Assignments of the X 4140 , X 4500 , X 4630 , and X 4685 Based on the QCD Sum Rules

In this article, we take into account our previous calculations based on the QCD sum rules, and tentatively assign the X 4630 as the D s ∗ D ¯ s 1 − D s 1 D ¯ s ∗ tetraquark molecular state or c s P c ¯ s ¯ A + c s A c ¯ s ¯ P tetraquark state with the J P C = 1 − + , and assign the X 3915 and X 4500 as the 1S and 2S c s A c ¯ s ¯ A tetraquark states, respectively, with the J P C = 0 + + . Then, we extend our previous works to investigate the LHCb’s new tetraquark candidate X 4685 as the first radial excited state of the X 4140 with the QCD sum rules and obtain the mass M X = 4.70 ± 0.12 GeV , which is in very good agreement with the experimental value 4684 ± 7 − 16 + 13 MeV . Furthermore, we investigate the two-meson scattering state contributions in details and observe that the two-meson scattering states alone cannot saturate the QCD sum rules, the contributions of the tetraquark states play an unsubstitutable role, and we can saturate the QCD sum rules with or without the two-meson scattering states.

Does vacuum saturation work for the higher-dimensional vacuum condensates in the QCD sum rules?

In the QCD sum rules for the tetraquark (molecular) states, the higher-dimensional vacuum condensates play an important role in extracting the tetraquark masses. We carry out the operator product expansion up to the vacuum condensates of dimension-10 and observe that the vacuum condensates of dimensions 6, 8 and 10 have the same expressions but opposite signs for the [Formula: see text]-type and [Formula: see text]-type four-quark currents, which make their influences distinguishable, and they are excellent channels to examine the vacuum saturation approximation. We introduce a parameter [Formula: see text] to parametrize the derivation from the vacuum saturation or factorization approximation, and choose two sets of parameters to examine the influences on the predicted tetraquark masses, which can be confronted to the experimental data in the future. In all the channels, smaller value of the [Formula: see text] leads to better convergent behavior in the operator product expansion, which favors the vacuum saturation approximation.

QCD sum rules analysis of weak decays of doubly heavy baryons: the $$b\rightarrow c$$ processes

A comprehensive study of $$b\rightarrow c$$ b → c weak decays of doubly heavy baryons is presented in this paper. The transition form factors as well as the pole residues of the initial and final states are respectively obtained by investigating the three-point and two-point correlation functions in QCD sum rules. Contributions from up to dimension-6 operators are respectively considered for the two-point and three-point correlation functions. The obtained form factors are then applied to a phenomenological analysis of semi-leptonic decays.

Strong and electromagnetic decays of the radially excited $$D_s$$ and $$B_s$$ mesons in light cone QCD sum rules

Recently, LHCb Collaboration announced the discovery of radial excitations of $$D_s$$ D s and $$B_s$$ B s mesons. In present work, we calculate the most promising strong and electromagnetic decay widths of radially excited $$D_s(2S)$$ D s ( 2 S ) and $$B_s(2S)$$ B s ( 2 S ) mesons within the light cone QCD sum rules method.

Tetraquark molecular states in the DsD̄s1 and Ds∗D̄s0∗ mass spectrum

In this work, we construct the color-singlet-color-singlet type four-quark currents to investigate the [Formula: see text] and [Formula: see text] tetraquark molecular states with the [Formula: see text] and [Formula: see text] via the QCD sum rules and obtain satisfactory results. We can search for the [Formula: see text] and [Formula: see text] tetraquark molecular states with the [Formula: see text] and [Formula: see text] at the BESIII and Belle II in the future.