Constraining Astrophysical Neutrino Flavor Composition from Leptonic Unitarity

The recent IceCube observation of ultra-high-energy astrophysical neutrinos has begun the era of neutrino astronomy. In this work, using the unitarity of leptonic mixing matrix, we derive nontrivial unitarity constraints on the flavor composition of astrophysical neutrinos detected by IceCube. Applying leptonic unitarity triangles, we deduce these unitarity bounds from geometrical conditions, such as triangular inequalities. These new bounds generally hold for three flavor neutrinos, and are independent of any experimental input or the pattern of leptonic mixing. We apply our unitarity bounds to derive general constraints on the flavor compositions for three types of astrophysical neutrino sources (and their general mixture), and compare them with the IceCube measurements. Furthermore, we prove that for any sources without $\nu_\tau$ neutrinos, a detected $\nu_\mu$ flux ratio $< 1/4$ will require the initial flavor composition with more $\nu_e$ neutrinos than $\nu_\mu$ neutrinos.Comment: JCAP Final Version. 24pp. Only minor refinements, references adde

Origin of Constrained Maximal CP Violation in Flavor Symmetry

Current data from neutrino oscillation experiments are in good agreement with $\delta =-\frac{\pi}{2}$ and $\theta_{23}^{} = \frac{\pi}{4}$. We define the notion of "constrained maximal CP violation" (CMCPV) for predicting these features and study their origin in flavor symmetry. We derive the parametrization-independent solution of CMCPV and give a set of equivalent definitions for it. We further present a theorem on how the CMCPV can be realized. This theorem takes advantage of residual symmetries in the neutrino and charged lepton mass matrices, and states that, up to a few minor exceptions, $(|\delta |, \theta_{23}) =(\frac{\pi}{2}, \frac{\pi}{4})$ is generated when those symmetries are real. The often considered $\mu$-$\tau$ reflection symmetry, as well as specific discrete subgroups of O(3), are special cases of our theorem.Comment: Phys.Lett.B Final Version, 13pp. All conclusions unchanged, only minor improvement to stress the parametrization-independence of our CMCP

Quantum spatial-periodic harmonic model for daily price-limited stock markets

We investigate the behavior of stocks in daily price-limited stock markets by purposing a quantum spatial-periodic harmonic model. The stock price is presumed to oscillate and damp in a quantum spatial-periodic harmonic oscillator potential well. Complicated non-linear relations including inter-band positive correlation and intra-band negative correlation between the volatility and the trading volume of stocks are derived by considering the energy band structure of the model. The validity of price limitation is then examined and abnormal phenomena of a price-limited stock market (Shanghai Stock Exchange) of China are studied by applying our quantum model.Comment: 8 pages, 9 figure