Virtual photons in chiral perturbation theory

Chiral loop corrections and isospin violation effects in ɛ'/ɛ

“…It involves the O(p 6 ) strong [21,30] and O(e 2 p 2 ) [31,32] electromagnetic chiral lagrangians, together with the non-leptonic O(G F p 4 ) [33,34] and O(G F e 2 p 2 ) [35,36] electroweak lagrangians.…”

Virtual photons in SU(2) chiral perturbation theory and electromagnetic corrections to ππ scattering

“…The difference to the three flavor case considered in refs. [8] [9] comes largely from the fact that for two flavors there are less independent operators. This reduced number of terms is the natural basis to consider purely pionic processes.…”

“…Since ππ scattering can be described purely within SU(2) CHPT, we construct here the generating functional including virtual photons to one loop for the two flavor case. As proposed in [8], we assign the chiral dimension one to the electric charge, so the lowest order effective Lagrangian coupling the virtual photons to the pions is of O(e 2 ) ∼ O(q 2 ). The difference to the three flavor case considered in refs.…”

“…The construction of the generating functional proceeds along standard lines making use of heat kernel techniques for elliptic Euclidean differential operators. We follow here the approach outlined in [8] and combine the expansion around the classical solutions for the meson and photons fields, set of fluctuations variables η = (ξ 1 , . .…”

“…It is therefore of importance to get a handle on the electromagnetic corrections for the ππ scattering amplitude to further sharpen the theoretical predictions. Virtual photons have already been included in three flavor CHPT [8][9] and various effects like e.g. the violation of Dashen's theorem or the electromagnetic (em) corrections to the decay η → 3π [10] have been calculated.…”