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Phase transitions governed by spontaneous time reversal symmetry breaking (TRSB) have long been sought in many quantum systems, including materials with anomalous Hall effect (AHE), cuprate high temperature superconductors, Iridates and so on. However, experimentally identifying such a phase transition is extremely challenging because the transition is hidden from many experimental probes. Here, using zero-field muon spin relaxation (ZF-$\mu$SR) technique, we observe strong TRSB signals below 70 K in the newly discovered kagome superconductor CsV$_3$Sb$_5$. The TRSB state emerges from the 2 x 2 charge density wave (CDW) phase present below ~ 95 K. By carrying out optical second-harmonic generation (SHG) experiments, we also find that inversion symmetry is maintained in the temperature range of interest. Combining all the experimental results and symmetry constraints, we conclude that the interlayer coupled chiral flux phase (CFP) is the most promising candidate for the TRSB state among all theoretical proposals of orbital current orders. Thus, this prototypical kagome metal CsV3Sb5 can be a platform to establish a TRSB current-ordered state and explore its relationship with CDW, giant AHE, and superconductivity., Comment: 17 pages, 3 figures

The anomalous dimensions for the interpolating currents of baryons are indispensable inputs in a serious QCD analysis of baryon. However, the results in the literature are vague. In view of this, in this work, we investigate the one-loop anomalous dimensions for some interpolating currents such as those of $\Lambda_{Q}$ and proton. Under the requirement of precise testing the Standard Model, this study is essential and significant for the QCD analysis in the future., Comment: 7 pages, 1 figure

CsV$_3$Sb$_5$ is a newly discovered Kagome superconductor that attracts great interest due to its topological nontrivial band structure and the coexistence of superconductivity and charge-density-wave (CDW) with many exotic properties. Here, we report the detailed characterization of the CDW gap in high-quality CsV$_3$Sb$_5$ single crystals using high-resolution angle-resolved photoemission spectroscopy. We find that the CDW gap is strongly momentum dependent. While gapped around the $M$ point, the electronic states remain gapless around the $\Gamma$ point and along the $\Gamma$-$K$ direction. Such momentum dependence indicates that the CDW is driven by the scattering of electrons between neighboring $M$ points, where the band structure hosts multiple saddle points and the density of state diverges near the Fermi level. Our observations of the partially gapped Fermi surface and strongly momentum-dependent CDW gap not only provide a foundation for uncovering the mechanism of CDW in CsV$_3$Sb$_5$, but also shed light on the understanding of how the CDW coexists with superconductivity in this topological Kagome superconductor., Comment: 10 pages, 4 figures

In the seesaw framework, in the basis of $M^{}_{\rm R}$ being diagonal, we explore the simplified textures of $M^{}_{\rm D}$ that can naturally yield the trimaximal neutrino mixings and their consequences for the neutrino parameters and leptogenesis. We first formulate the generic textures of $M^{}_{\rm D}$ that can naturally yield the trimaximal mixings and then examine if their parameters can be further reduced. Our analysis is restricted to the simple but instructive scenario that there is only one phase parameter $\phi$ responsible for both the CP violating effects at low energies and leptogenesis. Our attention is paid to the textures of $M^{}_{\rm D}$ that possess some vanishing or equal elements. On the basis of these results, we further examine if $\phi$ can also take a particular value. The consequences of the phenomenologically-viable simplified textures for the neutrino parameters and leptogenesis are studied. A concrete flavor-symmetry model that can realize one representation of them is given., Comment: 27 pages, 5 figures, 10 tables, version accepted for publication in PRD

We systematically measure the superconducting (SC) and mixed state properties of high-quality CsV3Sb5 single crystals with Tc ~ 3.5 K. We find that the upper critical field Hc2(T) exhibits a large anisotropic ratio of Hc2^(ab)/Hc2^(c) ~ 9 at zero temperature and fitting its temperature dependence requires a minimum two-band effective model. Moreover, the ratio of the lower critical field, Hc1^(ab)/Hc1^(c), is also found to be larger than 1, which indicates that the in-plane energy dispersion is strongly renormalized near Fermi energy. Both Hc1(T) and SC diamagnetic signal are found to change little initially below Tc ~ 3.5 K and then to increase abruptly upon cooling to a characteristic temperature of ~2.8 K. Furthermore, we identify a two-fold anisotropy of in-plane angular-dependent magnetoresistance in the mixed state. Interestingly, we find that, below the same characteristic T ~ 2.8 K, the orientation of this two-fold anisotropy displays a peculiar twist by an angle of 60o characteristic of the Kagome geometry. Our results suggest an intriguing superconducting state emerging in the complex environment of Kagome lattice, which, at least, is partially driven by electron-electron correlation., Comment: 11 pages, 4 figures

There exists a significant deviation between the most recent Lattice QCD simulation and experimental measurement by Belle for $\Xi_{c}^{0}\to\Xi^{-}\ell^{+}\nu_{\ell}$. In this work, we investigate the $\Xi_{c}\to\Xi$ form factors in QCD sum rules. To this end, the two-point correlation functions of $\Xi_{c}$ and $\Xi$, and the three-point correlation functions of $\Xi_{c}\to\Xi$ are calculated. At the QCD level, contributions from up to dimension-6 four-quark operators are considered, and the leading order results of the Wilson coefficients are obtained. For the form factors, relatively stable Borel windows can be found. Our form factors are comparable with those of Lattice QCD, except for $f_{\perp}$. The obtained form factors are then used to predict the branching ratios of $\Xi_{c}\to\Xi \ell^{+}\nu_{\ell}$, and our predictions are consistent with the most recent data of ALICE and Belle, and those of Lattice QCD within error. Given that the branching ratios only contain limited information, we suggest the experimentalists directly measure the form factors of $\Xi_{c}\to\Xi$., Comment: 18 pages, 7 figures; version accepted by PRD