Forming molecular states with hadronic rescattering

A method for modelling the prompt production of molecular states using the hadronic rescattering framework of the general-purpose Pythia event generator is introduced. Production cross sections of possible exotic hadronic molecules via hadronic rescattering at the LHC are calculated for the $$\chi _{c1}(3872)$$ χ c 1 ( 3872 ) resonance, a possible tetraquark state, as well as three possible pentaquark states, $$P_c^+(4312)$$ P c + ( 4312 ) , $$P_c^+(4440)$$ P c + ( 4440 ) , and $$P_c^+(4457)$$ P c + ( 4457 ) . For the $$P_c^+$$ P c + states, the expected cross section from $$\Lambda _b$$ Λ b decays is compared to the hadronic-rescattering production. The $$\chi _{c1}(3872)$$ χ c 1 ( 3872 ) cross section is compared to the fiducial $$\chi _{c1}(3872)$$ χ c 1 ( 3872 ) cross-section measurement by LHCb and found to contribute at a level of $${\mathcal {O}({1\%})}$$ O ( 1 % ) . Finally, the expected yields of $$\mathrm {P_c^{+}}$$ P c + production from hadronic rescattering during Run 3 of LHCb are estimated. The prompt background is found to be significantly larger than the prompt $$\mathrm {P_c^{+}}$$ P c + signal from hadronic rescattering.

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.

Tetraquark state X(6900) and the interaction between diquark and antidiquark

Recently LHCb declared a new structure X(6900) in the final state di-$$J/\psi $$ J / ψ which is popularly regarded as a cc-$$\bar{c}\bar{c}$$ c ¯ c ¯ tetraquark state. Within the Bethe–Salpeter (B–S) framework we study the possible cc-$$\bar{c}\bar{c}$$ c ¯ c ¯ bound states and the interaction between diquark (cc) and antidiquark ($$\bar{c}\bar{c}$$ c ¯ c ¯ ). In this work cc ($$\bar{c}\bar{c}$$ c ¯ c ¯ ) is treated as a color anti-triplet (triplet) axial-vector so the quantum numbers of cc-$$\bar{c}\bar{c}$$ c ¯ c ¯ bound state are $$0^+$$ 0 + , $$1^+$$ 1 + and $$2^+$$ 2 + . Learning from the interaction in meson case and using the effective coupling we suggest the interaction kernel for the diquark and antidiquark system. Then we deduce the B–S equations for different quantum numbers. Solving these equations numerically we find the spectra of some excited states can be close to the mass of X(6900) when we assign appropriate values for parameter $$\kappa $$ κ introduced in the interaction (kernel). We also briefly calculate the spectra of bb-$$\bar{b}\bar{b}$$ b ¯ b ¯ bound states. Future measurement of bb-$$\bar{b}\bar{b}$$ b ¯ b ¯ state will help us to determine the exact form of effective interaction.

Scalar fully-heavy tetraquark states $$QQ^\prime {\bar{Q}} \bar{Q^\prime }$$ in QCD sum rules

Very recently, the LHCb Collaboration observed distinct structures with the $$cc{\bar{c}}{\bar{c}}$$ c c c ¯ c ¯ in the $$J/\Psi $$ J / Ψ -pair mass spectrum. In this work, we construct four scalar ($$J^{PC} = 0^{++}$$ J PC = 0 + + ) $$[8_c]_{Q\bar{Q^\prime }}\otimes [8_c]_{Q^\prime {\bar{Q}}}$$ [ 8 c ] Q Q ′ ¯ ⊗ [ 8 c ] Q ′ Q ¯ type currents to investigate the fully-heavy tetraquark state $$Q Q^\prime {\bar{Q}} \bar{Q^\prime }$$ Q Q ′ Q ¯ Q ′ ¯ in the framework of QCD sum rules, where $$Q=c, b$$ Q = c , b and $$Q^\prime = c, b$$ Q ′ = c , b . Our results suggest that the broad structure around 6.2-6.8 GeV can be interpreted as the $$0^{++}$$ 0 + + octet–octet tetraquark states with masses $$6.44\pm 0.11$$ 6.44 ± 0.11 GeV and $$6.52\pm 0.10$$ 6.52 ± 0.10 GeV, and the narrow structure around 6.9 GeV can be interpreted as the $$0^{++}$$ 0 + + octet–octet tetraquark states with masses $$6.87\pm 0.11$$ 6.87 ± 0.11 GeV and $$6.96\pm 0.11$$ 6.96 ± 0.11 GeV, respectively. Extending to the b-quark sector,the masses of their fully-bottom partners are found to be around 18.38-18.59 GeV. Additionally, we also analyze the spectra of the $$[8_c]_{c{\bar{c}}}\otimes [8_c]_{b {\bar{b}}}$$ [ 8 c ] c c ¯ ⊗ [ 8 c ] b b ¯ and $$[8_c]_{c{\bar{b}}}\otimes [8_c]_{b {\bar{c}}}$$ [ 8 c ] c b ¯ ⊗ [ 8 c ] b c ¯ tetraquark states, which lie in the range of 12.51–12.74 GeV and 12.49–12.81 GeV, respectively.

Mass spectrum and strong decays of tetraquark $${\bar{c}}{\bar{s}} qq$$ states

We systematically study the mass spectrum and strong decays of the S-wave $${\bar{c}}{\bar{s}} q q$$ c ¯ s ¯ q q states in the compact tetraquark scenario with the quark model. The key ingredients of the model are the Coulomb, the linear confinement, and the hyperfine interactions. The hyperfine potential leads to the mixing between different color configurations, and to the large mass splitting between the two ground states with $$I(J^P)=0(0^+)$$ I ( J P ) = 0 ( 0 + ) and $$I(J^P)=1(0^+)$$ I ( J P ) = 1 ( 0 + ) . We calculate their strong decay amplitudes into the $${\bar{D}}^{(*)}K^{(*)}$$ D ¯ ( ∗ ) K ( ∗ ) channels with the wave functions from the mass spectrum calculation and the quark-interchange method. We examine the interpretation of the recently observed $$X_0(2900)$$ X 0 ( 2900 ) as a tetraquark state. The mass and decay width of the $$I(J^P)=1(0^+)$$ I ( J P ) = 1 ( 0 + ) state are $$M=2941$$ M = 2941 MeV and $$\Gamma _X=26.6$$ Γ X = 26.6 MeV, respectively, which indicates that it might be a good candidate for $$X_0(2900)$$ X 0 ( 2900 ) . Meanwhile, we also obtain an isospin partner state $$I(J^P)=0(0^+)$$ I ( J P ) = 0 ( 0 + ) with $$M=2649$$ M = 2649 MeV and $$\Gamma _{X\rightarrow {\bar{D}} K}=48.1$$ Γ X → D ¯ K = 48.1 MeV, respectively. Future experimental search for X(2649) will be very helpful.

Analysis of the X0(2900) as the scalar tetraquark state via the QCD sum rules

In this article, we study the axialvector-diquark–axialvector-antidiquark (AA)-type and scalar-diquark–scalar-antidiquark (SS) type fully open flavor [Formula: see text] tetraquark states with the spin-parity [Formula: see text] via the QCD sum rules. The predicted masses [Formula: see text] GeV and [Formula: see text] GeV support assigning the [Formula: see text] to be the AA-type scalar [Formula: see text] tetraquark state.