标题： 重子质量在大-$N$有效奇素子理论的二阶情形 显示英文标题

标题： Baryon masses at second order in large-$N$ chiral perturbation theory

摘要： 我们考虑在大-$N$有效奇素子理论的二阶中八重态和十重态重子质量的味对称性破缺，其中 $N$ 是QCD色数。 我们假设 $1/N \sim 1/N_F \sim m_s / \Lambda \gg m_{u,d}/\Lambda, \alpha_{EM}$，其中 $N_F$ 是轻夸克味数， $m_{u,d,s} / \Lambda$ 是控制有效奇素子理论中 $SU(N_F)$ 味对称性破缺的参数。 我们始终在$m_q^{3/2}$、$m_q^2 \ln m_q$和$(m_q \ln m_q) / N$阶次中包含重子质量的非解析贡献。 从$SU(N_F)$对称性单独得出的关系中，$m_q^{3/2}$修正较小，但对大$N$关系的修正较大且符号错误。 手征幂次计数和大-$N$一致性允许在阶数$m_q^2 \ln m_q$处有二环贡献，需要进行非平凡的显式计算来证明该贡献为零。在展开的二阶中，有八个关系是$1/N$展开的非平凡结果，所有这些关系都在实验误差范围内得到了很好的满足。 该阶的平均偏差为$7 \MeV$对于$\De I = 0$质量差和$0.35 \MeV$对于$\De I \ne 0$质量差，这与误差为$1/N^2 \sim 10\%$阶的预期一致。 显示英文摘要

摘要： We consider flavor breaking in the the octet and decuplet baryon masses at second order in large-$N$ chiral perturbation theory, where $N$ is the number of QCD colors. We assume that $1/N \sim 1/N_F \sim m_s / \Lambda \gg m_{u,d}/\Lambda, \alpha_{EM}$, where $N_F$ is the number of light quark flavors, and $m_{u,d,s} / \Lambda$ are the parameters controlling $SU(N_F)$ flavor breaking in chiral perturbation theory. We consistently include non-analytic contributions to the baryon masses at orders $m_q^{3/2}$, $m_q^2 \ln m_q$, and $(m_q \ln m_q) / N$. The $m_q^{3/2}$ corrections are small for the relations that follow from $SU(N_F)$ symmetry alone, but the corrections to the large-$N$ relations are large and have the wrong sign. Chiral power-counting and large-$N$ consistency allow a 2-loop contribution at order $m_q^2 \ln m_q$, and a non-trivial explicit calculation is required to show that this contribution vanishes. At second order in the expansion, there are eight relations that are non-trivial consequences of the $1/N$ expansion, all of which are well satisfied within the experimental errors. The average deviation at this order is $7 \MeV$ for the $\De I = 0$ mass differences and $0.35 \MeV$ for the $\De I \ne 0$ mass differences, consistent with the expectation that the error is of order $1/N^2 \sim 10\%$.