Sharp Bounds on Eigenvalues via Spectral Embedding Based on Signless Laplacians

Using spectral embedding based on the signless Laplacian, we obtain bounds on the spectrum of transition matrices on graphs. As a consequence, we bound return probabilities and the uniform mixing time of simple random walk on graphs. In addition, spectral embedding is used in this article to bound the spectrum of graph adjacency matrices. Our method is adapted from [Lyons and Oveis Gharan, 2017].Comment: Comments are welcom

Production of the bottom analogues and the spin partner of the X(3872) at hadron colliders

Using the Monte Carlo event generator tools Pythia and Herwig, we simulate the production of bottom/charm meson and antimeson pairs at hadron colliders in proton-proton/antiproton collisions. With these results, we derive an order-of-magnitude estimate for the production rates of the bottom analogues and the spin partner of the $X(3872)$ as hadronic molecules at the LHC and Tevatron experiments. We find that the cross sections for these processes are at the nb level, so that the current and future data sets from the Tevatron and LHC experiments offer a significant discovery potential. We further point out that the $X_b/X_{b2}$ should be reconstructed in the $\gamma \Upsilon(nS) (n=1,2,3)$, $\Upsilon(1S)\pi^+\pi^-\pi^0$, or $\chi_{bJ}\pi^+\pi^-$ instead of the $\Upsilon(nS)\pi^+\pi^-$ final states.Comment: 11 pages, 3 figures, updated calculation based on effective field theory method, one author added, accepted by European Physics Journal

Number of Matchings of Low Order in (4,6)-Fullerene Graphs

We obtain the formulae for the numbers of 4-matchings and 5-matchings in terms of the number of hexagonal faces in (4, 6)-fullerene graphs by studying structural classification of 6-cycles and some local structural properties, which correct the corresponding wrong results published. Furthermore, we obtain a formula for the number of 6-matchings in tubular (4, 6)-fullerenes in terms of the number of hexagonal faces, and a formula for the number of 6-matchings in the other (4,6)-fullerenes in terms of the numbers of hexagonal faces and dual-squares.Comment: This article was already published in 2017 in MATCH Commun. Math. Comput. Chem. We are uploading it to arXiv for readers' convenienc

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.