论文标题
$ππ$散射的晶格研究大$ n_ \ text {c} $
A lattice study of $ππ$ scattering at large $N_\text{c}$
论文作者
论文摘要
我们介绍了带有不同颜色数量的Pion-Pion散射的第一个晶格研究，$ n_ \ text {c} $。我们使用带有四个变性夸克口味的晶格模拟，$ n_ \ text {f} = 4 $，$ n_ \ text {c} = 3-6 $。我们专注于两个不涉及真空图的散射通道。这些对应于SU（4）味道组的两个不可约的表示：完全对称的一个，$ ss $和完全反对称的一个，$ aa $。前者是一个相当于SU的Isospin-2通道的排斥通道（2）。相比之下，后者很有吸引力，仅出于$ n_ \ text {f} \ geq 4 $而存在。代表性状态为$ \ left（| d_s^+π^+ \ rangle- | d^+ k^+ \ \ rangle \ right）/\ sqrt {2} $。使用Lüscher的形式主义，我们提取了近阈值散射幅度，并将结果与手性扰动理论（CHPT）相匹配，该理论（CHPT）很大$ n_ \ text {c} $。为此，我们计算分析u $（n_ \ text {f}）$ CHPT预测两杆散射的预测，并使用晶格结果来约束相关低富集耦合的$ n_ \ text {c} $缩放。
We present the first lattice study of pion-pion scattering with varying number of colors, $N_\text{c}$. We use lattice simulations with four degenerate quark flavors, $N_\text{f}=4$, and $N_\text{c}=3-6$. We focus on two scattering channels that do not involve vacuum diagrams. These correspond to two irreducible representations of the SU(4) flavor group: the fully symmetric one, $SS$, and the fully antisymmetric one, $AA$. The former is a repulsive channel equivalent to the isospin-2 channel of SU(2). By contrast, the latter is attractive and only exists for $N_\text{f} \geq 4$. A representative state is $\left( |D_s^+ π^+\rangle - |D^+ K^+\rangle\right)/\sqrt{2}$. Using Lüscher's formalism, we extract the near-threshold scattering amplitude and we match our results to Chiral Perturbation Theory (ChPT) at large $N_\text{c}$. For this, we compute the analytical U$(N_\text{f})$ ChPT prediction for two-pion scattering, and use the lattice results to constrain the $N_\text{c}$ scaling of the relevant low-energy couplings.
