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arXiv 1402.6427hep-ph
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含粲重子手征拉格朗日量的大N_c和重夸克算符联合分析

Combined large-N_c and heavy-quark operator analysis for the chiral Lagrangian with charmed baryons

M. F. M. Lutz, D. Samart, Y. Yan

摘要:

分析了具有自旋为$J^P=1/2^+$和$J^P=3/2^+$的粲重子的手征$SU(3)$拉格朗日量。我们考虑所有的计数器项,是相关的次-主导秩序(N $^3$ LO)的手征外推的粲重子质量。在N $^2$ LO,我们发现16个低能量参数。反三重态和两个六重态重子的质量参数有3个,描述介子-重子顶点的参数有6个,对称性破缺参数有7个。重夸克自旋对称性预言了两个重子六重态场的介子-重子顶点和简并质量的四个求和定则。在这里,一个大的$N_c$运营商在NLO的分析表明,一个进一步的自旋对称性破缺参数的相关性。从N $^2$ LO到N $^3$ LO增加了17个手征对称性破缺参数和24个对称性保持参数。对于包含两个重子场和两个Goldstone玻色子场的主对称守恒两体计数器项,我们发现36项。虽然重夸克自旋对称性导致$36-16=20$求和规则,但在次领先阶(NLO)下的$1/N_c$展开产生$36-7= 29$参数关系。一个组合展开只留下3个未知参数。对于对称性破缺的计数项,我们找到了17项,其中有重夸克自旋对称性的$17-9=8$求和规则和非线性光学$1/N_c$展开的$17-5=12 $求和规则。

英文摘要:

The chiral $SU(3)$ Lagrangian with charmed baryons of spin $J^P=1/2^+$ and $J^P=3/2^+$ is analyzed. We consider all counter terms that are relevant at next-to-next-to-next-to-leading order (N$^3$LO) in a chiral extrapolation of the charmed baryon masses. At N$^2$LO we find 16 low-energy parameters. There are 3 mass parameters for the anti-triplet and the two sextet baryons, 6 parameters describing the meson-baryon vertices and 7 symmetry breaking parameters. The heavy-quark spin symmetry predicts four sum rules for the meson-baryon vertices and degenerate masses for the two baryon sextet fields. Here a large-$N_c$ operator analysis at NLO suggests the relevance of one further spin-symmetry breaking parameter. Going from N$^2$LO to N$^3$LO adds 17 chiral symmetry breaking parameters and 24 symmetry preserving parameters. For the leading symmetry conserving two-body counter terms involving two baryon fields and two Goldstone boson fields we find 36 terms. While the heavy-quark spin symmetry leads to $36-16=20$ sum rules, an expansion in $1/N_c$ at next-to-leading order (NLO) generates $36-7= 29$ parameter relations. A combined expansion leaves 3 unknown parameters only. For the symmetry breaking counter terms we find 17 terms, for which there are $17-9=8$ sum rules from the heavy-quark spin symmetry and $17-5=12 $ sum rules from a $1/N_c$ expansion at NLO.

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