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 $\delta_{CP}$ to be less than $\pi/4$ for it to be distinguishable on a $2\pi$ 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 $2\pi$ cycle, it is not possible to determine an arbitrary leptonic CP phase in the range of $2\pi$ with the statistics from a single detector because of the existence of two singular points. An efficiency factor $\eta$ is defined to characterize the distinguishable range of $\delta_{CP}$. To cover the entire possible $\delta_{CP}$ range, a combined efficiency factor $\eta^*$ corresponding to multiple sets of detection parameters with different neutrino beam energies and distances is proposed. The combined efficiency factors $\eta^*$ of various major experiments are also presented.Comment: 9 pages, 5 figure

Superconducting cosmic strings as sources of cosmological fast radio bursts

In this paper we calculate the radio burst signals from three kinds of structures of superconducting cosmic strings. By taking into account the observational factors including scattering and relativistic effects, we derive the event rate of radio bursts as a function of redshift with the theoretical parameters $G\mu$ and $\mathcal{I}$ of superconducting strings. Our analyses show that cusps and kinks may have noticeable contributions to the event rate and in most cases cusps would dominate the contribution, while the kink-kink collisions tend to have secondary effects. By fitting theoretical predictions with the normalized data of fast radio bursts, we for the first time constrain the parameter space of superconducting strings and report that the parameter space of $G\mu \sim [10^{-14}, 10^{-12}]$ and $\mathcal{I} \sim [10^{-1}, 10^{2}] ~ \rm{GeV}$ fit the observation well although the statistic significance is low due to the lack of observational data. Moreover, we derive two types of best fittings, with one being dominated by cusps with a redshift $z = 1.3$, and the other dominated by kinks at the range of the maximal event rate.Comment: 13 pages, 2 figures, 1 table; references update