Virtual photons in SU(2) chiral perturbation theory and electromagnetic corrections to ππ scattering [Phys. Lett. B 406 (1997) 154]

Measurement of the η→3π0 Dalitz plot distribution with the WASA detector at COSY

“…In 2004 a cusp like structure in the π 0 π 0 invariant mass for the K + → π 0 π 0 π + decay was observed by the NA48/2 collaboration [22]. The effect was predicted already in 1997 by Meißner et al [23] and the interpretation of the NA48/2 results was given by Cabibbo [24]. The process provides a precise determination of a combination of the I = 0 and I = 2 pion-pion s-wave scattering lengths, a 0 and a 2 .…”

Electromagnetic corrections toγπ±→π0π±

“…Actually, we shall use the two-flavour version of the formalism, discussed in Refs. [16] and [22] to order one loop. As far as notation is concerned, we follow the first of these two last references.…”

“…In the even intrinsic sector, the counterterms consist of the strong interaction low-energy constants l i of Ref. [8], and of the electromagnetic constants k i [16,22], corresponding to the decomposition (there are also O(e 4 ) counterterms, but we shall not consider radiative corrections of this order)…”

“…This information has been obtained independently, using functional techniques, for the low-energy constants l r i (µ) [8] and k r i (µ) [16,22], but not for the remaining ones 1 . On the other hand, we may however use our present results in order to pin down the scale dependence of several combinations of the renormalized constants A r i (µ) and of B r eff (µ).…”

“…(2.15) are the finite, scale independent contributions of the electromagnetic counterterms k i . The precise relations among the non-renormalized k i , the scale dependent renormalized k r i (µ) and the scale independentk i have been worked out by several authors [22,16]. In [16], the following estimates, based on naive dimensional analysis, were givenk…”