论文标题
新的Fayet-iliopoulos项的大型Gravitino散射幅度和单位性截止
Massive gravitino scattering amplitudes and the unitarity cutoff of the new Fayet-Iliopoulos terms
论文作者
论文摘要
我们计算了$ 2 \ rightarrow 2 $ gravitino散射幅度在树级的超级性理论中自发断裂。在单一量表中，通过吸收Goldstino，重力变得巨大（质量$ M_ {3/2} $），其纵向极性的散射幅度随$κ^2 E^4/m_/m_/m_ {3/2}^2 $增长，以$κ^2 e^4/m_^4/m_ m _ {\ mathrm {susy}}^2 $。正如我们在Polonyi模型中明确显示的那样，该领先术语被来自Goldstino（Sgoldstino）的标量合作伙伴（Sgoldstino）的贡献取消，从而将敏感性单位性恢复到Planck量表。这是可以预期的，因为与标准模型中的情况相比，超对称性会自发折断，一旦我们考虑了希格斯玻色子的贡献，大量仪表散射就可以保持高能的单位性。但是，当新的fayet-iliopoulos $ d $ term损坏超对称性，并带有未加盖的R-对称性，则不会发生上述取消。在这种情况下，不间断的阶段是奇异的，没有能力取消振幅的四分化差异，导致有效理论破裂的截止$λ\ sim \ sim m_ \ mathrm {susy} $。当超对称性非线性实现时，可以获得相同的行为。
We compute the $2\rightarrow 2$ gravitino scattering amplitudes at tree level in supergravity theories where supersymmetry is spontaneously broken. In the unitary gauge, the gravitino becomes massive (of mass $m_{3/2}$) by absorbing the Goldstino, and the scattering amplitudes of its longitudinal polarisations grow with energy as $κ^2 E^4/m_{3/2}^2$, signaling a potential breakdown of unitarity at a scale $Λ^2\sim m_{3/2}/κ\sim M_{\mathrm{SUSY}}^2$. As we show explicitly in the Polonyi model, this leading term is cancelled by the contributions coming from the scalar partner of the Goldstino (sgoldstino), restoring perturbative unitarity up to the Planck scale. This is expected since supersymmetry is spontaneously broken, in analogy with the situation occuring in the Standard Model, where massive gauge bosons scattering preserves unitarity at high energy once we consider the contributions from the Higgs boson. However, when supersymmetry is broken by the new Fayet-Iliopoulos $D$-term, with ungauged R-symmetry, the above cancellation does not occur. In this case, the unbroken phase is singular and there is no contribution able to cancel the quartic divergences of the amplitudes, leading to a cutoff $Λ\sim M_\mathrm{SUSY}$ where the effective theory breaks down. The same behaviour is obtained when supersymmetry is non-linearly realised.
