Flavor-changing interactions of Goldstone bosons with fermions

In theories with gauge ''horizontal'' symmetry with respect to generations of fermions, the possibility is discussed of existence of a Goldstone boson whose interactions with the fermions are off-diagonal with respect to the flavors. The probabilities of K+→π+α and μ→eα decays (α is a Goldstone boson) are found within the framework of the SU(5) x SU(3) theory recently proposed by Z. Berezhiani and Dzh. Chkarueli (JETP Lett. 35, 612 (1982); Sov. J. Nucl. Phys 37, 618 (1983)]. The experimental limit on the width of the K+→π+α decay imposes in this case a restriction on the vacuum mean value responsible for the horizontal-symmetry breaking, > or approx. =1010 GeV. The possible nature of the coupling between a Goldstone boson and fermions is also discussed. It is shown that only pseudoscalar coupling is possible for interactions that are diagonal in flavor, whereas off-diagonal interactions can be both scalar and pseudoscalar