We study statistics dependence of the probability distributions and the means of measured moments of conserved quantities, respectively. The required statistics of all interested moments and their products are estimated based on a simple simulation.
We also explain why the measured moments are underestimated when the statistics are insufficient.With the statistics at RHIC/BES, the second and third order moments can be reliably obtained based on the method of Centrality bin width correction (CBWC), which can not be applied for the fourth order moments at low energy. With planning statistics at RHIC/BES II, and improved CBWC method, $kappasigma^2$ in a finer centrality bin scale should be measurable. This will help us to understand the current observation of energy and centrality dependence of high-order moments.
Varying the Standard Model (SM) fermion Yukawa couplings universally by a generic positive scale factor ($F_{Yu}$), we study the phenomenological fit to the current available experimental results for the Higgs boson search at hadron colliders. We poi
nt out that the Higgs production cross section and its decay branching ratio to $gammagamma$ can be varied oppositely by $F_{Yu}$ to make their product almost invariant. Thus, our scenario and the SM Higgs are indistinguishable in the inclusive $Hto gammagamma$ channel. The current measurements on direct Yukawa coupling strength in the $Hto bbar{b}/tautau$ channel are not precise enough to fix the scale factor $F_{Yu}$. The most promising is the vector-boson-fusion channel in which the CMS has already observed possible suppression effect on the Yukawa couplings. Further more, the global $chi^2$ fit of the experimental data can get the optimal value by introducing a suppression factor $F_{Yu}sim1/2$ on the SM Yukawa couplings.
