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

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.

Magnetic Rotation in \(^{60}\)Ni: A Semiclassical Description

“…We set the energy scale µ = V to obtain the ideal energy scales of the QCD spectral densities [26][27][28]31]. The energy scale formula works well for the hidden-charm (and hidden-bottom) tetraquark states, for example, X * (3860), X(3872), Z c (3900/3885), X(3915), Z c (4020/4025), X(4140), Z c (4250), X(4360), Z c (4430), X(4500), X(4660/4630), X(4700), Z b (10610), Z b (10650), and also works well for the hidden-charm pentaquark states, for example, P c (4380) and P c (4450) [32,33].…”

“…In Ref. [31], we introduce the relative P -wave between the diquark and antidiquark constituents explicitly to construct the vector tetraquark currents and take the modified energy scale formula…”

“…With the help of the (modified) energy scale formula, we can choose the acceptable or optimal energy scales of the QCD spectral densities in a consistent way. The values of the effective heavy quark masses M Q are universal for all the diquark-antidiquark-type hidden-charm and hidden-bottom tetraquark states [26,27,30,31]. Now, we search for the optimal Borel parameters T 2 and continuum threshold parameters s 0 to satisfy the following four criteria:…”

Analysis of the hidden-charm tetraquark mass spectrum with the QCD sum rules

“…In Ref. [21], we introduce a relative P wave between the diquark and antidiquark operators explicitly for constructing the tetraquark currents to systematically study the vector tetraquark states with the QCD sum rules and obtain the lowest vector tetraquark masses up to now, which support assigning the Yð4220=4260Þ, Yð4320=4360Þ, Yð4390Þ, and Z c ð4250Þ to be the vector hidden-charm tetraquark states. While novel analysis of the masses and widths of the vector hidden-charm tetraquark states without a relative P wave between the diquark and antidiquark constituents indicate that the Yð4660Þ can be assigned to be a ½sc P ½sc A − ½sc A ½sc P type tetraquark state [22], in those studies, the energy scale formula and modified energy scale formula play an important role in enhancing the pole contributions and in improving the convergent behavior of the operator product expansion.…”

“…In 2006, R. D. Matheus et al took the Xð3872Þ as the J PC ¼ 1 þþ diquark-antidiquark type tetraquark state and studied its mass with the QCD sum rules by carrying out the operator product expansion up to the vacuum condensates of dimension 8 [16]. Thereafter, the QCD sum rules became a powerful theoretical approach for studying the masses and widths of the X, Y, and Z states, irrespective of the hidden-charm (or hidden-bottom) tetraquark states or hadronic molecular states [10,[16][17][18][19][20][21][22][23][24][25]. In the QCD sum rules, we choose the color-antitriplet-color-triplet (3 c 3 c ) type, in other words, the diquark-antidiquark type, colorsextet-color-antisextet (6 c6c ) type, color-singlet-colorsinglet (1 c 1 c ) type, and color-octet-color-octet (8 c 8 c ) type local four-quark currents to study the tetraquark states.…”