Possible assignments of the $$X(3872)$$ X ( 3872 ) , $$Z_c(3900)$$ Z c ( 3900 ) , and $$Z_b(10610)$$ Z b ( 10610 ) as axial-vector molecular states

Abstract

In this article, we construct both the color singlet-singlet type and octet-octet type currents to interpolate the X(3872), Zc(3900), Z b (10610), and calculate the vacuum condensates up to dimension-10 in the operator product expansion. Then we study the axial-vector hidden charmed and hidden bottom molecular states with the QCD sum rules, explore the energy scale dependence of the QCD sum rules for the heavy molecular states in details, and use the formula µ = M 2 X/Y /Z − (2MQ) 2 with the effective masses MQ to determine the energy scales. The numerical results support assigning the X(3872), Zc(3900), Z b (10610) as the color singletsinglet type molecular states with J P C = 1 ++ , 1 +− , 1 +− , respectively, more theoretical and experimental works are still needed to distinguish the molecule and tetraquark assignments; while there are no candidates for the color octet-octet type molecular states.

The hidden-charm pentaquark and tetraquark states

“…The molecular type of interpolating currents were employed to investigate the Z c (3900) and Z c (4020) states in QCD sum rules in Refs [432,433,475,476,430,431,477,478]. The extracted mass agrees with the experimental values within errors.…”

“…The method of QCD sum rules was also used to study the two Z b states [428,429,430,431,432,433,434,435]. Using the BB * and B * B * molecule-type interpolating currents with I G J P = 1 + 1 + , their extracted masses were roughly consistent with the masses of the Z b (10610) and Z b (10650) mesons, respectively.…”

Treating Zc(3900) and Z(4430) as the ground state and first radially excited tetraquarks

“…Indeed, there are attempts to treat it as the tightly bound diquark-antidiquark state [27][28][29][30], as the four-quark bound state composed of conventional mesons [31][32][33][34][35][36][37][38][39], or as the threshold cusp [40,41].…”

Magnetic and quadrupole moments of the Zc(3900)

“…Since the mass of Z ± c (3900) is very close to X(3872), it can be advised as the charged partner of the X(3872) in a tetraquark scenario. The properties of the Z ± c (3900) particle have been investigated with different theoretical models and approaches [18][19][20][21][22][23][24][25][26][27][28][29][30][31]. Although the spectroscopic properties of these particles have been studied adequately, the internal structure and nature of the X(3872) and Z ± c (3900) particles have not been fully understood yet.…”