Discussions on the stability of diquarks

Since the birth of the quark model, the diquark, which is composed of two quarks, has been considered as a substantial structure of a color anti-triplet. This is not only a mathematical simplification for dealing with baryons, but also provides a physical picture where the diquark would behave as a whole object. It is natural to ask whether such a structure is sufficiently stable against external disturbance. The mass spectra of the ground states of the scalar and axial-vector diquarks, which are composed of two-light (L-L), one-light-one-heavy (H-L) and two-heavy (H-H) quarks, respectively, have been calculated in terms of the QCD sum rules. We suggest a criterion as the quantitative standard for the stability of the diquark. It is the gap between the masses of the diquark and √s₀ where s₀ is the threshold of the excited states and continuity, namely the larger the gap is, the more stable the diquark would be. In this work, we calculate the masses of the H-H type to complete the series of the spectra of the ground state diquarks. However, as the criterion being taken, we find that all the gaps for the various diquarks are within a small range. In particular, the gap for the diquark with two heavy quarks, which is believed to be a stable structure, is slightly smaller than that of the other two types of diquarks. Therefore we conclude that because of the large theoretical uncertainty, we cannot use the numerical results obtained with the QCD sum rules to assess the stability of diquarks, but need to invoke other theoretical framework.     

限制零的m进制数集之Hausdorff测度

对于任意整数表示mkz的分数部分.给出了数集Fm的Hausdorff测度是Fm的HausdorfF维数.     

用于铯芯片级原子钟的4.596GHz射频源研制（英文）

芯片级原子钟主要包括射频模块、物理封装模块以及其他的外围控制模块。射频模块的设计关系到芯片级原子钟的短期稳定度,所以射频模块在芯片级原子钟的设计时是非常重要的一部分。本文利用数字锁相环技术实现频率为4.596GHz的射频源,射频源由三部分组成,包括小数分频频率综合器、压控振荡器和环路滤波器。数字锁相环具有相位噪声低,频谱稳定度高等特点。此外,由于小数分频频率综合器是可编程的,可以通过配置N分频器与R分频器实现输出频率的快速扫描。与此同时,根据相关公式,可以计算出三阶无源环路滤波器的近似参数值,所设计的环路滤波器具有300kHz的环路带宽以及55°的相位裕度。最后,整个基于数字锁相环技术实现的射频源通过仿真、硬件实现以及测试。测试结果显示,射频源的相位噪声为-74.02dBc/Hz@300Hz,符合芯片级原子钟射频源的设计要求。