{Q}{^(('))s}Molecular States in QCD Sum Rules

We systematically investigate the mass spectra of {Qs}{Q（＇）s} molecular states in the framework of QCD sum rules. The interpolating currents representing the molecular states are proposed. Technically, contributions of the operators up to dimension six are included in operator product expansion （OPE）. The masses for molecular states with various {Qs}{Q（＇）s} configurations are presented. The result 4.36 ± 0.08 Ge V for theDs＊ Ds0- ＊ molecular state is consistent with the mass 4350＋4.6 -5.1± 0.7 MeV of the newly observed X（4350）, which could support X（4350） interpreted as a D＊D＊so molecular state.

Analysis of the tetraquark and hexaquark molecular states with the QCD sum rules

In this article,we construct the color-singlet-color-singlet type currents and the color-singlet-colorsinglet-color-singlet type currents to study the scalar D*■*,D*D*tetraquark molecular states and the vector D*D*■*,D*D*D*hexaquark molecular states with the QCD sum rules in details.In calculations,we choose the pertinent energy scales of the QCD spectral densities with the energy scale formula■for the tetraquark and hexaquark molecular states respectively in a consistent way.We obtain stable QCD sum rules for the scalar D*■*,D*D*tetraquark molecular states and the vector D*D*■*hexaquark molecular state,but cannot obtain stable QCD sum rules for the vector D*D*D*hexaquark molecular state.The connected(nonfactorizable)Feynman diagrams at the tree level(or the lowest order)and their induced diagrams via substituting the quark lines make positive contributions for the scalar D*D*tetraquark molecular state,but make negative or destructive contributions for the vector D*D*D*hexaquark molecular state.It is of no use or meaningless to distinguish the factorizable and nonfactorizable properties of the Feynman diagrams in the color space in the operator product expansion so as to interpret them in terms of the hadronic observables,we can only obtain information about the short-distance and long-distance contributions.

Dynamical study of the possible molecular state X(3872) with the s-channel one gluon exchange interaction

The recently observed X（3872） resonance, which is difficult to assign a conventional cc charmonium state in the quark model, may be interpreted as a molecular state. Such a molecular state is a hidden flavor four quark state because of its charmonium-like quantum numbers. The s-channel one gluon exchange is an interaction which only acts in the hidden flavor multi-quark system. In this paper, we will study the X（3872） and other similiar hidden flavor molecular states in a quark model by taking into account the s-channel one gluon exchange interaction.

Study of the heavy molecular states in the quark model with meson exchange interaction

Some charmonium-like resonances such as X（3872） can be interpreted as possible D （＊） （＊） molecular states.Within the quark model,we study the structure of such molecular states and the similar B （＊） （＊） molecular states by taking into account the light meson exchange （π,η,ρ,ω and σ） between two light quarks from different mesons.

Mass spectra of meson molecular states for heavy and light sectors

We obtain mass spectra of the light and heavy nonrelativistic potential model with Coulomb and one pion meson-antimeson （molecular states） sectors by using a exchange potential terms for meson-meson interaction. The digamma decay widths are also obtained for the light sector. We compare our results with available experimental and theoretical data.

Study on the possible molecular state composed of D^∗sD^¯s1 within the Bethe-Salpeter framework

Recently,a vector charmonium-like state Y(4626)was observed in the portal of D+sDs1(2536)−.This intrigues an active discussion on the structure of the resonance because it has obvious significance for gaining a better understanding on its hadronic structure that contains suitable inner constituents.Therefore,this observation concerns the general theoretical framework about possible structures of exotic states.Since the mass of Y(4626)is slightly above the production threshold of D+sDs1(2536)−,whereas it is below that of D^∗sD^¯s1(2536)with the same quark contents as that of D+sDs1(2536)−,it is natural to conjecture that Y(4626)is a molecular state of D^∗sD^¯s1(2536),as suggested in the literature.Confirming or negating this allegation would shed light on the goal we are concerned with.We calculate the mass spectrum of a system composed of a vector meson and an axial vector i.e.,D^∗sD^¯s1(2536)within the framework of the Bethe-Salpeter equations.Our numerical results show that the dimensionless parameterλin the form factor,which is phenomenologically introduced to every vertex,is far beyond the reasonable range for inducing even a very small binding energyΔE.It implies that the D^∗sD^¯s1(2536)system cannot exist in the nature as a hadronic molecule in this model.Therefore,we may not be able to assume the resonance Y(4626)to be a bound state of D^∗sD^¯s1(2536),and instead,it could be attributed to something else,such as a tetraquark.

