Analysis the f 0(980) and a 0(980) mesons as four-quark states with the QCD sum rules

In this article, we take the point of view that the scalar mesons f₀(980) and a₀(980) are the diquark-antidiquark states , and we devote our attention to the determination of their masses in the framework of the QCD sum rule approach with the interpolating currents constructed from scalar-scalar type and pseudoscalar-pseudoscalar type diquark pairs respectively. The numerical results indicate that the scalar mesons f₀(980) and a₀(980) may have two possible diquark-antidiquark substructures.Received: 27 January 2005, Revised: 22 March 2005, Published online: 31 May 2005PACS: 12.38.Lg; 13.25.Jx; 14.40.Cs     

QCD sum rules with finite masses

The concept of QCD sum rules is extended to bound states composed of particles with finite mass such as scalar quarks or strange quarks. It turns out that mass corrections become important in this context. The number of relevant corrections is analyzed in a systematic discussion of the IR- and UV-divergencies, leading in general to a finite number of corrections. The results are demonstrated for a system of two massless quarks and two heavy scalar quarks.We wish to thank Dr. Lech Mankiewicz for very helpful discussions. This work was supported by DFG (G. Hess program).     

Thermal QCD sum rules study of vector charmonium and bottomonium states

We calculate the masses and leptonic decay constants of the heavy vector quarkonia, J/ψ and ϒ mesons at finite temperature. In particular, considering the thermal spectral density as well as additional operators coming up at finite temperature, the thermal QCD sum rules are acquired. Our numerical calculations demonstrate that the masses and decay constants are insensitive to the variation of temperature up to T ≅ 100 MeV, however after this point, they start to fall altering the temperature. At deconfinement temperature, the decay constants attain roughly to 45% of their vacuum values, while the masses are diminished about 12%, and 2.5% for J/ψ and ϒ states, respectively. The obtained results at zero temperature are in good consistency with the existing experimental data as well as predictions of the other nonperturbative models.     

Analysis of the <Emphasis Type="Italic">Y</Emphasis>(4140) and related molecular states with QCD sum rules

In this article, we assume that there exist scalar D^*[`(D)]<sup>*</sup>{D}^{\ast}{\bar {D}}^{\ast}, D<sub>s</sub><sup>*</sup>[`(D)]_s^*{D}_{s}^{\ast}{\bar{D}}_{s}^{\ast}, B^*[`(B)]<sup>*</sup>{B}^{\ast}{\bar {B}}^{\ast} and B<sub>s</sub><sup>*</sup>[`(B)]_s^*{B}_{s}^{\ast}{\bar{B}}_{s}^{\ast} molecular states, and study their masses using the QCD sum rules. The numerical results indicate that the masses are about (250–500) MeV above the corresponding D ^*–[`(D)]<sup>*</sup>{\bar{D}}^{\ast}, D <sub>s</sub> <sup>*</sup>–[`(D)]_s^*{\bar {D}}_{s}^{\ast}, B ^*–[`(B)]<sup>*</sup>{\bar{B}}^{\ast} and B <sub>s</sub> <sup>*</sup>–[`(B)]_s^*{\bar {B}}_{s}^{\ast} thresholds, the Y(4140) is unlikely a scalar D_s^*[`(D)]<sub>s</sub><sup>*</sup>{D}_{s}^{\ast}{\bar{D}}_{s}^{\ast} molecular state. The scalar D<sup>*</sup>[`(D)]^*D^{\ast}{\bar{D}}^{\ast}, D_s^*[`(D)]<sub>s</sub><sup>*</sup>D_{s}^{\ast}{\bar{D}}_{s}^{\ast}, B<sup>*</sup>[`(B)]^*B^{\ast}{\bar{B}}^{\ast} and B_s^*[`(B)]<sub>s</sub><sup>*</sup>B_{s}^{\ast}{\bar{B}}_{s}^{\ast} molecular states maybe not exist, while the scalar D￠<sup>*</sup>[`(D)]^￠*{D'}^{\ast}{\bar{D}}^{\prime\ast}, D_s^￠*[`(D)]<sub>s</sub><sup>￠*</sup>{D}_{s}^{\prime\ast}{\bar{D}}_{s}^{\prime\ast}, B<sup>￠*</sup>[`(B)]^￠*{B}^{\prime\ast}{\bar{B}}^{\prime\ast} and B_s^￠*[`(B)]_s^￠*{B}_{s}^{\prime\ast}{\bar{B}}_{s}^{\prime\ast} molecular states maybe exist.     

