Analysis of the charmonium-like states X~*(3860), X(3872), X(3915),X(3930) and X(3940) according to their strong decay behaviors

Inspired by the newly observed state X＊（3860）, we analyze the strong decay behaviors of some charmonium-like states, X＊（3860）, X（3872）, X（3915）, X（3930） and X（3940）, with the 3P0 model. We carry out our work based on the hypothesis that all of these states are charmonium systems. Our analysis indicates that, as a 0＋＋ charmonium state, X＊（3860） can reproduce the experimental data. As for X（3872）, it can tentatively be interpreted as the mixture of a m cc system and a D＊0D0 molecular state. If we consider X（3940） as a 31S0 state, its total width in the present work is much lower than the experimental result. Thus, the 31S0 charmonium state seems not to be a good candidate for X（3940）. Furthermore, our analysis implies that it is reasonable to assign X（3915） and X（3930） to be the same state, 2＋＋. However, combining our analysis with that in Refs.[14,71], we speculate that X（3915）/X（3930） might also be the mixture of a m cc system and a molecular state.

Determination of the strong coupling constant using available experimental data

We determine the strong coupling constant α s up to 4-loop in perturbative QCD.Testing QCD requires the measurement of α s over ranges of energy scales.In this analysis,the value of α s is determined from the unpolarized structure functions data points by minimizing the χ ^2 function between the theory result and experimental data.Using perturbative QCD calculations from threshold corrections,we obtain α s （M 2 Z ） = 0.1139±0.0020 at N ^3 LO which is in good agreement with the very recently results from the inclusive jet cross section in pp collisions at√ s=1.96 TeV.

Magnetic Field Effect on β^＋ Decay in the Crusts of Accreting Neutron Stars

Based on shell model of nuclei, the influence of a high magnetic field on β^＋ decay in the crusts of accreting neutron stars is analyzed. The magnetic field effect on 54 Mn is discussed. The results show that a weak magnetic field makes little effect on β^＋ decay but a strong magnetic field （B 〉 10^11 G） improves β^＋ decay rates obviously. The conclusion derived will benefit to develop further research on nuclear astrophysics in the future.

Strong decays of the low-lying bottom strange baryons

In this work,the strong decay behaviors of theλ-mode low-lyingΞ_(b) andΞ^(’)_(b) baryons are investigated within the 3 P0 model.Our results suggest that all of the low-lying 3F statesΞ_(b)(2 S),Ξ_(b)(1 P),andΞ_(b)(1 D)have small decay widths of less than 20 MeV,and these states have good potentials to be observed in theΞ^(’)_(b)πandΞ^(’)_(b)^(*)πinvariant masses.Further,most of the 6F multiplets are relatively narrow and may decay into theΞ_(b)π,Ξ^(’)_(b)π,Ξ^(’)_(b)^(^(*))π,andΔbK final states.Considering the masses and strong decay behaviors,we can assign the newly observedΞ_(b)(6100)resonance as theΞ_(b)(1 P)state with J^(P)=3/2-and interpret theΞ_(b)(6227)structure as the J^(P)=3/2-Ξ^(’)_(b)(1 P)state with a proper mixing angle.We expect that our predictions for these excited bottom strange baryons will provide helpful information for future experimental research.

Strong decays of newly observed heavy flavor hadrons

In this talk, we briefly review the experimental status of newly observed charmed hadrons during the past years. Then we introduce the theoretical progresses on these charmed hadrons, especially our studies on the strong decays of new charmed hadrons during the past one year.

A Remark on Extension of Into Isometries

In this paper, we prove that an into isometry form S（l（n）^∞） to S（E）, which under some conditions, can be extended to be a linear isometry defined on the whole space. Therefore we improve the results of [Ding, G. G.： The isometric extension of an into mapping from the unit sphere S（l（2）^∞） to S（Lμ^1）. Acta Mathematica Sinica, English Series, 22（6）, 1721-1724 （2006）].