Radiative decays of f1(1285)as the K∗K molecular state

With f1(1285)as a dynamically generated resonance from K∗K interactions,we estimate the rates of the radiative transitions of the f1(1285)meson to the vector mesons ρ^0,ω and ϕ.These radiative decays proceed via the kaon loop diagrams.The calculated results are in a fair agreement with experimental measurements.Some predictions can be tested experimentally;their analysis will be valuable for decoding the strong coupling of the f1(1285)state to the KK∗ channel.

Analysis of the Y(4220)and Y(4390)as molecular states with QCD sum rules

In this article, we assign the Y（4390） and Y（4220） to be the vector molecular states D1（2420） and D＊ ＊0（2400）, respectively, and study their masses and pole residues in detail with the QCD sum rules. The present calculations only favor assigning the Y（4390） to be the D1（1^--） molecular state.

Exotic D_(s)^(*)D^(*) molecular states and scqc tetraquark states with J^(P)=0^(+),1^(+),2^(+)

We have calculated the mass spectra for the D_(s)^(*)D^(*) molecular states and scqc tetraquark states with J^(P)=0^(+),1^(+),2^(+).The masses of the axial-vector D_(s)^(*)D^(*),D_(s)^(*)D molecular states and 1_([sc])㊉0_([qc]),0_([sc])©1_([qc])tetraquark states are predicted to be approximately 3.98 GeV,in good agreement with the mass of Z_(cs)(3985)^(-)from BE-SIII.In both the molecular and diquark-antidiquark scenarios,our results suggest that there may exist two almost degenerate states,as the strange partners of X(3872)and Z_(c)(3900).We propose to carefully examine Z_(cs)(3985)in future experiments to verify this.One may also search for more hidden-charm four-quark states with strangeness in not only the open-charm D_(s)^(*)D^(*) channels but also the hidden-charm channels η_(c)K/K^(*),J/ψK/K^(*).

Possible heavy molecular states composed of a pair of excited charm-strange mesons

The P-wave charm-strange mesons Ds0（2317） and Ds1（2460） lie below the DK and D＊K threshold respectively. They are extremely narrow because their strong decays violate the isospin symmetry. We study the possible heavy molecular states composed of a pair of excited charm strange mesons. As a byproduct, we also present the numerical results for the bottonium-like analogue.

Ξbb and Ωbbb molecular states

Using the vector exchange interaction in the local hidden gauge approach,which in the light quark sector generates the chiral Lagrangians and has produced realistic results for Ωc,Ξc,Ξb and the hidden charm pentaquark states,we study the meson-baryon interactions in the coupled channels that lead to the Ξbb and Ωbbb excited states of the molecular type.We obtain seven states of the Ξbb type with energies between 10408 and 10869 MeV,and one Ωbbb state at 15212 MeV.

Search for the D∗D¯∗molecular state Zc(4000)in the reaction B−→J/ψρ^0K^−

Based on the prediction of a D^∗D^¯∗molecular state Zc(4000)with isospin I=1 in the coupled channel approach,we suggest the search for this state in the reaction B−→J/ψρ0K−.By considering the final state interactions of J/ψρand D^∗0D^¯∗0 and the contribution from the K1(1270)resonance,we observed that the J/ψρmass distribution shows a peak around 4000 MeV,which might be associated with the D^∗D^¯∗molecular state Zc(4000).The search for Zc(4000)in the reaction B−→J/ψρ^0K−is critical for understanding the internal structures of exotic hadrons.Our predictions can be tested by the Belle II and LHCb in future studies.

Analysis of the strong decays of Pc(4312)as a pentaquark molecular state with QCD sum rules

Abstract:In this article,we tentatively assign Pc(4312)to be the^ˉDΣc pentaquark molecular state with the spin-parity JP=12−,and discuss the factorizable and non-factorizable contributions in the two-point QCD sum rules for the^ˉDΣc molecular state in detail to prove the reliability of the single pole approximation in the hadronic spectral density.We study its two-body strong decays with the QCD sum rules,and special attention is paid to match the hadron side with the QCD side of the correlation functions to obtain solid duality.We obtain the partial decay widthsΓ(Pc(4312)→ηcp)=0.255MeV andΓ(Pc(4312)→J/ψp)=9.296+19.542−9.296MeV,which are compatible with the experimental value of the total width,and support assigning Pc(4312)to be the^ˉDΣc pentaquark molecular state.

Possible molecular states from interactions of charmed strange baryons

In this study,we investigate possible molecular states composed of two charmed strange baryons from theΞ_(c)^((′,∗))Ξ_(c)^((′,∗))interaction and their hidden-charm hidden-strange partners from theΞ_(c)^((′,∗))Ξ¯_(c)^((′,∗))interaction.With the aid of heavy quark chiral effective Lagrangians,the interactions of charmed strange baryons are described with light meson exchanges.The potential kernels are constructed and inserted into the quasipotential Bethe–Salpeter equation.The bound states are produced from most interactions considered,which suggests that strong attractions exist widely between the charmed strange baryons.Experimental search for these types of molecular states is suggested in future high-precision measurements.

