The hidden symmetries in the PMNS matrix and the light sterile neutrino(s)

The approximately symmetric form of the PMNS matrix suggests that there could exist a hidden symmetry which makes the PMNS matrix different from the CKM matrix for quarks. In literature, all the proposed fully symmetric textures exhibit an explicit $\mu-\tau$ symmetry in addition to other symmetries which may be different for various textures. Observing obvious deviations of the practical PMNS matrix elements from those in the symmetric textures, there must be a mechanism to distort the symmetry. It might be due to existence of light sterile neutrinos. In this work, we study the case of the Tribimaximal texture and propose that its apparent symmetry disappears due to existence of a sterile neutrino. We observe that introducing just one sterile neutrino is still not sufficient to recover the data, thus a slight $\mu-\tau$ symmetry breaking is also needed. By considering those factors, we obtain the PMNS matrix elements which are consistent with data within the experimental tolerance.Comment: 4 pages. Accepted by Modern Physics Letters

Study on radiative decays of DsJ∗(2860)D^*_{sJ}(2860) and Ds1∗(2710)D^*_{s1}(2710) into DsD_s by means of LFQM

The observed resonance peak around 2.86 GeV has been carefully reexamined by the LHCb collaboration and it is found that under the peak there reside two states $D^*_{s1}(2860)$ and $D^*_{s3}(2860)$ which are considered as $1^3D_1(c\bar s)$ and $1^3D_3(c\bar s)$ with slightly different masses and total widths. Thus, the earlier assumption that the resonance $D^*_{s1}(2710)$ was a $1D$ state should not be right. We suggest to measure the partial widths of radiative decays of $D^*_{sJ}(2860)$ and $D^*_{s1}(2710)$ to confirm their quantum numbers. We would consider $D^*_{s1}(2710)$ as $2^3S_1$ or a pure $1^3D_1$ state, or their mixture and respectively calculate the corresponding branching ratios as well as those of $D^*_{sJ}(2860)$. The future precise measurement would provide us information to help identifying the structures of those resonances .Comment: 8 pages, 4 figures, 1 tabl

Some results on best approximation in locally convex spaces

利用奶牛初乳对170只中国美利奴军垦型细毛羊(断奶80d)在非繁殖季节进行诱导发情处理。结果表明,发情率为92.35%,受精率86.64%,双羔率3.3%;对照组发情率33.33%(10/30),差异极显著(P<0.01)。IEEEZero knowledge sets is a new cryptographic primitive introduced by Micali, Rabin, and Kilian in FOCS 2003. It has been intensively studied recently. However all the existing ZKS schemes follow the basic structure by Micali et al. That is, th

Bayesian analysis of the break in DAMPE lepton spectra

Recently, DAMPE has released its first results on the high-energy cosmic-ray electrons and positrons (CREs) from about $25$ GeV to $4.6$ TeV, which directly detect a break at $\sim 1$ TeV. This result gives us an excellent opportunity to study the source of the CREs excess. In this work, we used the data fo proton and helium flux (from AMS-02 and CREAM), $\bar{\mathrm{p}}/\mathrm{p}$ ratio (from AMS-02), positron flux (from AMS-02) and CREs flux (from DAMPE without the peak signal point at $\sim 1.4$ TeV) to do global fitting simultaneously, which can account the influence from the propagation model, the nuclei and electron primary source injection and the secondary lepton production precisely. For extra source to interpret the excess in lepton spectrum, we consider two separate scenarios (pulsar and dark matter annihilation via leptonic channels) to construct the bump ($\gtrsim 100$ GeV) and the break at $\sim 1$ TeV. The result shows: (i) in pulsar scenario, the spectral index of the injection should be $\nu_{\mathrm{psr}} \sim 0.65$ and the cut-off should be $R_{c} \sim 650$ GV; (ii) in dark matter scenario, the dark matter particle's mass is $m_{\chi} \sim 1208$ GeV and the cross section is $\langle \sigma v \rangle \sim 1.48 \times 10^{-23} \mathrm{cm}^{3} \mathrm{s}^{-1}$. Moreover, in the dark matter scenario, the $\tau \bar{\tau}$ annihilation channel is highly suppressed, and a DM model is built to satisfy the fitting results.Comment: 17 pages, 12 figures. PRD versio