Some Predictions of Diquark Model for Hidden Charm Pentaquark Discovered at the LHCb

The LHCb has discovered two new states with preferred $J^P$ quantum numbers $3/2^-$ and $5/2^+$ from $\Lambda_b$ decays. These new states can be interpreted as hidden charm pentaquarks. It has been argued that the main features of these pentaquarks can be described by diquark model. The diquark model predicts that the $3/2^-$ and $5/2^+$ are in two separate octet multiplets of flavor $SU(3)$ and there is also an additional decuplet pentaquark multiplet. Finding the states in these multiplets can provide crucial evidence for this model. The weak decays of b-baryon to a light meson and a pentaquark can have Cabibbo allowed and suppressed decay channels. We find that in the $SU(3)$ limit, for $U$-spin related decay modes the ratio of the decay rates of Cabibbo suppressed to Cabibbo allowed decay channels is given by $|V_{cd}|^2/|V_{cs}|^2$. There are also other testable relations for b-baryon weak decays into a pentaquark and a light pseudoscalar. These relations can be used as tests for the diquark model for pentaquark.Comment: revtex, 19 pages, 3 figures. one reference added and some typos correcte

Quantum Criticality of one-dimensional multicomponent Fermi Gas with Strongly Attractive Interaction

Quantum criticality of strongly attractive Fermi gas with $SU(3)$ symmetry in one dimension is studied via the thermodynamic Bethe ansatz (TBA) equations.The phase transitions driven by the chemical potential $\mu$, effective magnetic field $H_1$, $H_2$ (chemical potential biases) are analyzed at the quantum criticality. The phase diagram and critical fields are analytically determined by the thermodynamic Bethe ansatz equations in zero temperature limit. High accurate equations of state, scaling functions are also obtained analytically for the strong interacting gases. The dynamic exponent $z=2$ and correlation length exponent $\nu=1/2$ read off the universal scaling form. It turns out that the quantum criticality of the three-component gases involves a sudden change of density of states of one cluster state, two or three cluster states. In general, this method can be adapted to deal with the quantum criticality of multi-component Fermi gases with $SU(N)$ symmetry.Comment: 20 pages, 5 figures, submitted to J.Phys.A, revised versio

Professor Chen Ping Yang's early significant contributions to mathematical physics

In the 60's Professor Chen Ping Yang with Professor Chen Ning Yang published several seminal papers on the study of Bethe's hypothesis for various problems of physics. The works on the lattice gas model, critical behaviour in liquid-gas transition, the one-dimensional (1D) Heisenberg spin chain, and the thermodynamics of 1D delta-function interacting bosons are significantly important and influential in the fields of mathematical physics and statistical mechanics. In particular, the work on the 1D Heisenberg spin chain led to subsequent developments in many problems using Bethe's hypothesis. The method which Yang and Yang proposed to treat the thermodynamics of the 1D system of bosons with a delta-function interaction leads to significant applications in a wide range of problems in quantum statistical mechanics. The Yang and Yang thermodynamics has found beautiful experimental verifications in recent years.Comment: 5 pages + 3 figure

Exact Entanglement dynamics in Three Interacting Qubits

Motivated by recent experimental study on coherent dynamics transfer in three interacting atoms or electron spins \cite{Barredo:2015,Rosenfeld:2018}, here we study entanglement entropy transfer in three interacting qubits. We analytically calculate time evolutions of wave function, density matrix and entanglement of the system. We find that initially entangled two qubits may alternatively transfer their entanglement entropy to other two qubit pairs. So that dynamical evolution of three interacting qubits may produce a genuine three-partite entangled state through entanglement entropy transfers. In particular, different pairwise interactions of the three qubits endow symmetric and asymmetric evolutions of the entanglement transfer, characterized by the quantum mutual information and concurence. Finally, we discuss an experimental proposal of three Rydberg atoms for testing the entanglement dynamics transfer of this kind.Comment: 6 pages + 5 figure

Predictive CPCP Violating Relations for Charmless Two-body Decays of Beauty Baryons Ξb−, 0\Xi^{-,\;0}_b and Λb0\Lambda_b^0 With Flavor SU(3)SU(3) Symmetry

Several baryons containing a heavy b-quark have been discovered. The decays of these states provide new platform for testing the standard model (SM). We study $CP$ violation in SM for charmless two-body decays of the flavor $SU(3)$ anti-triplet beauty baryon (b-baryon) ${\cal B} = (\Xi^-_b,\;\Xi^0_b,\;\Lambda_b^0)$ in a model independent way. We found, in the flavor $SU(3)$ symmetry limit, a set of new predictive relations among the branching ratio $Br$ and $CP$ asymmetry $A_{CP}$ for $\cal B$ decays, such as $A_{CP}(\Xi_b^-\to K^0 \Xi^-)/A_{CP}(\Xi_b^-\to \bar K^0 \Sigma^-) = - Br(\Xi_b^- \to \bar K^0 \Sigma^-)/Br(\Xi_b^- \to K^0 \Sigma^-)$, $A_{CP}(\Lambda_b^0 \to \pi^- p)/A_{CP} (\Xi^0_b \to K^- \Sigma^+) = -Br(\Xi^0_b \to K^- \Sigma^+)\tau_{\Lambda_b^0}/Br(\Lambda_b^0 \to \pi^- p)\tau_{\Xi^0_b}$,and $A_{CP}(\Lambda_b^0 \to K^- p)/ A_{CP} (\Xi^0_b \to \pi^- \Sigma^+) = -Br(\Xi^0_b \to \pi^- \Sigma^+)\tau_{\Lambda_b^0}/ Br(\Lambda_b^0 \to K^- p)\tau_{\Xi^0_b}$. Future data from LHCb can test these relations and also other relations found.Comment: 13 pages, no figure, 6 tables, several missing terms in eq.11 are adde

CP violation in neutrino mixing with δ=−π/2\delta = -\pi/2 in A4A_4 Type-II seesaw model

We study a class of models for neutrino mass matrix in Type-II seesaw with $A_4$ family symmetry. The resulting neutrino mass matrix can be naturally made to respect a $\mu-\tau$ exchange plus CP conjugate symmetry (GLS) with the CP violating phase $\delta$ and the mixing angle $\theta_{23}$ predicted to be $\pm\pi/2$ and $\pi/4$, respectively. When GLS is explicitly broken by complex Yukawa couplings, the model predictions for $\delta$ and $\theta_{23}$ can be significantly modified. Should future experiments will indeed determine $\theta_{23}$ and $\delta_{CP}$ away from the GLS limit values, one then had to consider models with broken GLS. We study several simple scenarios to show how the modifications arise when GLS is broken and how future experiments can test this class of models.Comment: 15 pages, 3 figures, minor errors corrected. Version appeared in Phys.Lett.B. arXiv admin note: text overlap with arXiv:1504.0156