Analysis of the decay B^0→χc1~π~0 with light-cone QCD sum rules

In this article, we calculate the contribution from the nonfactorizable soft hadronic matrix element to the decay B^0→Xc1π^0 with the light-cone quantum chromo-dynamic （QCD） sum rules. The numerical results show that its contribution is rather large and should not be neglected. The total amplitudes lead to a branching fraction which is in agreement with the experimental data marginally.

Strong decay of Y(4230)→ J/ψ f0(980) in light cone sum rules

In this study,we assign the tetraquark state for the Y(4230) resonance and investigate the mass and decay constant of Y(4230) in the framework of SVZ sum rules through a different calculation technique.Then,we calculate the strong coupling gYJ/ψf0 by considering soft-meson approximation techniques within the framework of light cone sum rules,and we use the strong coupling gYJ/ψf0 to obtain the width of the decay Y(4230)→J/ψf0(980).Our prediction for the mass agrees with the experimental measurement,and that for the decay width of Y(4230)→J/ψf0(980) is within the upper limit.

Strong decays of the P_(c)(4312) and its isospin cousin via the QCD sum rules

In this study,considering the conservation of isospin in the strong decays,we investigate the strong decays of the pentaquark molecule candidate P_(c)(4312)and its possible higher isospin cousin P_(c)(4330)in the framework of the QCD sum rules.Further,the pole residue of theΔbaryon with isospin eigenstate|II3>=|3/21/2)is obtained.If the possible pentaquark molecule candidate P_(c)(4330)could be determined,it would shed light on the interpretations of the P_(c) states in future experiments.

Fully-light vector tetraquark states with explicit P-wave via QCD sum rules

In this study,we apply the QCD sum rules to investigate the vector fully-light tetraquark states with an explicit P-wave between the diquark and antidiquark pairs.We observed that the Cγα⊗↔∂μ⊗γαC(or Cγα⊗↔Dμ⊗γαC)type current with fully-strange quarks couples potentially to a tetraquark state with a mass 2.16±0.14GeV,which supports assigning Y(2175)/ϕ(2170)as the diquark-antidiquark type tetraquark state with JPC=1−−.The qsˉqˉs and ssˉsˉs vector tetraquark states with the structure Cγμ⊗↔∂α⊗γαC+Cγα⊗↔∂α⊗γμ(or Cγμ⊗↔Dα⊗γαC+Cγα⊗↔Dα⊗γμ)are consistent with X(2200)and X(2400),respectively,which lie in the region from 2.20 to 2.40GeV.The central values of the masses of the fully-strange vector tetraquark states with an explicit P-wave are approximately 2.16−3.13GeV(or 2.16−3.16GeV).Predictions for other fully-light vector tetraquark states with and without hidden-strange are also presented.

The Λ-type P-wave bottom baryon states via the QCD sum rules

Our study focuses on the Λ-type P-wave bottom baryon states with spin-parity JP=1/2−, 3/2−. We introduce an explicit P-wave between the two light quarks in the interpolating currents (these light quarks are antisymmetric in the flavor space, thus giving rise to the designation of Λ-type baryon) to investigate the Λb and Ξ_(b) states within the framework of the full QCD sum rules. The predicted masses show that Ξ_(b)(6087) and Ξ_(b)(6095/6100) could be the P-wave bottom-strange baryon states with spin-parity JP=1/2− and 3/2−, respectively;meanwhile, Λb(5912) and Λb(5920) could be the P-wave bottom baryon states with spin-parity JP=1/2− and 3/2−, respectively. Moreover, Λb(5920) and Ξ_(b)(6095/6100) may have two remarkable under-structures or Fock components at least.

Constraints ofξ-moments computed using QCD sum rules on pion distribution amplitude models

To date,the behavior of the pionic leading-twist distribution amplitude(DA)φ2;π(x,μ)-which is a universal physical quantity and is introduced into high-energy processes involving pions based on the factorization theorem-is not completely consistent.The form ofφ2;π(x,μ)is usually described by phenomenological models and constrained by the experimental data on exclusive processes containing pions or the moments computed using QCD sum rules and the lattice QCD theory.Evidently,an appropriate model is extremely important to determine the exact behavior ofφ2;π(x,μ).In this paper,by adopting the least squares method to fit theξ-moments calculated using QCD sum rules based on the background field theory,we perform an analysis on several commonly used models of the pionic leading-twist DA in the literature;these include the truncation form of the Gegenbauer polynomial series,the light-cone harmonic oscillator model,the form extracted from the Dyson-Schwinger equations,the model from the light-front holographic AdS/QCD,and a simple power-law parametrization form.

