Following previous study, in the Littlest Higgs model (LHM), the heavy photon is supposed to be a possible dark matter candidate and its relic abundance of the heavy photon is estimated in terms of the Boltzman-Lee-Weinberg time-evolution equation. T
he effects of the T-parity violation is also considered. Our calculations show that when Higgs mass $M_H$ taken to be 300 GeV and dont consider T-parity violation, only two narrow ranges $133<M_{A_{H}}<135$ GeV and $167<M_{A_{H}}<169$ GeV are tolerable with the current astrophysical observation and if $135<M_{A_{H}}<167$ GeV, there must at least exist another species of heavy particle contributing to the cold dark matter. As long as the T-parity can be violated, the heavy photon can decay into regular standard model particles and would affect the dark matter abundance in the universe, we discuss the constraint on the T-parity violation parameter based on the present data. Direct detection prospects are also discussed in some detail.
One of the most important tasks in high energy physics is search for the exotic states, such as glueball, hybrid and multi-quark states. The transitions $psi(ns)to psi(ms)+pipi$ and $Upsilon(ns)to Upsilon(ms)+pipi$ attract great attentions because th
ey may reveal characteristics of hybrids. In this work, we analyze those transition modes in terms of the theoretical framework established by Yan and Kuang. It is interesting to notice that the intermediate states between the two gluon-emissions are hybrids, therefore by fitting the data, we are able to determine the mass spectra of hybrids. The ground hybrid states are predicted as 4.23 GeV (for charmonium) and 10.79 GeV (for bottonium) which do not correspond to any states measured in recent experiments, thus it may imply that very possibly, hybrids mix with regular quarkonia to constitute physical states. Comprehensive comparisons of the potentials for hybrids whose parameters are obtained in this scenario with the lattice results are presented.
