We study multipole decompositions of the electromagnetic currents of spin-1/2, 1, and 3/2 particles described in terms of Lagrangians designed to reproduce representation specific wave equations which are second order in the momenta and which emerge within the recently elaborated Poincaré covariant projector method. We calculate the electric multipoles of the above spins for the spinor, the four-vector, and the four-vector--spinor representations, attend to the most general non-Lagrangian spin-3/2 currents which are allowed by Lorentz invariance to be of third order in the momenta and construct the linear current equivalent of identical multipole moments of one of them. We conclude that such non-Lagrangian currents are not necessarily more general than the two-term currents emerging within the covariant projector method. We compare our results with those of the conventional Proca-, and Rarita-Schwinger frameworks. Finally, we test the representation dependence of the multipoles by placing spin-1 and spin-3/2 in the respective (1,0)$\oplus$(0,1), and (3/2,0)$\oplus$(0,3/2) single-spin representations. We observe representation independence of the charge monopoles and the magnetic dipoles, in contrast to the higher multipoles, which turn out to be representation dependent. In particular, we find the bi-vector $(1,0)\oplus (0,1)$ to be characterized by an electric quadrupole moment of opposite sign to the one found in $(1/2,1/2)$, and consequently, to the $W$ boson. Our finding points toward the possibility that the $ρ$ meson could transform as part of an antisymmetric tensor with an $a_{1}$ meson-like state as its representation companion.
Hadronic and Electromagnetic Interactions of Quarkonia
我们研究了夸克偶素的强子相互作用，重点研究了衰变psi（2s）->psi pi pi和衰变updates（2s）-> updates pi pi。多极展开中的主要胶子算子被匹配到手征拉格朗日量上，手征拉格朗日量的系数与现有的数据相拟合，无论是在手征展开中的树级还是环级。与天真的期望松散的基础上的大$N_c$限制QCD在努力确定这一限制的可靠性，为其他观测，如绑定的$\ps$的核。交叉对称性用于估计非弹性$π\ps\toπ\pss$散射的截面，可能与重离子碰撞有关。在树水平上确定了手征拉格朗日量中的辐射衰变psi（2s）->psi pi pi gamma和upper（2s）-> upper pi pi gamma。对这种衰变的测量将提供对多极展开和手征展开的检验。我们简要地讨论了从uppertons（3s）的衰变，也从介子的夸克偶素的电磁极化率的贡献。
