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2. Though CP cannot be the spontaneously violated, the BC can still generate CP violation of the gauge fields to the fermions. The scalar (x) is massless at tree-level massless, so our results provide an illustraion of the so-called Georgi-Pais theorem [H. Georgi and A. Pais, Phys. Rev. D 10, 1246 (1974)] that precludes spontaneous symmetry breaking by radiative corrections unless the scalar potential has a flat direction at tree-level.
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