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Following the idea of [GJS09] for orthogonal groups, we introduce a newfamily of period integrals for cuspidal automorphic representations $\sigma$ ofunitary groups and investigate their relation with the occurrence of a simpleglobal Arthur parameter $(\chi,b)$ in the global Arthur parameter $\psi_\sigma$associated to $\sigma$, by the endoscopic classification of Arthur ([Art13],[Mok13], [KMSW14]). The argument uses the theory of theta correspondence. Thiscan be viewed as a part of the $(\chi,b)$-theory outlined in [Jia14] and can beregarded as a refinement of the theory of theta correspondences and poles ofcertain $L$-functions, which was outlined in [Ral91].

On $(\chi,b)$-factors of Cuspidal Automorphic Representations of Unitary Groups I