标题： 中间态$ΔΔ$在大$N_c$和幺正极限下的核子-核子散射以及$ΔΔ$和$ΩΩ$散射中的作用 显示英文标题

标题： The role of intermediate $ΔΔ$ states in nucleon-nucleon scattering in the large-$N_c$ and unitary limits, and $ΔΔ$ and $ΩΩ$ scattering

摘要： 我们探讨了为何使用大-$N_c$ （$N_c$是颜色的数量）尺度来确定少核子低能算符的相对大小时，即使没有明确包含动力学的$\Delta$，也能与实验结果一致的潜在解释。 鉴于大-$N_c$分析的前提是认为核子和$\Delta$是简并的，因此这是一个令人费解的结果。 我们证明了对于纯粹的$S$波相互作用，无论是否包含$\Delta$，由大$N_c$尺度决定的关系不受影响。 在那些不与$S$波混合的高阶部分波的情况下，$\Delta$的影响是微扰性的，这使得它与直观的（无$\Delta$）大$N_c$排序一致并不令人惊讶。 对于与$S$波混合的高部分波，为了与天真的大$N_c$排序一致，核子和$\Delta$需要解耦。 We find all $NN$, $\Delta N$, and $\Delta\Delta$ low energy coefficients for leading-order baryon-baryon scattering in $\Delta$-full pionless effective field theory in terms of the two independent parameters dictated by the SU($2F$) spin-flavor symmetry that arises in the $N_c \rightarrow \infty$ limit. Because of recent lattice QCD results and experimental interest, we extend our analysis to the three-flavor case to study $\Omega\Omega$ scattering. 我们证明，在幺正极限（散射长度变为无穷大时），两个 SU($2F$) 参数中的一个被驱动至零，导致对称性增强，这些对称性与自旋-1/2 纠缠研究中发现的对称性一致。 显示英文摘要

摘要： We explore potential explanations for why using large-$N_c$ ($N_c$ is the number of colors) scaling to determine the relative size of few-nucleon low-energy operators agrees with experiment even when dynamical $\Delta$'s are not explicitly included. Given that the large-$N_c$ analysis is predicated on the nucleons and $\Delta$'s being degenerate, this is a curious result. We show that for purely $S$-wave interactions the relationships dictated by large-$N_c$ scaling are unaffected whether the $\Delta$ is included or not. In the case of higher partial waves that do not mix with $S$-waves, the impact of the $\Delta$ is perturbative, which makes the agreement with naive ($\Delta$-less) large-$N_c$ ordering unsurprising. For higher partial waves that mix with $S$-waves, the nucleon and $\Delta$ would need to decouple to get agreement with naive large-$N_c$ ordering. We find all $NN$, $\Delta N$, and $\Delta\Delta$ low energy coefficients for leading-order baryon-baryon scattering in $\Delta$-full pionless effective field theory in terms of the two independent parameters dictated by the SU($2F$) spin-flavor symmetry that arises in the $N_c \rightarrow \infty$ limit. Because of recent lattice QCD results and experimental interest, we extend our analysis to the three-flavor case to study $\Omega\Omega$ scattering. We show that in the unitary limit (where scattering lengths become infinite) one of the two SU($2F$) parameters is driven to zero, resulting in enhanced symmetries, which agree with those found in spin-1/2 entanglement studies.