arXiv subjects
Publications and source records attributed to Masako Bando.
We consider a minimal SO(10) unified model with horizontal Peccei-Quinn symmetry. The hierarchical structure of quark-lepton mass matrices is naturally implemented by the remnants of certain irrelevant terms. Georgi-Jarlskog relations are also realized due to the horizontal symmetry.
A systematic method is given for obtaining consistent approximations to the Schwinger-Dyson(SD) and Bethe-Salpeter(BS) equations which maintain the external gauge invariance. We show that for any order of approximation to the SD equation there is a corresponding approximation to the BS equations such that the solutions to those equations satisfy the Ward-Takahashi identities of the external gauge symmetry. This formulation also clarifies the way how we can calculate the Green functions of current operators in a consistent manner with the gauge invariance and the axial anomaly. We show which type of diagrams for the $π^0\rightarrowγγ$ amplitude using the pion BS amplitude give result consistent with the low-energy theorem. An interesting phenomenon is observed in the ladder approximation that the low energy theorem is saturated by the zeroth order terms in the external momenta of the pseudoscalar BS amplitude and the vector vertex functions.
We investigate the properties of the amplitude induced by the anomaly. In a relatively high energy region those amplitudes are constructed by the vector meson poles and the anomaly terms, in which the anomaly terms can be essentially evaluated by the triangle quark graph. We pay our attention to the anomaly term and make intensive analysis of the existing experimental data, i.e., the electromagnetic $π^0$ and $ω$ transition form factors. Our result shows that it is essential to use the constituent quark mass instead of the current quark mass in evaluating the anomaly term from the triangle graph.
We propose an interpolating formula for the amplitude induced by the axial anomaly, concentrating on the $π^0γ^{\ast}γ^{\ast}$ transition form factor. The QCD corrections to this amplitude are generally described by two major contributions coming from the $q\bar{q}$ bound state and the background continuous spectrum, respectively. For the first contribution, we include the lowest vector bound state using the realization of the dynamical gauge boson of hidden local symmetry. The second contribution is included as the triangle quark loop in which a constituent mass is adopted as a internal quark mass and the amplitudes are smeared out around the threshold. Using the resulting form factor, we fit the experimental data for the $π^0γ$ and the $ωπ^0$ transition form factors and show that our result describes the experimental data well.
We propose an interpretation for the ($l\bar lγγ,\ M_{γγ}=60{\rm GeV}$) events, which have recently been reported by L3 group at LEP. This may be a first signal of `Technicolor' theory.
A general procedure is presented how to improve the effective potential by using the renormalization group equation (RGE) in MS bar scheme. If one knows the L-loop effective potential and the RGE coefficient functions up to (L+1)-loop level, this procedure gives an improved potential which satisfies the RGE and contains all of the leading, next-to-leading,... , and L-th-to-leading log terms.
Previously proposed procedure for improving the effective potential by using renormalization group equation (RGE) is generalized so as to be applicable to any system containing several different mass scales. If one knows L-loop effective potential and (L+1)-loop RGE coefficient functions, this procedure gives an improved potential which satisfies the RGE and contains all of the leading, next-to-leading,..., and L-th-to-leading log terms. Our procedure here also clarifies how naturally the so-called effective field theory can be incorporated in the RGE in MS bar scheme.