A note on the B*B,B*B*,D*,D** molecular states

In the framework of the one-boson-exchange model, we have performed an extensive study of the possible B＊B, B B＊ D＇D, D＇D＊ molecular states with various quantum numbers after considering the S-wave and D-wave mixing. We also discuss the possible experimental research of these interesting states.

Analysis of hidden-charm pentaquark molecular states with and without strangeness via the QCD sum rules

In this study,we investigate the,D∑c,D≡c',D∑c^(*),D^(*)∑c,D^(*)≡c',D^(*)∑c^(*),and D^(*)≡c'^(*)pentaquark mo-lecular states with and without strangeness via the QCD sum rules in detail,focusing on the light flavor,SU(3),breaking effects,and make predictions for new pentaquark molecular states besides assigning P_(c)(4312),P_(c)(4380),Pc(4440),P_(c)(4457),and P_(cs)(4459)self-consistently.In the future,we can search for these pentaquark molecular states in the decay of ∧_(b)^(0),≡H_(b)^(0),and ≡_(b)^(-) Furthermore,we discuss high-dimensional vacuum condensates in detail.

Analysis of Pcs(4338) and related pentaquark molecular states via QCD sum rules

In this study,we tentatively identify Pcs(4338)■Ξc molecular state and distinguish the isospins of current operators to explore in detail the■Ξc,■Λc,■sΞc,■sΛc,■*Ξc,■*Λc,■*sΞc,and■*sΛcmolecular states without strange,with strange,and with double strange in the framework of QCD sum rules.The present exploration favors identifying Pcs(4338)(Pcs(4459))as the■Ξc(■*Ξc)molecular state with the spin-parity JP=1/2-(3/2-)and(I,I3)=(0,0),and the observation of their cousins with the isospin(I,I3)=(1,0)J/ψΣ0/ηcΣ0in the invariant mass distributions would decipher their inner structures.

Effect of stress state on deformation and fracture of nanocrystalline copper:Molecular dynamics simulation

Deformation in a microcomponent is often constrained by surrounding joined material making the component under mixed loading and multiple stress states. In this study, molecular dynamics （MD） simulation are conducted to probe the effect of stress states on the deformation and fracture of nanocrystalline Cu. Tensile strain is applied on a Cu single crystal, bicrystal and polycrystal respectively, under two different tension boundary conditions. Simulations are first conducted on the bicrystal and polycrystal models without lattice imperfection. The results reveal that, compared with the performance of simulation models under free boundary condition, the transverse stress caused by the constrained boundary condition leads to a much higher tensile stress and can severely limit the plastic deformation, which in return promotes cleavage fracture in the model. Simulations are then performed on Cu single crystal and polycrystal with an initial crack. Under constrained boundary condition, the crack tip propagates rapidly in the single crystal in a cleavage manner while the crack becomes blunting and extends along the grain boundaries in the polycrystal. Under free boundary condition, massive dislocation activities dominate the deformation mechanisms and the crack plays a little role in both single crystals and polycrystals.

Ionic Interactions in Molecular and Liquid States ofPolyvalent Metal Halides

Progress in the development of phenomenological models for the microscoplc interactions in the halides of polyvalent metals is reviewed, with main attention to neutral and ionized molecular states and to the melts of these materials. The following physical problems are discussed: (1)bond bending in the molecules of the alkaline-earth halides, (2) binding of molecular dimers and halogen transfer reactions relevant to the melts of trivalent metal halides, (3) stability of molecular ions in liquid mixtures of polyvalent metal halides and alkali halides, and (4) stabilityof molecular ions and reduced-valence states in molten cryolite under addition of sodium metal.

Molecular Application of a State Specific Multi-Reference Brillouin-Wigner Perturbation Theory

The single reference second order Brillouin-Wigner perturbation theory recently developed, which eliminates its size-extensivity error, has been generalized to state-specific, multi-reference （SS-MR）, BWPT2 providing a size-extensive correction to the electron correlation problem for systems that demand the use of a multi-reference function. Illustrative numerical tests of the size-extensivity corrections are made for widely used molecules in their ground states, which are pronounced multi-reference characteristics. We have implemented two-reference and three-reference cases for CH2, BH and bond breaking process in the ground states of HF molecules. The results are compared with the rigorously size-extensive methods such as the M^ller-Plesset perturbation theory, i.e., MP2, full configuration interaction （Full-CI） and allied methods using the same basis sets.