Kanji Fujii

Remarks on flavor-neutrino propagators and oscillation formulas

We examine the general structure of the formulas of neutrino oscillations proposed by Blasone and Vitiello (BV). Reconstructing their formulas with the retarded propagators of the flavor-neutrino fields for the case of many flavors, we can get easily the formulas which satisfy the suitable boundary conditions and are independent of arbitrary mass parameters {l_brace}{mu}{sub {rho}}{r_brace}, as obtained by BV for the case of two flavors. In this two-flavor case, our formulas reduce to those obtained by BV under a T-invariance condition. Furthermore, the reconstructed probabilities are shown to coincide with those derived with recourse to the mass Hilbert space H{sub m} which is unitarily inequivalent to the flavor Hilbert space H{sub f}. Such a situation is not found in the corresponding construction in the manner of BV. Then the new factors in BV{close_quote}s formulas, which modify the usual oscillation formulas, are not the trace of the flavor Hilbert space construction, but come from Bogolyubov transformation among the operators of spin-1/2 neutrinos with different masses.

Quantum Mechanics in Riemannian Manifold. II

We have previously argued about the quantum mechanics on the hypersurface V N−1 embedded in Euclidean space R N . We generalize the formalism to the case of V L embedded in Euclidean space R N with 1≤L≤N. The result is essentially the same as the previous one and the additional term proportional to h 2 appears in the potential energy which is related to the extrinsic mean curvature of V L in R N

Geometrically Induced Gauge Structure on Manifolds Embedded in a Higher Dimensional Space

We explain in a context different from that of Maraner the formalism for describing the motion of a particle, under the influence of a confining potential, in a neighborhood of an n-dimensional curved manifold Mn embedded in a p-dimensional Euclidean space Rp with p ≥ n + 2. The effective Hamiltonian on Mn has a (generally non-Abelian) gauge structure determined by the geometry of Mn. Such a gauge term is defined in terms of the vectors normal to Mn, and its connection is called the N connection. This connection is nothing but the connection induced from the normal connection of the submanifold Mn of Rp. In order to see the global effect of this type of connections, the case of M1 embedded in R3 is examined, where the relation of an integral of the gauge potential of the N connection (i.e. the torsion) along a path in M1 to the Berry phase is given through Gauss mapping of the vector tangent to M1. Through the same mapping in the case of M1 embedded in Rp, where the normal and the tangent quantities are exchanged, the relation of the N connection to the induced gauge potential (the canonical connection of the second kind) on the (p - 1)-dimensional sphere Sp - 1 (p ≥ 3) found by Ohnuki and Kitakado is concretely established; the former is the pullback of the latter by the Gauss mapping. Further, this latter which has the monopole-like structure is also proved to be gauge-equivalent to the spin connection of Sp - 1. Thus the N connection is also shown to coincide with the pullback of the spin connection of Sp - 1. Finally, by extending formally the fundamental equations for Mn to the infinite-dimensional case, the present formalism is applied to the field theory that admits a soliton solution. The resultant expression is in some respects different from that of Gervais and Jevicki.

Structures of Expectation Values of Flavor Neutrino Charges with Respect to Neutrino-Source Hadrons

In the framework of quantum field theory, we examine what physical implications are included in the expectation values of the flavor neutrino charges at the time x 0 with respect to the state Ψ(x 0 ), which is taken so as to coincide with the neutrino source state, such as a charged pion at time x 0 ( <x 0 ). Purpose In quantum field theory, 1) the expectation value of a physical observable F (x) at a space-time point x =( x ,x 0 ) with respect to the state Ψ (x 0 ) is given by, in the interaction representation, Ψ (x 0 ) F (x) Ψ (x 0 ) = Ψ (x 0 ) S −1 (x 0 ,x 0 )F (x)S(x 0 ,x 0 ) Ψ (x 0 ) , (1) In the following, we consider the expectation values of the flavor neutrino charges Nρ(x 0 ), where ρ is the flavor suffix (e, µ, ··· ), with respect to the state Ψ (x 0 ) which coincides with the neutrino-source state Ψ (x 0 ) , such as a charged pion at time x 0 ( <x 0 ). We point out that these expectation values lead to a possible unified treatment of various weak decay probabilities of neutrino-source particles and neutrino oscillation. Finally, we suggest a method to construct the state of a flavor neutrino with momentum k. Relevant quantities and relations The total Lagrangian, L(x )= L0(x )+ Lint(x), concerning neutrinos is taken to be L0(x )= −¯F (x)(� ∂ + M )νF (x) ,M † = M, (3) Lint(x )= −(¯ νF (x)JF (x )+ ¯ JF (x)νF (x)) = −Hint(x). (4) Here, νF (x) represents the set of the flavor neutrino fields, νρ(x), and the set of the mass eigenfields νj(x )i s def ined byνF (x )= Z 1/2 νM (x) ,Z 1/2 † MZ 1/2 = Mdiag, where diag(Mdiag )=( m1 ,m 2, ··· ) ,Z 1/2 † Z 1/2 = I, Z 1/2 =( Z 1/2 ρj ), (5) νF (x )=( νe(x) ,ν µ(x), ··· ) T ,ν M (x )=( ν1(x) ,ν 2(x), ··· ) T. (6) For simplicity, the source function JF (x )=( Je(x) ,J µ(x), ··· ) T is assumed to in- clude no neutrino fields, and Lint(x) is the local Fermi interaction obtained in accor- dance with the electro-weak unified theory. We employ Greek and Roman indices,

