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CP-odd effective gluonic Lagrangian in Kobayashi-Maskawa model
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Schwinger operator method is applied for studying CP-odd pure gluonic effective Lagrangian in the Standard Model at three-loop level. The induced $\theta$-term vanishes by the same reasons as EDMs of quark and W-boson to two-loop approximation. A simple way is found to demonstrate these cancellations. All other terms of the effective Lagrangian acquire non-vanishing contributions. The effective operator of dimension six, Weinberg operator, is calculated explicitly. The corresponding contribution to the EDM of neutron is much smaller than that comes from large distances.
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Weak Scale Triggers in the SMEFT
No weak scale triggers exist in the SMEFT up to dimension six (and likely eight) that can solve the hierarchy problem far above the weak scale.
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