Analysis of Scalar Doubly Heavy Tetraquark States with QCD Sum Rules

In this article, we perform a detailed study of the mass spectrum of the scalar doubly charmed and doubly bottom tetraquark states using the QCD sum rules.

A Comparative Study of f_B within QCD Sum Rules with Two Typical Correlators up to Next-to-Leading Order

The B-meson decay constant fB is an important component for studying the B-meson decays, which can be studied through QCD sum rules. We make a detailed discussion on f B from two sum rules up to next-to- leading order, i.e. sum rules I and II, which are derived from the conventional correlator and the correlator with chiral currents respectively. It is found that these two sum rules are consistent with each other. The sum rules H involves less non-perturbative condensates as that of sum rules I, and in principle, it can be more accurate if we know the dimensionfour gluon condensate well. It is found that fB decreases with the increment of mb, and to compare with the Belle experimental data on fB, both sum rules I and H prefer smaller pole b-quark mass, mb= 4.68 ± 0.07 GeV. By varying all the input parameters within their reasonable regions and by adding all the uncertainties in quadrature, we obtain fB=172-25^＋23 MeV for sum rules I and fB =214-34^26 MeV for sum rules П.

Reanalyzing Pentaquark Θ^＋（1540） in Framework of QCD Sum Rules Approach with Direct Instantons

In this article, we study the pentaquark state Θ＋（1540） with a （scalar） diquark-（pseudoscalar） diquarkantiquark type interpolating current in the framework of the QCD sum rules approach by including the contributions from the direct instantons. The numerical results indicate that the contributions from the direct instantons are very small and can be safely neglected.

{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 Y(4660) and Related Bound States with QCD Sum Rules

In this article, we take the vector charmonium-like state Y（4660） as a φ＇ fo（980） bound state （irrespective of the hadro-charmonium and the molecular state） tentatively, and study its mass using the QCD sum rules. The numerical value My = 4.71 ±0.26 GeV is consistent with the experimental data. Considering the SU（3） symmetry of the light flavor quarks and the heavy quark symmetry, we also study the bound states φ＇a（400-1200）, γ′″ fo（980）, and γ′″σ（400-1200） with the QCD sum rules, and make reasonable predictions for their masses.

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 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.

Ground states and first radial excitations of vector tetraquark states with explicit P-waves via QCD sum rules

In this study,we chose the diquark-antidiquark type four-quark cuents with an explicit P-wave betweenthe diquark and antidiquark pairs to study the ground states and first radial exeitations of the hidden-charm tetra.quark states with quantum numbers J^(PC)=1^(--).We also obtained the lowest vector tetraguark masses and made pos.sible assignments of the existing Ystates,There indeed exists a hidden-charm tetraquark state with J^(PC)=1^(--) at anenergy of approximately 4.75 GeV as the first radial exeitation that accounts for the BESIII data.

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.

B_(c) meson and its scalar cousin with QCD sum rules

In this study,we use the optical theorem to calculate the next-to-leading order corrections to the QCD spectral densities directly in the QCD sum rules for the pseudoscalar and scalar B_(c) mesons.We use experimental data for guidance to perform an updated analysis.We obtain the masses and,in particular,decay constants,which are the fundamental input parameters in high energy physics.Ultimately,we obtain the pure leptonic decay widths,which can be compared with experimental data in the future.

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.

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.

Temperature Dependence of Decuplet Baryon Masses from Thermal QCD Sum Rules

In the present work, the masses of the decuplet baryons at finite temperature are investigated using thermM QCD sum rules. Making use of the quark propagator at finite temperature, we caiculate the spectral functions to T8 order, and find that there are no contributions to the spectral functions at T8 order and the temperature corrections mainly come from that containing T4 ones. The calculations show very little temperature dependence of the masses below T =0.11 GeV. While above that vaJue, the masses decrease with increasing temperature. The results indicate that the hadron-quark phase transition temperature may be Tc ≥ 0.11 GeV for the decuplet bayons.

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.

Semileptonic Decays B_c~*→η_cll with QCD Sum Rules

In this article, we calculate the B＊→ηc form-factors with the three-point QCD sum rules, then study the semileptonic decays B＊→ηclυl. The tiny decay widths may be observed experimentally in the future at the LHCb, while the B＊→ηc form-factors can be taken as basic input parameters in other phenomenologieal analysis.

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.