Weak Decays of Doubly Heavy Baryons: Multi-body Decay Channels

The newly-discovered $\Xi_{cc}^{++}$ decays into the $\Lambda_{c}^+ K^-\pi^+\pi^+$, but the experimental data has indicated that this decay is not saturated by any two-body intermediate state. In this work, we analyze the multi-body weak decays of doubly heavy baryons $\Xi_{cc}$, $\Omega_{cc}$, $\Xi_{bc}$, $\Omega_{bc}$, $\Xi_{bb}$ and $\Omega_{bb}$, in particular the three-body nonleptonic decays and four-body semileptonic decays. We classify various decay modes according to the quark-level transitions and present an estimate of the typical branching fractions for a few golden decay channels. Decay amplitudes are then parametrized in terms of a few SU(3) irreducible amplitudes. With these amplitudes, we find a number of relations for decay widths, which can be examined in future.Comment: 47pages, 1figure. arXiv admin note: substantial text overlap with arXiv:1707.0657

Unification of Flavor SU(3) Analyses of Heavy Hadron Weak Decays

Analyses of heavy mesons and baryons hadronic charmless decays using the flavor SU(3) symemtry can be formulated in two different forms. One is to construct the SU(3) irreducible representation amplitude (IRA) by decomposing effective Hamiltonian, and the other is to draw the topological diagrams (TDA). In the flavor SU(3) limit, we study various $B/D\to PP,VP,VV$, $B_c\to DP/DV$ decays, and two-body nonleptonic decays of beauty/charm baryons, and demonstrate that when all terms are included these two ways of analyzing the decay amplitudes are completely equivalent. Furthermore we clarify some confusions in drawing topological diagrams using different ways of describing beauty/charm baryons.Comment: 36 pages, 6 figures, 16 table

Electronic transport in a Cantor stub waveguide network

We investigate theoretically, the character of electronic eigenstates and transmission properties of a one dimensional array of stubs with Cantor geometry. Within the framework of real space re-normalization group (RSRG) and transfer matrix methods we analyze the resonant transmission and extended wave-functions in a Cantor array of stubs, which lack translational order. Apart from resonant states with high transmittance we unravel a whole family of wave-functions supported by such an array clamped between two-infinite ordered leads, which have an extended character in the RSRG scheme, but, for such states the transmission coefficient across the lead-sample-lead structure decays following a power-law as the system grows in size. This feature is explained from renormalization group ideas and may lead to the possibility of trapping of electronic, optical or acoustic waves in such hierarchical geometries