Precise Formulation of Neutrino Oscillation in the Earth

We give a perturbation theory of neutrino oscillation in the Earth. The perturbation theory is valid for neutrinos with energy E \gsim 0.5 GeV. It is formulated using trajectory dependent average potential. Non-adiabatic contributions are included as the first order effects in the perturbation theory. We analyze neutrino oscillation with standard matter effect and with non-standard matter effect. In a three flavor analysis we show that the perturbation theory gives a precise description of neutrino conversion in the Earth. Effect of the Earth matter is substantially simplified in this formulation.Comment: References added, 21 pages, 10 figures, version to appear in PR

Effective energy-momentum tensor of strong-field QED with unstable vacuum

We study the influence of a vacuum instability on the effective energy-momentum tensor (EMT) of QED, in the presence of a quasiconstant external electric field, by means of the relevant Green functions. In the case when the initial vacuum, |0,in>, differs essentially from the final vacuum, |0,out>, we find explicitly and compared both the vacuum average value of EMT, , and the matrix element, . In the course of the calculation we solve the problem of the special divergences connected with infinite time T of acting of the constant electric field. The EMT of pair created by an electric field from the initial vacuum is presented. The relations of the obtained expressions to the Euler-Heisenberg's effective action are established.Comment: 8 pages, 1 figure, Talk given at "QFEXT'05", the 7-th workshop on quantum field theory under the influence of external conditions, Barcelona, Spain, Sept. 5-9, 2005; minor misprints correcte

Necessary and sufficient condition for hydrostatic equilibrium in general relativity

We present explicit examples to show that the `compatibility criterion' is capable of providing a {\em necessary} and {\em sufficient} condition for any regular configuration to be compatible with the state of hydrostatic equilibrium. This conclusion is drawn on the basis of the finding that the $M-R$ relation gives the necessary and sufficient condition for dynamical stability of equilibrium configurations only when the compatibility criterion for these configurations is appropriately satisfied. In this regard, we construct an appropriate sequence composed of core-envelope models on the basis of compatibility criterion, such that each member of this sequence satisfies the extreme case of causality condition $v = c = 1$ at the centre. The maximum stable value of $u \simeq 0.3389$ (which occurs for the model corresponding to the maximum value of mass in the mass-radius relation) and the corresponding central value of the local adiabatic index, $(\Gamma_1)_0 \simeq 2.5911$, of this model are found fully consistent with those of the corresponding {\em absolute} values, $u_{\rm max} \leq 0.3406$, and $(\Gamma_1)_0 \leq 2.5946$, which impose strong constraints on these parameters of such models. In addition to this example, we also study dynamical stability of pure adiabatic polytropic configurations on the basis of variational method for the choice of the `trial function', $\xi =re^{\nu/4}$, as well as the mass-central density relation, since the compatibility criterion is appropriately satisfied for these models. The results of this example provide additional proof in favour of the statement regarding compatibility criterion mentioned above.Comment: 31 pages (double-spaced) revtex style, 1 figure in `ps' forma

Solar neutrinos and 1-3 leptonic mixing

Effects of the 1-3 leptonic mixing on the solar neutrino observables are studied and the signatures of non-zero $\theta_{13}$ are identified. For this we have re-derived the formula for $3\nu$-survival probability including all relevant corrections and constructed the iso-contours of observables in the $\sin^2 \theta_{12} - \sin^2 \theta_{13}$ plane. Analysis of the solar neutrino data gives $\sin^2\theta_{13} = 0.007^{+ 0.080}_{-0.007}$ (90% C.L.) for $\Delta m^2 = 8 \cdot 10^{-5}$ eV$^2$. The combination of the ratio CC/NC at SNO and gallium production rate selects $\sin^2\theta_{13} = 0.017 \pm 0.026$ ($1\sigma$). The global fit of all oscillation data leads to zero best value of $\sin^2 \theta_{13}$. The sensitivity ($1\sigma$ error) of future solar neutrino studies to $\sin^2 \theta_{13}$ can be improved down to 0.01 - 0.02 by precise measurements of the pp-neutrino flux and the CC/NC ratio as well as spectrum distortion at high ($E > 4$ MeV) energies. Combination of experimental results sensitive to the low and high energy parts of the solar neutrino spectrum resolves the degeneracy of angles $\theta_{13}$ and $\theta_{12}$. Comparison of $\sin^2 \theta_{13}$ as well as $\sin^2 \theta_{12}$ measured in the solar neutrinos and in the reactor/accelerator experiments may reveal new effects which can not be seen otherwise.Comment: 36 pages, latex, 10 figures. Analysis and figures are updated with new (salt phase II) SNO results, several clarifications added, typos correcte

Energy-momentum tensor in thermal strong-field QED with unstable vacuum

The mean value of the one-loop energy-momentum tensor in thermal QED with electric-like background that creates particles from vacuum is calculated. The problem differes essentially from calculations of effective actions (similar to that of Heisenberg--Euler) in backgrounds that do not violate the stability of vacuum. The role of a constant electric background in the violation of both the stability of vacuum and the thermal character of particle distribution is investigated. Restrictions on the electric field and its duration under which one can neglect the back-reaction of created particles are established.Comment: 7 pages, Talk presented at Workshop "Quantum Field Theory under the Influence of External Conditions", Leipzig, September 17-21, 2007; introduction extended, version accepted for publication in J.Phys.

On the global visibility of singularity in quasi-spherical collapse

We analyze here the issue of local versus the global visibility of a singularity that forms in gravitational collapse of a dust cloud, which has important implications for the weak and strong versions of the cosmic censorship hypothesis. We find conditions as to when a singularity will be only locally naked, rather than being globally visible, thus preseving the weak censorship hypothesis. The conditions for formation of a black hole or naked singularity in the Szekeres quasi-spherical collapse models are worked out. The causal behaviour of the singularity curve is studied by examining the outgoing radial null geodesics, and the final outcome of collapse is related to the nature of the regular initial data specified on an initial hypersurface from which the collapse evolves. An interesting feature that emerges is the singularity in Szekeres spacetimes can be ``directionally naked''.Comment: Latex file, 32 pages, 12 postscript figures. To appear in the Journal of General Relativity and Gravitatio

nuMSM--Predictions for Neutrinoless Double Beta Decay

We give the prediction on the effective Majorana mass for neutrinoless double $\beta$ decay in a simple extension of the Standard Model (nuMSM). The model adds three right-handed neutrinos with masses smaller than the electroweak scale, and explains dark matter of the Universe. This leads to constraints 1.3meV<m_{bb}^{NH}<3.4meV in normal neutrino mass hierarchy and 13meV<m_{bb}^{IH}<50meV in inverted hierarchy.Comment: 5 page

Unified Angular Momentum of Dyons

Unified quaternionic angular momentum for the fields of dyons and gravito-dyons has been developed and the commutation relations for dynamical variables are obtained in compact and consistent manner. Demonstrating the quaternion forms of unified fields of dyons (electromagnetic fields) and gravito-dyons (gravito-Heavisidian fields of linear gravity), corresponding quantum equations are reformulated in compact, simpler and manifestly covariant way