Radiative Corrections to K_{e3}^{0} Decays and the ∆I=12 Rule
Abstract
The radiative corrections to the Dalitz plot in K_{e3}^{0} decays are calculated assuming a phenomenological weak Kπ vertex and using perturbation theory. The answer depends logarithmically on a cutoff, as is the case for nuclear β decay. An interesting feature of these decays is that they offer a means of measuring the q^{2} dependence of the form factors f_{+/}(q^{2}). The radiative corrections contribute an additional energy dependence which cannot be separated experimentally. It is found that the radiative corrections are considerable, i.e., greater than 3% in absolute magnitude, over a large portion of the Dalitz plot, and are not particularly sensitive to a reasonable choice of cutoff. The corrections to the lepton and pion spectra, and the decay rate are also given. A comparison with previous results for K_{e3}^{0} reveals that the K_{e3}^{+} correction is of the same order of magnitude but everywhere more positive. In particular, the ratio of the decay rates Γ(K_{e3}^{0})Γ(K_{e3}^{+}), which is equal to 2 according to the ∆I=12 rule, must be modified by a factor (1+δ) due to the radiative corrections. It is found that δ~=114% and is independent of the cutoff.
 Publication:

Physical Review
 Pub Date:
 July 1968
 DOI:
 10.1103/PhysRev.171.1675
 Bibcode:
 1968PhRv..171.1675G