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.

Study of spin sum rules (and the strong coupling constant at large distances)

We present recent results from Jefferson Lab on sum rules related to the spin structure of the nucleon. We then discuss how the Bjorken sum rule with its connection to the Gerasimov-Drell-Hearn sum, allows us to conveniently define an effective coupling for the strong force at all distances.

Heavy flavor baryon spectra via QCD sum rules

In this talk, we give a short review of our recent works on studying the singly heavy baryon, doubly heavy baryon, and triply heavy baryon Spectra from QCD sum rules.

B→A transitions in the light-cone QCD sum rules with the chiral current

In this article, we calculate the form-factors of the transitions B → a1（1260）, b1（1235） in the leading-order approximation using the light-cone QCD sum rules. In calculations, we choose the chiral current to interpolate the B-meson, which has the outstanding advantage that the twist-3 light-cone distribution amplitudes of the axial-vector mesons makes no contributions, and the resulting sum rules for the form-factors suffer from far fewer uncertainties. Then we study the semi-leptonic decays B → a1（1260） lvl, b1（1235） lvl （l=e,μ,τ）, and make predictions for the differential decay widths and decay widths, which can be compared with the experimental data in the coming future

NLO effects for Ω_(QQQ) baryons in QCD Sum Rules

We study the triply heavy baryonsΩ_(QQQ)(Q=c,b)in the QCD sum rules by performing the first calculation of the next-to-leading order(NLO)contribution to the perturbative QCD part of the correlation functions.Compared with the leading order(LO)result,the NLO contribution is found to be very important to theΩ_(QQQ).This is because the NLO not only results in a large correction but also reduces the parameter dependence,making the Borel platform more distinct,especially for the Q_(bbb)in the MS scheme,where the platform appears only at NLO but not at LO.Particularly,owing to the inclusion of the NLO contribution,the renormalization schemes(MS and On-Shell)dependence and the scale dependence are significantly reduced.Consequently,after including the NLO contribution to the perturbative part in the QCD sum rules,the masses are estimated to be 4.53_)0.11)^(+0.26) GeV forΩ_(ccc) and14.27_(-0.32)^(+0.33) GeV forΩ_(bbb),where the results are obtained atμ=M_(B) with errors including those from the variation of the renormalization scaleμin the range(0.8-1.2)M_(B).A careful study of theμdependence in a wider range is further performed,which shows that the LO results are very sensitive to the choice ofμwhereas the NLO results are considerably better.In addition to theμ=M_(B) result,a more stable value,(4.75-4.80)GeV,for theΩ_(ccc) mass is found in the range ofμ=(1.2-2.0)M_(B),which should be viewed as a more relevant prediction in our NLO approach because of μ dependence.

D^+→η(′)l+ν_l semileptonic decays in light-cone sum rules

We calculate the D → η transition form factor in light-cone sum rules by taking improved current correlators to avoid the pollution from the twist-3 wave function. We get consistent results of the D＋ → η^（＇）l＋νl decays with the experimental data. By comparing the difference between the results of the branching ratios of D＋ → η^（＇）l＋νl from a two-pole parameterization model and from a BZ parameterization model, we find that the two-pole model and the BZ model are comparably believable. One way is supposed for the determination of the η-η mixing angle from the dependence of the branching ratios of D＋ → η^（＇）l＋νl decays on the η-η mixing angle.

Analysis of the strong coupling form factors of Σ_bNB and Σ_cND in QCD sum rules

In this article, we study the strong interaction of the vertices ΣbNB and ΣcND using the three-point QCD sum rules under two different Dirac structures. Considering the contributions of the vacuum condensates up to dimension 5 in the operation product expansion, the form factors of these vertices are calculated. Then, we fit the form factors into analytical functions and extrapolate them into time-like regions, which gives the coupling constants. Our analysis indicates that the coupling constants for these two vertices are G（ΣbNB）= 0.43±0.01 GeV^-1 and GΣcND=3.76±0.05 GeV^-1.

