Coupled-channel analysis of the possible D(∗)D(∗)D^{(*)}D^{(*)}, Bˉ(∗)Bˉ(∗)\bar{B}^{(*)}\bar{B}^{(*)} and D(∗)Bˉ(∗)D^{(*)}\bar{B}^{(*)} molecular states

We perform a coupled-channel study of the possible deuteron-like molecules with two heavy flavor quarks, including the systems of $D^{(*)}D^{(*)}$ with double charm, $\bar{B}^{(*)}\bar{B}^{(*)}$ with double bottom and $D^{(*)}\bar{B}^{(*)}$ with both charm and bottom, within the one-boson-exchange model. In our study, we take into account the S-D mixing which plays an important role in the formation of the loosely bound deuteron, and particularly, the coupled-channel effect in the flavor space. According to our calculation, the states $D^{(*)}D^{(*)}[I(J^P)=0(1^+)]$ and $(D^{(*)}D^{(*)})_s[J^P=1^+]$ with double charm, the states $\bar{B}^{(*)}\bar{B}^{(*)}[I(J^P)=0(1^+),0(2^+),1(0^+),1(1^+),1(2^+)]$, $(\bar{B}^{(*)}\bar{B}^{(*)})_s[J^P=0^+,1^+,2^+]$ and $(\bar{B}^{(*)}\bar{B}^{(*)})_{ss}[J^P=0^+,1^+,2^+]$ with double bottom, and the states $D^{(*)}\bar{B}^{(*)}[I(J^P)=0(0^+),0(1^+)]$ and $(D^{(*)}\bar{B}^{(*)})_s[J^P=0^+,1^+]$ with both charm and bottom are good molecule candidates. However, the existence of the states $D^{(*)}D^{(*)}[I(J^P)=0(2^+)]$ with double charm and $D^{(*)}\bar{B}^{(*)}[I(J^P)=1(1^+)]$ with both charm and bottom is ruled out.Comment: 1 figure added, published in Physical Review

Hadronic molecules with both open charm and bottom

With the one-boson-exchange model, we study the interaction between the S-wave $D^{(*)}/D^{(*)}_s$ meson and S-wave $B^{(*)}/B^{(*)}_s$ meson considering the S-D mixing effect. Our calculation indicates that there may exist the $B_c$-like molecular states. We estimate their masses and list the possible decay modes of these $B_c$-like molecular states, which may be useful to the future experimental search.Comment: 7 pages, 2 figures, 5 tables. Typos corrected. Version published in Phys. Rev.

The masses and axial currents of the doubly charmed baryons

The chiral dynamics of the doubly heavy baryons is solely governed by the light quark. In this work, We have derived the chiral corrections to the mass of the doubly heavy baryons up to N$^3$LO. The mass splitting of $\Xi_{cc}$ and $\Omega_{cc}$ at the N$^2$LO depends on one unknown low energy constant $c_7$. With the experimental mass of $\Xi_{cc}(3520)$ as the input, we estimate the mass of $\Omega_{cc}$ to be around 3.678 GeV. Moreover, we have also performed a systematical analysis of the chiral corrections to the axial currents and axial charges of the doubly heavy baryons. The chiral structure and analytical expressions will be very useful to the chiral extrapolations of the future lattice QCD simulations of the doubly heavy baryons.Comment: 10 pages, 2 tables, 3 figure. Accepted by Phys. Rev.

Maximum norm error estimates of efficient difference schemes for second-order wave equations

AbstractThe three-level explicit scheme is efficient for numerical approximation of the second-order wave equations. By employing a fourth-order accurate scheme to approximate the solution at first time level, it is shown that the discrete solution is conditionally convergent in the maximum norm with the convergence order of two. Since the asymptotic expansion of the difference solution consists of odd powers of the mesh parameters (time step and spacings), an unusual Richardson extrapolation formula is needed in promoting the second-order solution to fourth-order accuracy. Extensions of our technique to the classical ADI scheme also yield the maximum norm error estimate of the discrete solution and its extrapolation. Numerical experiments are presented to support our theoretical results

Emergence of diverse array of phases in an exactly solvable model

We propose an exactly solvable lattice model, motivated by the significance of the extended Hubbard model ($t-U-V$ model) and inspired by the work of Hatsugai and Kohmoto. The ground state exhibits a diverse array of phases, including the charge-$4e$ condensed phase, the charge-$2e$ superconducting phase, the half-filled insulating phase, the quarter-filled insulating phase, the metallic phase, and an unconventional metallic phase. Among them, the unconventional metallic phase could be of particular significance, for the coexistence of electrons and pairs at zero energy. These findings are poised to advance our understanding and exploration of strongly correlated physics.Comment: 34pages, 15 figure