Yoji Higasida

Analytical calculations of four-neutrino oscillations in matter

Abstract. We analytically derive the transition probabilities for four-neutrino oscillations in matter. The time-evolution operator giving the neutrino oscillations is expressed by a finite sum of terms up to the third power of the Hamiltonian in a matrix form, using the Cayley-Hamilton theorem. The result of the computation for the probabilities in some mass patterns tells us that it is actually difficult to observe the resonance between one of the three active neutrinos and the fourth (sterile) neutrino near the earth, even if the fourth neutrino exists.

TORSION DEPENDENCE OF THE COVARIANT TAYLOR EXPANSION IN RIEMANN-CARTAN SPACE

We clarify the dependence on the torsion tensor of all coefficients in the covariant Taylor expansion of the HMDS coefficient in the heat kernel for the fermion of spin in Riemann-Cartan space. The dependence on the torsion tensor of the quantities in the expansion coefficients is determined by the matrices in the quantities, except for that of the matrix potential X itself. The quantities with matrices contain the torsion tensor only in a peculiar form, and the others are independent of the torsion tensor.

CHIRAL ANOMALY IN d=4, N=1 SUPERGRAVITY

The chiral U(1) anomaly in d=4, N=1 supergravity is evaluated on the basis of the heat kernel method. We consider all gravitino interactions of the theory, i.e. not only the minimal coupling of gravitino and gravitational fields, but also four-gravitino interactions which are treated as two-gravitino interactions in the background field method. We show the explicit form of a new contribution from the four-gravitino interactions to the anomaly.

An irreducible form for the asymptotic expansion coefficients of the heat kernel of fermions in four-dimensional curved space

We consider the heat kernel for a massless fermion of spin 1/2 interacting with all types of non-Abelian boson fields, i.e. scalar, pseudo-scalar, vector, axial-vector and antisymmetric tensor fields, in a four-dimensional Riemannian space. The couplings of the fermion with the boson fields contain irreducible matrices of the product of the γ-matrices. In this model, the components of the first and second asymptotic expansion coefficients of the heat kernel with respect to the irreducible matrices are explicitly presented. The form of the second coefficients is useful for evaluation of some fermionic anomalies in four-dimensional curved space, and the concrete forms of the chiral U(1) and the trace anomalies are presented.