$γ^\ast N \to Δ(1232)$库仑四极形状因子、π介子云参数化和Siegert定理的新的低$Q^2$测量
New low-$Q^2$ measurements of the $γ^\ast N \to Δ(1232)$ Coulomb quadrupole form factor, pion cloud parametrizations and Siegert's theorem
摘要：
在$Q^2=0.04$-0.13 GeV $^2$范围内对$γ^\ast N \to Δ(1232)$库仑四极形状因子的新测量改变了以前数据的趋势。与新的数据的电和库仑形状因子都在显着的协议与估计的π介子云的贡献，在低$Q^2$的四极形状因子。π介子云对电子形状因子和库仑形状因子的贡献可以通过关系$G_E \propto G_{En}/ \left(1 + \frac{Q^2}{2M_Δ(M_Δ-M)}\right)$和$G_C \propto G_{En}$来参数化，其中$G_{En}$是中子电子形状因子，$M$和$M_Δ$分别是核子和$Δ$质量。这些参数化与Siegert定理完全一致，Siegert定理指出，当$Q^2=-(M_Δ-M)^2$时，在伪阈值处$G_E= \frac{M_Δ-M}{2M_Δ} G_C$，并且改进了先前的参数化。此外，一个小的价夸克分量估计的协变夸克模型有助于这种协议。新数据与$G_E$的新参数化的结合结束了在低$Q^2$下研究$γ^\ast N \to Δ(1232)$四极形状因子的密集期，理论与数据之间具有一致性。
英文摘要：
The novel measurements of the $γ^\ast N \to Δ(1232)$ Coulomb quadrupole form factor in the range $Q^2=0.04$--0.13 GeV$^2$ changed the trend of the previous data. With the new data the electric and Coulomb form factors are both in remarkable agreement with estimates of the pion cloud contributions to the quadrupole form factors at low $Q^2$. The pion cloud contributions to the electric and Coulomb form factors can be parametrized by the relations $G_E \propto G_{En}/ \left(1 + \frac{Q^2}{2M_Δ(M_Δ-M)}\right)$ and $G_C \propto G_{En}$, where $G_{En}$ is the neutron electric form factor, and $M$, $M_Δ$ are the nucleon and $Δ$ masses, respectively. Those parametrizations are in full agreement with Siegert's theorem, which states that $G_E= \frac{M_Δ-M}{2M_Δ} G_C$ at the pseudothreshold, when $Q^2=-(M_Δ-M)^2$, and improve previous parametrizations. Also a small valence quark component estimated by a covariant quark model contributes to this agreement. The combination of the new data with the new parametrization for $G_E$ concludes an intense period of studying the $γ^\ast N \to Δ(1232)$ quadrupole form factors at low $Q^2$, with the agreement between theory and data.
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