Weak Decays of Doubly-Heavy Tetraquarks bcˉqqˉ{b\bar c}{q\bar q}

We study the weak decays of exotic tetraquark states ${b\bar c}{q\bar q}$ with two heavy quarks. Under the SU(3) symmetry for light quarks, these tetraquarks can be classified into an octet plus a singlet: $3\bigotimes\bar 3=1\bigoplus8$. We will concentrate on the octet tetraquarks with $J^{P}=0^{+}$, and study their weak decays, both semileptonic and nonleptonic. Hadron-level effective Hamiltonian is constructed according to the irreducible representations of the SU(3) group. Expanding the Hamiltonian, we obtain the decay amplitudes parameterized in terms of a few irreducible quantities. Based on these amplitudes, relations for decay widths are derived, which can be tested in future. We also give a list of golden channels that can be used to look for these states at various colliders.Comment: 14 pages,3 figure

Reliable H∞ control for discrete-time piecewise linear systems with infinite distributed delays

In this paper, the reliable H∞ control problem is investigated for discrete-time piecewise linear systems with time delays and actuator failures. The time delays are assumed to be infinitely distributed in the discrete-time domain, and the possible failure of each actuator is described by a variable varying in a given interval. The aim of the addressed reliable H∞ control problem is to design a controller such that, for the admissible infinite distributed delays and possible actuator failures, the closed-loop system is exponentially stable with a given disturbance attenuation level γ. The controller gain is characterized in terms of the solution to a linear matrix inequality that can be easily solved by using standard software packages. A simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures

Nucleation in binary polymer blends: Effects of adding diblock copolymers

The effects of adding AB diblock copolymers to A/B binary blends on the structure and thermodynamics of critical nuclei are studied using the self-consistent field theory. At a fixed ratio of the amount of the two homopolymers, depending on the degree of polymerization and composition of the diblocks, their addition to the blends can either increase or decrease the nucleation free energy barrier relative to the pure A/B blends. The qualitative trend can be deduced from the shift in the coexistence boundary and the spinodal. The distribution of diblock copolymers in critical nuclei depends on the composition of the diblocks and the quench depth. Near the coexistence, symmetric diblocks exhibit surfactant behavior, being highly concentrated on the interface of the critical nuclei. Near the spinodal, they act more like co-solvent with a relatively uniform distribution