Analysis of the excited Ω_(c) states as the 1/2^(±) pentaquark states with QCD sum rules

We construct both the scalar-diquark-scalar-diquark-antiquark type and axialvector-diquark-axialvector-diquark-antiquark type interpolating currents to study the charmed pentaquark:states suscu with J^(p)=1/2^(±).We employ the QCD sum rules to investigate the masses and pole residues of the charmed pentaquark states by taking into account the vacuum condensates up to dimension 13 in the operator product expansion.Our calculation results indicate that the scalar-diquark-scalar-diquark-antiquark type and axialvector-diquark-axialvector-diquark-antiquark type charmed pentaquark states suscu with J^(p)=1/2^(-) can be possible candidates of the excited states observed in the LHCb collaboration.

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.

Mixing of X and Y states from QCD sum rules analysis

We study QQqq and QqQq states as mixed states in QCD sum rules.By calculating the two-point correlation functions of pure states of their corresponding currents,we review the mass and coupling constant predictions of J^(PC)=1^(++),1^(--),and 1^(-+)states.By calculating the two-point mixed correlation functions of QQqq and QqQq currents,we estimate the mass and coupling constants of the corresponding"physical state"that couples to both QQqq and QqQq currents.Our results suggest that for 1^(++)states,the QQqq and QqQq components are more likely to mix,while for 1^(--)and 1^(-+)states,there is less mixing between QQqq and QqQq.Our results suggest the Y series of states have more complicated components.

Hadronic coupling constants of the lowest hidden-charm pentaquark state,using QCD sum rules with rigorous quark-hadron duality

In this article,we illustrate how to calculate the hadronic coupling constants of the pentaquark states with QCD sum rules based on rigorous quark-hadron quality.We then study the hadronic coupling constants of the lowest diquark-diquark-antiquark type hidden-charm pentaquark state with spin-parity J^(P)=1^(1)/2in detail,and calculate the partial decay widths.The total widthτ(Pc)=14:32±3:31 MeV is compatible with the experimental valueτP_(c)(4312)=9:8±±2:7^(+3:7)_(-4:5)MeV from the LHCb collaboration,and favors assigning P_(c)(4312)the to be the pentaquark state with J^(P)=1^(1)/2.The hadronic coupling constants have the relation|G_(PD)++∑_(c)^(++)|=√2|GPD^(0)Σ_(c)^(+)|≫|G_(PD^(0))_(c)^(+)|,and favor the hadronic dressing mechanism.The P_(c)(4312)may have a diquark-diquark-antiquark type pentaquark core with the typical size of the-type baryon states.The strong couplings to the meson-baryon pairsD_(c)lead to some pentaquark molecule components,and the P_(c)(4312)may spend a rather large time as the molecular state.

Λ_(b)→Λ_(c) form factors from QCD light-cone sum rules

In this study,we calculate the transition form factors of Λ_(b) decaying into Λ_(c) within the framework of light-cone sum rules with the distribution amplitudes(DAs)of the Λ_(b)-baryon.In the hadronic representation of the correlation function,we isolate both the Λ_(c) and Λ_(c)^(∗) states so that the Λ_(b)→Λ_(c) form factors can be obtained without ambiguity.We investigate the P-type and A-type currents to interpolate light baryons for comparison because the interpolation current for the baryon state is not unique.We also employ three parametrization models for the DAs of Λ_(b) in the numerical calculation.We present the numerical predictions for the Λ_(b)→Λ_(c) form factors and branching fractions,averaged forward-backward asymmetry,averaged final hadron polarization,and averaged lepton polarization of the Λ_(b)→Λ_(c)ℓμ decays,as well as the ratio of the branching ratios RΛ_(c).The predicted RΛ_(c) is consistent with LHCb data.

Analysis of (1/2)^+ baryon states containing fourth-family quarks from QCD sum rules

When the fourth generation of quarks have sufficiently small mixing with ordinary standard-model 1＋ quarks, the hadrons made up from these quarks can be long-lived enough. We analyze the 1/2 baryon states containing fourth-generation quarks and standard-model quarks, i.e. the charm or bottom quarks, in the QCD sum rules approach. Considering the perturbative and two gluon condensate contributions in the calculation, we give the numerical results of the masses and pole residues.

D^*Dρ and B^*Bρ strong couplings in light-cone sum rules

We present an improved calculation of the strong coupling constants gD*Dp and gB*Bp in light-cone sum rules,including one-loop QCD corrections of leading power with meson distribution amplitudes.We further compute subleading-power corrections from two-particle and three-particle higher-twist contributions at leading order up to twist-4 accuracy.The next-to-leading order corrections to the leading power contribution numerically offset the subleading-power corrections to a certain extent,and our numerical results are consistent with those of previous studies on sum rules.A comparison between our results and existing model-dependent estimations is also made.