Dynamically Running Mass of Light Quark and QCD Vacuum Condensates

Based on Dyson-Schwinger equations (DSEs) in “rainbow”approximation, the dynamically running mass of light quark and QCD vacuum condensate are investigated. The structure of non-local quark vacuum condensate, the values of local vacuum condensate of quarks and quark-gluon mixture, and dynamical transition of quark mass from current quark to constituent quark are illustrated. At the same time, according to the knowledge and experience learned from an extensive study of the solutions of DSEs， a parameterized form of confining quark propagator is suggested for a practical use. The new parameterized form of quark propagator is analytic everywhere in the finite complex p^2-plane and has no Lehmann representation. The predictions for p^2-dependence of effective quark masses, Mr(p^2), defined by the self-energy functions Af(p^2) and Bf(p^2), both from the numerical solutions of DSEs and from its parameterized form, are shown dynamically. Our conclusion is that all numerical results are consistent with empirical values used in(QCD sum rules and lattice QCD calculations. For a qualitative study, the parameterized form is a sumciently good approximation to confining quark propagator.     

Dynamically Running Mass of Light Quark and QCD Vacuum Condensates

Based on Dyson-Schwinger equations (DSEs) in “rainbow“ approximation, the dynamically running mass of light quark and QCD vacuum condensate are investigated. The structure of non-local quark vacuum condensate, the values of local vacuum condensate of quarks and quark-gluon mixture, and dynamical transition of quark mass from current quark to constituent quark are illustrated. At the same time, according to the knowledge and experience learned from an extensive study of the solutions of DSEs, a parameterized form of confining quark propagator is suggested for a practical use. The new parameterized form of quark propagator is analytic everywhere in the finite complex p2-plane and has no Lehmann representation. The predictions for p2-dependence of effective quark masses, Mf(p2), defined by the self-energy functions Af(p2) and Bf(p2), both from the numerical solutions of DSEs and from its parameterized form, are shown dynamically. Our conclusion is that all numerical results are consistent with empirical values used in QCD sum rules and lattice QCD calculations. For a qualitative study, the parameterized form is a sufficiently good approximation to confining quark propagator.     

B-Meson Wavefunction by a Comparative Analysis of the B → π, K Transition Form Factors

Properties of the B-meson light-cone wavefunction up to next-to-leading order Fock state expansion are studied by a comparative study of the B → π, K form factors within the kT factorization approach and the light-cone sum rule analysis. The form factors F＋,0,T^B→ π and F＋,0,T^B→ K are carefully re-calculated up to O（1/mb^2） within the kT factorization approach in the large recoil region. The QCD light-cone sum rule is applicable in the large and intermediate energy regions, and the QCD light-cone sum rule results in Ref. [12] are adopted for such a comparative study. It is found that when the two phenomenological parameters ∧^-∈ [0.50, 0.55] and δ∈ [0.25, 0.30], the results of F＋,0,T^B→ π （Q^2 ） and F＋,0,T^B→ K（Q ^2） from these two approaches are consistent with each other in the large recoil energy region.     

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 de...     

Stabilization and Consistency for Subtracted and Unsubtracted QCD Sum Rules for 0^＋＋ Scalar Glueball

Based on a semi-classical expansion for quantum chromodynamics in the instanton liquid background, the correlation function of the 0^＋＋ scalar glueball current is calculated. Besides the pure classical and quantum contributions, the contributions arising from the interactions between the classical instanton fields and quantum gluon ones come into play. It turns out that the latter contributions have a great role not only in making the stabilization of the subtracted and unsubtracted Laplace-transformed QCD sum rules for 0^＋＋ scalar glueball, but also in bring back the consistency between the two related sum rules, or equivalently between the QCD asymptotic expression and low energy theorem. The result for the scalar glueball mass is predicted to be mG= 1.35 GeV.     

Ds（0^±） Meson Spectroscopy in Gaussian Sum Rules

Masses of the Ds（0^±） mesons are investigated from a view-point of ordinary light-heavy system in the framework of the Gaussian sum rules, which are worked out by means of the Laplacian transformation to the usual Borel sum rules. Using the standard input of QCD non-perturbative parameters, the corresponding mass spectra and couplings of the currents to the Ds（0^±） mesons are obtained. Our results are mDs（0-） = 1.968±0.016±0.003 GeV and mDs（0＋） = 2.320 ±0.014 ± 0.003 GeV, which are in good accordance with the experimental data, 1.969 GeV and 2.317 GeV.     

Ratio of a strange quark mass ms to up or down quark mass mu,d predicted by a quark propagator in the framework of the chiral perturbation theory

Based on the fully dressed quark propagator and chiral perturbation theory, we study the ratio of the strange quark mass ms to up or down quark mass mu,d . The ratio is related to the determination of quark masses which are fundamental input parameters of QCD Lagrangian in the Standard Model of particle physics and can not be directly measured since the quark is confined within a hadron. An accurate determination of these QCD free parameters is extremely important for both phenomenological and theoretical applications. We begin with a brief introduction to the non-perturbation QCD theory, and then study the mass ratio in the framework of the chiral perturbation theory (χPT) with a parameterized fully dressed quark propagator which describes confining fully dressed quark propagation and is analytic everywhere in the finite complex p2-plane and has no Lehmann representation so there are no quark production thresholds in any theoretical calculations of observable data. Our prediction for the ratio ms/mu,d is consistent with other model predictions such as Lattice QCD, instanton model, QCD sum rules and the empirical values used widely in the literature. As a by-product of this study, our theoretical results, together with other predictions of physical quantities that used this quark propagator in our previous publications, clearly show that the parameterized form of the fully dressed quark propagator is an applicable and reliable approximation to the solution of the Dyson-Schwinger Equation of quark propagator in the QCD.     

Analysis of the decay B^0→Xc1π^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.     

Properties of the P_c(4312) pentaquark and its bottom partner

We present an analysis of the newly observed pentaquark P_c(4312)~+ to shed light on its quantum numbers.To do that,the QCD sum rules approach is used.The measured mass of this particle is close to the ∑_c~(++)D~-threshold and has a small width,which supports the possibility of its being a molecular state.We consider an interpolating current in a molecular form and analyze both the positive and negative parity states with spin-1/2.We also consider the bottom counterpart of the state with similar molecular form.Our mass result for the charm pentaquark state supports that the quantum numbers of the observed state are consistent with J~P=1/2~-.     

Light four-quark states and QCD sum rule

The relations among four-quark states, diquarks and QCD sum rules are discussed. The situation of the existing, but incomplete studies of four-quark states with QCD sum rules is analyzed. Masses of some diquark clusters were attempted to be determined by QCD sum rules, and masses of some light tetraquark states were obtained in terms of the diquarks.