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arXiv 2103.07260hep-phhep-lat
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协变重子手征微扰理论中自旋-$\frac{3}{2}$双粲重子的磁矩

Magnetic moments of the spin-$\frac{3}{2}$ doubly charmed baryons in covariant baryon chiral perturbation theory

Rui-Xiang Shi, Li-Sheng Geng

摘要:

受自旋-$\frac{1}{2}$双粲重子$Ξ_{cc}^{++}$的发现及其磁矩的理论研究的启发,我们在协变重子手征微扰理论(BChPT)中采用扩展质量壳重整化(EOMS)方案研究了其自旋-$\frac{3}{2}$重夸克自旋对称对应物的次领先级的磁矩.树能级贡献由夸克模型固定,而控制环贡献的两个低能常数(LEC)$C$和$H$以两种方式确定:利用夸克模型(情形1)和格点QCD模拟结合夸克模型(情形2),研究了磁矩对夸克质量的依赖性,并与重子手征微扰理论(HB ChPT)的预言进行了比较.结果表明,在情况1中,差异是相当大的,但在情况2中,由于较小的LEC $C$和$H$,类似于自旋-$\frac{1}{2}$双粲重子的情况。其次,我们预言了自旋-$\frac{3}{2}$双粲重子的磁矩,并与其它方法的结果进行了比较。对于自旋-$\frac{3}{2}$双粲重子,在第2种情况下的预测磁矩更接近于其它方法的结果。另外,第一种情况和第二种情况下预测的磁矩之间的巨大差异可能表明了夸克模型和格点量子色动力学模拟之间的不一致性,这需要通过未来的实验或更多的格点量子色动力学数据来检验。

英文摘要:

Inspired by the discovery of the spin-$\frac{1}{2}$ doubly charmed baryon $Ξ_{cc}^{++}$ and the subsequent theoretical studies of its magnetic moments, we study the magnetic moments of its spin-$\frac{3}{2}$ heavy quark spin symmetry counterparts, up to the next-to-leading order in covariant baryon chiral perturbation theory (BChPT) with the extended-on-mass-shell renormalization (EOMS) scheme. With the tree-level contributions fixed by the quark model while the two low energy constants (LECs) $C$ and $H$ controlling the loop contributions determined in two ways: the quark model (case 1) and lattice QCD simulations together with the quark model (case 2), we study the quark mass dependence of the magnetic moments and compare them with the predictions of the heavy baryon chiral perturbation theory (HB ChPT). It is shown that the difference is sizable in case 1, but not in case 2 due to the smaller LECs $C$ and $H$, similar to the case of spin-$\frac{1}{2}$ doubly charmed baryons. Second, we predict the magnetic moments of the spin-$\frac{3}{2}$ doubly charmed baryons and compare them with those of other approaches. The predicted magnetic moments in case 2 for the spin-$\frac{3}{2}$ doubly charmed baryons are closer to those of other approaches. In addition, the large differences in case 1 and case 2 for the predicted magnetic moments may indicate the inconsistency between the quark model and the lattice QCD simulations, which should be checked by future experimental or more lattice QCD data.

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