Virtual Photon Correction to the $K^{+}\to {\pi }^{+}{\pi }^0{\pi }^0$ Decay

Abstract

We consider electromagnetic corrections to the non-leptonic kaon decay, $K^{+}\to {\pi }^{+}{\pi }^0{\pi }^0$, due to explicit virtual photons only. The decay amplitude is calculated at one-loop level in the framework of Chiral Perturbation Theory. The interest in this process is twofold: It is actually measured by the NA48 collaboration from one side, and, the value of the amplitude at the $\pi \pi$ threshold gives access to $\pi \pi$ scattering lengths from the other side. We found that the present correction is about 5 to 6% the value of the Born amplitude squared. Combined with another piece published recently, this fixes the size of isospin breaking correction to the amplitude squared to 7% its one-loop level value in the absence of isospin breaking and at the center of Dalitz plot.

29 pages, 1 LaTeX file, 1 pdf file including all figures

References in corpus (2)

• Charged Kaon K \to 3 pi CP Violating Asymmetries at NLO in CHPT
• Isospin Breaking in $K_{\ell 4}$ Decays of the Neutral Kaon

Cited by in corpus (8)

• Radiative corrections in K --> 3 pi decays
• Cusps in K --> 3pi decays: a theoretical framework
• K -> 3 pi Final State Interactions at NLO in CHPT and Cabibbo's Proposal to Measure a_0-a_2
• Isospin Breaking in $K\to 3\pi$ Decays III: Bremsstrahlung and Fit to Experiment
• Isospin-Breaking quark condensates in Chiral Perturbation Theory
• Size of Isospin Breaking in Charged K(L4) Decay
• Measuring the a0-a2 pion scattering lengths through K to 3 pi decays
• CP conserved nonleptonic $K\to \pi \pi \pi$ decays in the Chiral Quark Model