Production of doubly heavy baryons via Higgs boson decays

We systematically analyzed the production of semi-inclusive doubly heavy baryons ($\Xi_{cc}$, $\Xi_{bc}$ and $\Xi_{bb}$) for the process $H^0 \rightarrow \Xi_{QQ'}+ \bar {Q'} + \bar {Q}$ through four main Higgs decay channels within the framework of non-relativistic QCD. The contributions from the intermediate diquark states, $\langle cc\rangle[^{1}S_{0}]_{\mathbf{6}}$, $\langle cc\rangle[^{3}S_{1}]_{\mathbf{\bar 3}}$, $\langle bc\rangle[^{3}S_{1}]_{\mathbf{\bar 3}/ \mathbf{6}}$, $\langle bc\rangle[^{1}S_{0}]_{\mathbf{\bar 3}/ \mathbf{6}}$, $\langle bb\rangle[^{1}S_{0}]_{\mathbf{6}}$ and $\langle bb\rangle[^{3}S_{1}]_{\mathbf{\bar 3}}$, have been taken into consideration. The differential distributions and three main sources of the theoretical uncertainties have been discussed. At the High Luminosity Large Hadron Collider, there will be about 0.43$\times10^4$ events of $\Xi_{cc}$, 6.32$\times10^4$ events of $\Xi_{bc}$ and 0.28$\times10^4$ events of $\Xi_{bb}$ produced per year. There are fewer events produced at the Circular Electron Positron Collider and the International Linear Collider, about $0.26\times 10^{2}$ events of $\Xi_{cc}$, $3.83\times 10^{2}$ events of $\Xi_{bc}$ and $0.17\times 10^{2}$ events of $\Xi_{bb}$ in operation.Comment: 15 pages, 3 figures, 7 table

Color Behavior Of BL Lacertae Object OJ 287 During Optical Outburst

This paper aims to study the color behavior of the BL Lac object OJ 287 during optical outburst. According to the revisit of the data from the OJ-94 monitoring project and the analysis the data obtained with the 60/90 cm Schmidt Telescope of NAOC, we found a bluer-when-brighter chromatism in this object. The amplitude of variation tends to decrease with the decrease of frequency. These results are consistent with the shock-in-jet model. We made some simulations and confirmed that both amplitude difference and time delay between variations at different wavelengths can result in the phenomenon of bluer-when-brighter. Our observations confirmed that OJ 287 underwent a double-peaked outburst after about 12 years from 1996, which provides further evidence for the binary black hole model in this object.Comment: 25 pages, 13 figure

Degeneracy Relations in QCD and the Equivalence of Two Systematic All-Orders Methods for Setting the Renormalization Scale

The Principle of Maximum Conformality (PMC) eliminates QCD renormalization scale-setting uncertainties using fundamental renormalization group methods. The resulting scale-fixed pQCD predictions are independent of the choice of renormalization scheme and show rapid convergence. The coefficients of the scale-fixed couplings are identical to the corresponding conformal series with zero $\beta$-function. Two all-orders methods for systematically implementing the PMC-scale setting procedure for existing high order calculations are discussed in this article. One implementation is based on the PMC-BLM correspondence \mbox{(PMC-I)}; the other, more recent, method \mbox{(PMC-II)} uses the ${\cal R}_\delta$-scheme, a systematic generalization of the minimal subtraction renormalization scheme. Both approaches satisfy all of the principles of the renormalization group and lead to scale-fixed and scheme-independent predictions at each finite order. In this work, we show that PMC-I and PMC-II scale-setting methods are in practice equivalent to each other. We illustrate this equivalence for the four-loop calculations of the annihilation ratio $R_{e^+ e^-}$ and the Higgs partial width $\Gamma(H\to b\bar{b})$. Both methods lead to the same resummed (`conformal') series up to all orders. The small scale differences between the two approaches are reduced as additional renormalization group $\{\beta_i\}$-terms in the pQCD expansion are taken into account. We also show that {\it special degeneracy relations}, which underly the equivalence of the two PMC approaches and the resulting conformal features of the pQCD series, are in fact general properties of non-Abelian gauge theory.Comment: 7 pages, 1 figur