Scalar or Vector Tetraquark State Candidate: Z_c(4100)

In this article, we separate the vector and axialvector components of the tensor diquark operators explicitly,construct the axialvector-axialvector type and vector-vector type scalar tetraquark currents and scalar-tensor type tensor tetraquark current to study the scalar, vector and axialvector tetraquark states with the QCD sum rules in a consistent way. The present calculations do not favor assigning the Zc(4100) to be a scalar or vector tetraquark state. If the Zc(4100) is a scalar tetraquark state without mixing effects, it should have a mass about 3.9 GeV or 4.0 GeV rather than4.1 GeV;on the other hand, if the Zc(4100) is a vector tetraquark state, it should have a mass about 4.2 GeV rather than 4.1 GeV. However, if we introduce mixing, a mixing scalar tetraquark state can have a mass about 4.1 GeV. As a byproduct, we obtain an axialvector tetraquark candidate for the Zc(4020).