
² Department of Physics, Purdue University, West Lafayette IN 47907, USA
³ Dipartimento di Fisica, Università di Padova and INFN, Via Marzolo 8, 35131 Padova, Italy
⁴ Groupe de Physique Théorique, Institut de Physique Nucléaire, 91406 Orsay-Cedex, France

(Received: 11 December 2001 / Revised version: 28 March 2002 / Published online: 7 June 2002 )

Abstract
The recently published E865 data on charged K_e4 decays and $\pi\pi$ phases are reanalyzed to extract values of the two S-wave scattering lengths, of the subthreshold parameters $\alpha$ and $\beta$ , of the low-energy constants $\bar{\ell}_3$ and $\bar{\ell}_4$ as well as of the main two-flavour order parameters: $\langle\bar uu\rangle$ and $F_{\pi}$ in the limit m_u = m_d = 0 taken at the physical value of the strange quark mass. Our analysis is exclusively based on direct experimental information on $\pi\pi$ phases below 800 MeV and on the new solutions of the Roy equations by Ananthanarayan et al. The result is compared with the theoretical prediction relating 2a₀⁰-5a₀² and the scalar radius of the pion, which was obtained in two-loop Chiral Perturbation Theory. A discrepancy at the 1- $\sigma$ level is found and commented upon.