29,815 research outputs found
Statistical Constraints on the Error of the Leptonic CP Violation of Neutrinos
A constraint on the error of leptonic CP violation, which require the phase
to be less than for it to be distinguishable on a
cycle, is presented. Under this constraint, the effects of neutrino detector 's
distance, beam energy, and energy resolution are discussed with reference to
the present values of these parameters in experiments. Although an optimized
detector performances can minimize the deviation to yield a larger
distinguishable range of the leptonic CP phase on a cycle, it is not
possible to determine an arbitrary leptonic CP phase in the range of
with the statistics from a single detector because of the existence of two
singular points. An efficiency factor is defined to characterize the
distinguishable range of . To cover the entire possible
range, a combined efficiency factor corresponding to
multiple sets of detection parameters with different neutrino beam energies and
distances is proposed. The combined efficiency factors of various
major experiments are also presented.Comment: 9 pages, 5 figure
Semi-linear Degenerate Backward Stochastic Partial Differential Equations and Associated Forward Backward Stochastic Differential Equations
In this paper, we consider the Cauchy problem of semi-linear degenerate
backward stochastic partial differential equations (BSPDEs in short) under
general settings without technical assumptions on the coefficients. For the
solution of semi-linear degenerate BSPDE, we first give a proof for its
existence and uniqueness, as well as regularity. Then the connection between
semi-linear degenerate BSPDEs and forward backward stochastic differential
equations (FBSDEs in short) is established, which can be regarded as an
extension of Feynman-Kac formula to non-Markov frame.Comment: 23 page
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