Helicity suppression mechanism of decay amplitudes in relativistic quark model

Structures of the matrix elements of two-and four-quark operators are investigated in connection with the argument of “helicity suppression” in the decay amplitudes. The analysis is made by expanding the quark operators in terms of the constituentquark modes in a relativistic way. It is shown that the naive consideration of helicity suppression can be applied to the case of two-quark operators. The situation is quite different in the case of four-quark operators; sometimes we find maximum value of the decay amplitude, which is suppressed according to the naive helicity suppression. It is made clear which aspects of the constituent-quark picture are essential to cause the difference between our results and those from the free quark picture. Remarks are given on nonleptonic decays ofK-andD-mesons.

Strong D0 → K− ϱ+ signal and implications for a (c̄s)R current

Abstract The observed much larger branching ratio of D 0 → K − π + π 0 than that of D 0 → K − π + is shown to suggest the existence of a (cs) R current. The observation of F → φπ and ϱπ is also important to determine whether this current exists or not.

Charmed meson decays and right-handed currents

In the presence of right-handed currents including (cs)R, it is emphasized that the dominant parity-violating (-conserving) Hamiltonian for nonleptonic decays of charmed hadrons transforms like 45 + 45∗ (20″ + 84) of SU(4), and leads to distinctive results especially in D+ → KSπ+, F+ → μ+νμ and D0 → K−e+νe, etc.

Remark on state vector construction when flavor mixing exists

In the framework of quantum field theory, we consider the way to construct the one-particle state (with definite 3-momentum) when particle mixing exists, such as in the case of flavor-neutrino mixing. In the preceding report (Prog. Theor. Phys. 112, 901 (2004)), we have examined the structure of expectation values of the flavor neutrino charges (at time t) with respect to a neutrino-source state prepared at time t′ (earlier than t). When there is no mixing, each of various contributions to the expectation value is equal, in its dominant part, to the transition probability corresponding to the respective neutrino-production process. On the basis of the assumption that such an equality holds also in the mixing case, we can find an appropriate form of one-flavor-neutrino state with 3-momentum and helicity. Along the same way, we examine the boson case when flavor mixing exists. We give remarks on the relation and difference between the ordinary and the present approaches to flavor oscillation.

Centre-of-mass motion effects in static properties of baryons

SummaryEffects due to the centre-of-mass motion in the static properties of baryons (theGA/Gv value, the proton magnetic moment, the mean square radius of the proton charge, andA(1) andA(2) constants appearing in the nonleptonic decays of baryons) are examined for some kinds of mean-field confining potentials. Certain indications about the potential form are obtained in order to get favourable values of the mean square radius as well asA(1) andA(2) constants.RiassuntoSi esaminano gli effetti dovuti al moto nel centro di massa nelle proprietà statiche dei barioni (il valoreGA/GV, l’impulso magnetico del protone, il raggio quadratico medio della carica del protone e le costantiA(1) eA(2) che compaiono nei decadimenti non leptonici dei barioni) per alcuni tipi di potenziali che confinano il campo medio. Si ottengono alcune indicazioni sulla forma del potenziale per ottenere valori favorevoli del raggio quadratico medio cosí come le costantiA(1) eA(2).

Remark on the lorentz boost of the confined quark system

Abstract Properties of the state vector that is obtained by boosting the zero three-momentum state constructed from the “bag” state are investigated. This state vector is expressed in a form similar to the one constructed in order to recover the three-space translational and rotational invariances.