Parameter degeneracies and new plots in neutrino oscillations

It is shown that plots of constant probabilities in the $(\sin^22\theta_{13}, 1/s^2_{23})$ plane enable us to see eightfold degeneracy easily. Using this plot, I discuss how an additional long baseline measurement resolves degeneracies after the JPARC experiment measures the oscillation probabilities $P(\nu_\mu\to\nu_e)$ and $P(\bar{\nu}_\mu\to\bar{\nu}_e)$ at $|\Delta m^2_{31}|L/4E=\pi/2$.Comment: 1 page, 2 figures, uses espcrc2.sty. Poster presented at 21st International Conference on Neutrino Physics and Astrophysics (Neutrino 2004), Paris, France, 14-19 Jun 200

Degeneracy and strategies of long baseline and reactor experiments

Assuming that the JPARC experiment measures the oscillation probabilities $P(\nu_\mu\to\nu_e)$ and $P(\bar{\nu}_\mu\to\bar{\nu}_e)$ at $|\Delta m^2_{31}|L/4E=\pi/2$, I discuss what kind of extra experiment (long baseline or reactor) can contribute to determination of $\theta_{13}$ and the CP phase $\delta$.Comment: 3 pages, 3 sets of figures, uses espcrc2.sty. Talk given at 6th International Workshop on Neutrino Factories and Superbeams (NuFact 04), Osaka, Japan, 26 Jul - 1 Aug 200

A Generalized Analytical Mechanics in which Quantum Phenomena Appear

We propose a mechanics of a massive particle in a potential field effective for both classical and quantum system as a modified classical analytical mechanics (modified CM). We transform, under coordinate transformation, the covariant tensor of order two in the Hamilton-Jacobi (H-J) eq. of CM, not with the classical action, but with extended action of diffeomorphism group. Then, the H-J eq., a first-order partial differential eq., is modified to a third-order one. The Euler-Lagrange (E-L) eq. of CM, a second-order ordinary differential eq., related to the H-J eq. through the action integral is accordingly modified to a fourth-order one. Thus obtained mechanics accommodates quantum phenomena due to the higher-order eqs., and always gives trajectory unlike quantum mechanics (QM) due to the E-L eq. Discrete energy levels of a particle in a confining potential are the same as those of QM because quantization criterion is equivalent. Particle distribution in an ensemble disagrees with that of QM even if initial distribution is set identical because dynamics is different; it however agrees with observed data to date within experimental uncertainty. The mechanics thus is a testable alternative to QM.Comment: 51 pages, 8 figures. A reason for 1-D energy quantization which works on real line (R1) is given; the one in previous versions works only on real projective line (RP1). Some other improvements were incorporate