Neutrino Oscillations in Intermediate States.II -- Wave Packets

We analyze oscillations of intermediate neutrinos in terms of the scattering of particles described by Gaussian wave packets. We study a scalar model as in a previous paper (I) but in realistic situations, where the two particles of the initial state and final state are wave packets and neutrinos are in the intermediate state. The oscillation of the intermediate neutrino is found from the time evolution of the total transition probability between the initial state and final state. The effect of a finite lifetime and a finite relaxation time are also studied. We find that the oscillation pattern depends on the magnitude of wave packet sizes of particles in the initial state and final state and the lifetime of the initial particle. For $\Delta m^2_{21}=3\times 10^{-2}$ eV$^2$, the oscillation probability deviates from that of the standard formula if the wave packet sizes are around $10^{-13}$ m for 0.4 MeV neutrino.Comment: 29 pages, 11 figures. typos corrected, appendix adde

How to construct a coordinate representation of a Hamiltonian operator on a torus

The dynamical system of a point particle constrained on a torus is quantized \`a la Dirac with two kinds of coordinate systems respectively; the Cartesian and toric coordinate systems. In the Cartesian coordinate system, it is difficult to express momentum operators in coordinate representation owing to the complication in structure of the commutation relations between canonical variables. In the toric coordinate system, the commutation relations have a simple form and their solutions in coordinate representation are easily obtained with, furthermore, two quantum Hamiltonians turning up. A problem comes out when the coordinate system is transformed, after quantization, from the Cartesian to the toric coordinate system.Comment: 17 pages, LaTeX, 1 Figure included as a compressed uuencoded postscript fil

Results of a Search for Paraphotons with Intense X-ray Beams at SPring-8

A search for paraphotons, or hidden U(1) gauge bosons, is performed using an intense X-ray beamline at SPring--8. "Light Shining through a Wall" technique is used in this search. No excess of events above background is observed. A stringent constraint is obtained on the photon--paraphoton mixing angle, $\chi < 8.06\times 10^{-5}\ (95$ for $0.04\ {\rm eV}<m_{\gamma^{\prime}} < 26\ {\rm keV}$.Comment: 10 pages, 4 figure

Non-trivial Center Dominance in High Temperature QCD

We investigate the properties of quarks and gluons above the chiral phase transition temperature $T_c,$ using the RG improved gauge action and the Wilson quark action with two degenerate quarks mainly on a $32^3\times 16$ lattice. In the one-loop perturbation theory, the thermal ensemble is dominated by the gauge configurations with effectively $Z(3)$ center twisted boundary conditions, making the thermal expectation value of the spatial Polyakov loop take a non-trivial $Z(3)$ center. This is in agreement with our lattice simulation of high temperature QCD. We further observe that the temporal propagator of massless quarks at extremely high temperature $\beta=100.0 \, (T \simeq10^{58} T_c)$ remarkably agrees with the temporal propagator of free quarks with the $Z(3)$ twisted boundary condition for $t/L_t \geq 0.2$, but differs from that with the $Z(3)$ trivial boundary condition. As we increase the mass of quarks $m_q$, we find that the thermal ensemble continues to be dominated by the $Z(3)$ twisted gauge field configurations as long as $m_q \le 3.0 \, T$ and above that the $Z(3)$ trivial configurations come in. The transition is essentially identical to what we found in the departure from the conformal region in the zero-temperature many-flavor conformal QCD on a finite lattice by increasing the mass of quarks. We argue that the behavior is consistent with the renormalization group analysis at finite temperature.Comment: 16 pages, 9 figures; 4 tables, an appendix adde