Analysis of the vector tetraquark states with P-waves between the diquarks and antidiquarks via the QCD sum rules

Zhi-Gang Wang

doi:10.1140/epjc/s10052-019-6568-z

Abstract

In this article, we introduce a P-wave between the diquark and antidiquark explicitly to construct the vector tetraquark currents, and study the vector tetraquark states with the QCD sum rules systematically, and obtain the lowest vector tetraquark masses up to now. The present predictions support assigning the Y(4220 / 4260), Y(4320 / 4360), Y(4390) and Z(4250) to be the vector tetraquark states with a relative P-wave between the diquark and antidiquark pair.

Highlights

The attractive interactions induced by one-gluon exchange favor formation of the diquarks in color antitriplet, flavor antitriplet and spin singlet [1, 2].The diquarks εi jkq T jC qk have five structures in Dirac spinor space, where the i, j and k are color indexes, C = Cγ5, C, Cγμγ5, Cγμ and Cσμν for the scalar, pseudoscalar, vector, axialvector and tensor diquarks, respectively
We can take the C and Cγμγ5 diquark states as the P-wave excitations of the Cγ5(or Cγα) and Cγμ diquark states, respectively, the net effects of the P-waves are embodied in the underlined γ5 in the Cγ5γ5 and Cγμγ5
We extend our previous work [29] to study other vector tetraquark states with an explicit relative P-wave between the diquark and antidiquark with the QCD sum rules in a systematic way

Summary

Introduction

The attractive interactions induced by one-gluon exchange favor formation of the diquarks in color antitriplet, flavor antitriplet and spin singlet [1, 2]. C qk have five structures in Dirac spinor space, where the i, j and k are color indexes, C = Cγ5, C, Cγμγ, Cγμ and Cσμν for the scalar, pseudoscalar, vector, axialvector and tensor diquarks, respectively. The favored or stable configurations are the scalar and axialvector diquark states from the QCD sum rules [3,4,5,6,7,8]. We can introduce the P-wave explicitly in the Cγ5 and Cγμ diquark states and obtain the vector diquark states εi j k q. In the QCD sum rules for the hidden-charm (or hidden-bottom) tetraquark states and molecular states, the integrals s0 s dsρQC D(s, μ) exp. Variations of the heavy quark masses or the energy scales μ lead to variations of integral ranges s0 of the

QCD sum rules for the vector tetraquark states

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Numerical results and discussions

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Conclusion