Analysis of the QCD sum rules for the heavy quarkonium

We study phenomenologically the QCD sum rules given by Shifman et al. for the heavy quarkonium. In the charmonium sum rules, we find that the contribution of the physical continuum to the moment ?_n is consistent with that of the effective one. As for the bottonium, the sum rules corrected by the Coulomb-like interaction are saturated very well by the four resonances observed at CESR. It is predicted that the³S₁ ground state of the toponium must exist in the range of \(M_{t\bar t} \) =30–44GeV, if the sum rules for the top quark are assumed.     

Analysis of the scalar doubly charmed hexaquark state with QCD sum rules

In this article, we study the scalar-diquark–scalar-diquark–scalar-diquark type hexaquark state with the QCD sum rules by carrying out the operator product expansion up to the vacuum condensates of dimension 16. We obtain a lowest hexaquark mass of \(6.60^{+0.12}_{-0.09}\,\mathrm {GeV}\), which can be confronted with the experimental data in the future.     

0~+ tetraquark states from improved QCD sum rules:delving into X(5568)

In order to investigate the possibility of the recently observed X(5568) being a 0~+ tetraquark state, we make an improvement to the study of the related various configuration states in the framework of the QCD sum rules. Particularly, to ensure the quality of the analysis, condensates up to dimension 12 are included to inspect the convergence of operator product expansion(OPE) and improve the final results of the studied states. We note that some condensate contributions could play an important role on the OPE side. By releasing the rigid OPE convergence criterion, we arrive at the numerical value 5.57+0.35 for the scalar-scalar diquark-antidiquark 0~+ -0.23 Ge Vstate, which agrees with the experimental data for the X(5568) and could support its interpretation in terms of a 0~+ tetraquark state with the scalar-scalar configuration. The corresponding result for the axial-axial current is calculated to be 5.77+0.44 still consistent with the mass of X(5568) in view of the uncertainty. The feasibility of-0.33 Ge V, which isX(5568) being a tetraquark state with the axial-axial configuration therefore cannot be definitely excluded. For the pseudoscalar-pseudoscalar and the vector-vector cases, their unsatisfactory OPE convergence make it difficult to find reasonable work windows to extract the hadronic information.     

QCD sum rules and pion wave functions

We consider light cone sum rules for a vertex function involving a pion state. These incorporate radiative corrections, continuum effects and power corrections; the latter depend on the non-asymptotic form of a higher twist component of the pion wave function. We derive restrictions on this component from sum rules for two-point functions and propose a model wave function for it. Finally we analyse our vertex sum rules in the light of this information and find results for the lowest twist component in good agreement with those already obtained from two-point function sum rules with derivative currents.     

Three-body nuclear interactions in the QCD sum rules

The QCD sum rules used to calculate the characteristics of single-particle nucleons are reviewed briefly. The contribution from three-body forces to the nucleon self-energies are calculated.     

QCD sum rules for nucleon-nucleon and hyperon-nucleon interactions

The QCD sum rules for spin-dependent nucleon-nucleon (N N) and hyperon-nucleon (Y N) interactions are formulated and their physical implications are clarified. A dispersion integral around the nucleon threshold can be identified as a measure of interaction strength. Calculating the operator product expansion (OPE) of the correlation function, we have found that the spin-dependent operators are related to the axial and tensor charges. The obtained sum rules relate the interaction strengths to the nucleon matrix elements of the quark-gluon operators. The spin-dependent parts are smaller than the spin-independent parts in the N N and the Y N channels. The spin-independent N N interaction strength is greater than the spin-independent Y N interaction strengths. The results are consistent with the empirical result in the N N channel.     

A Bayesian analysis of the nucleon QCD sum rules

QCD sum rules of the nucleon channel are reanalyzed, using the maximum-entropy method (MEM). This new approach, based on the Bayesian probability theory, does not restrict the spectral function to the usual “pole + continuum” form, allowing a more flexible investigation of the nucleon spectral function. Making use of this flexibility, we are able to investigate the spectral functions of various interpolating fields, finding that the nucleon ground state mainly couples to an operator containing a scalar diquark. Moreover, we formulate the Gaussian sum rule for the nucleon channel and find that it is more suitable for the MEM analysis to extract the nucleon pole in the region of its experimental value, while the Borel sum rule does not contain enough information to clearly separate the nucleon pole from the continuum.