It is shown that the conserved magnetic charge discovered by ’t Hooft in non−Abelian gauge theories with spontaneous symmetry breaking is not associated with the invariance of the action under a symmetry group. Rather, it is a topological characteristic of an isotriplet of Higgs fields in a three−dimensional space: the Brouwer degree of the mapping between a large sphere in configuration space and the unit sphere in field space provided by the normalized Higgs field ?a = φa (φbφb)−1/2. The use of topological methods in determining magnetic charge configurations is outlined. A peculiar interplay between Dirac strings and zeros of the Higgs field under gauge transformations is pointed out. The monopole−antimonopole system is studied.

We examine how large violation effects of CP and T are allowed in long baseline neutrino experiments. When we attribute only the atmospheric neutrino anomaly to neutrino oscillation we may have large CPviolation effects. When we attribute both the atmospheric neutrino anomaly and the solar neutrino deficit to neutrino oscillation we may have sizable T violation effects proportional to the ratio of the two mass differences; it is difficult to see CP violation since we cannot ignore the matter effect. We give a simple expression for T violation in the presence of matter. ͓S0556-2821͑97͒00903-X͔ PACS number͑s͒: 14.60.Pq, 11.30.Er † Electronic address: joe@icrhp3.icrr.u-tokyo.ac.jp 1 We assume m 1 Ͻm 2

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We show simple methods how to separate pure CP violating effect from matter effect in long baseline neutrino oscillation experiments with three generations of neutrinos. We give compact formulae for neutrino oscillation probabilities assuming one of the three neutrino masses (presumably ν τ mass) to be much larger than the other masses and the effective mass due to matter effect. Two methods are shown: One is to observe envelopes of the curves of oscillation probabilities as functions of neutrino energy; a merit of this method is that only a single detector is enough to determine the presence of CP violation. The other is to compare experiments with at least two different baseline lengths; this has a merit that it needs only narrow energy range of oscillation data.

We have re-analyzed the results of various experiments which were not originally interested as searches for the Q-ball or the Fermi-ball. Based on these analyses, in addition to the available data on Q-balls, we obtained rather stringent bounds on flux, mass and typical energy scale of Q-balls as well as Fermi-balls. In case these nontopological solitons are the main component of the dark matter of the Galaxy, we found that only such solitons with very large quantum numbers are allowed. We also estimate how sensitive future experiments will be in the search for Q-balls and Fermi-balls.fragmentation [4], and that the electromagnetic properties at low energy is the same as the case of Z F = 137 unless the radius exceeds 1Å.

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