A γγ\gamma\gamma Collider for the 750 GeV Resonant State

Recent data collected by ATLAS and CMS at 13 TeV collision energy of the LHC indicate the existence of a new resonant state $\phi$ with a mass of 750 GeV decaying into two photons $\gamma\gamma$. The properties of $\phi$ should be studied further at the LHC and also future colliders. Since only $\phi \to \gamma\gamma$ decay channel has been measured, one of the best ways to extract more information about $\phi$ is to use a $\gamma\gamma$ collider to produce $\phi$ at the resonant energy. In this work we show how a $\gamma\gamma$ collider helps to verify the existence of $\phi$ and to provide some of the most important information about the properties of $\phi$, such as branching fractions of $\phi\to V_1V_2$. Here $V_i$ can be $\gamma$, $Z$, or $W^\pm$. We also show that by studying angular distributions of the final $\gamma$'s in $\gamma\gamma \to \phi \to \gamma\gamma$, one can obtain crucial information about whether this state is a spin-0 or a spin-2 state.Comment: ReTex, 12 page with 6 figures. Expanded discussion on distinguishing spin-0 and spin-2 cases. Several figures adde

Heavy Quarkonium Dissociation by Thermal Gluons at Next-to-leading Order in the Quark-Gluon Plasma

Using the chromo-electric dipole coupling Hamiltonian from QCD multipole expansion, we derive the dissociation cross sections of heavy quarkonia by thermal gluons at next-to-leading order (NLO, also known as inelastic parton scattering dissociation) in the Quark-Gluon Plasma (QGP) in the framework of second order quantum mechanical perturbation theory. While suffering divergence (infrared and soft-collinear divergences) in vacuum, the cross sections thus derived become finite in the QGP as rendered by the finite thermal gluon masses. In contrast to the leading order (LO, also known as gluo-dissociation) counterparts rapidly dropping off with increasing incident gluon energy, the NLO cross sections exhibits finite value toward high energies because of new phase space being opened up. We then carry out a full calculation of the dissociation rates for various charmonia and bottomonia within a non-relativistic in-medium potential model. The NLO process is shown to dominate the dissociation rate toward high temperatures when the binding energies of heavy quarkonia become smaller relative to the Debye screening mass.Comment: 11 pages, 6 figures; version accepted for publication in Phys. Lett.

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

Statistical computation of Boltzmann entropy and estimation of the optimal probability density function from statistical sample

In this work, we investigate the statistical computation of the Boltzmann entropy of statistical samples. For this purpose, we use both histogram and kernel function to estimate the probability density function of statistical samples. We find that, due to coarse-graining, the entropy is a monotonic increasing function of the bin width for histogram or bandwidth for kernel estimation, which seems to be difficult to select an optimal bin width/bandwidth for computing the entropy. Fortunately, we notice that there exists a minimum of the first derivative of entropy for both histogram and kernel estimation, and this minimum point of the first derivative asymptotically points to the optimal bin width or bandwidth. We have verified these findings by large amounts of numerical experiments. Hence, we suggest that the minimum of the first derivative of entropy be used as a selector for the optimal bin width or bandwidth of density estimation. Moreover, the optimal bandwidth selected by the minimum of the first derivative of entropy is purely data-based, independent of the unknown underlying probability density distribution, which is obviously superior to the existing estimators. Our results are not restricted to one-dimensional, but can also be extended to multivariate cases. It should be emphasized, however, that we do not provide a robust mathematical proof of these findings, and we leave these issues with those who are interested in them.Comment: 8 pages, 6 figures, MNRAS, in the pres