On QCD sum rules of the Laplace transform type and light quark masses

We discuss the relation between the usual dispersion relation sum rules and the Laplace transform type sum rules in QCD. Two specific examples corresponding to the ?-coupling constant sum rule and the light quark masses sum rules are considered. An interpretation, within QCD, of Leutwyler's formula for the current algebra quark masses is also given.     

QCD finite energy sum rule calculation of the K → vacuum weak amplitude

The kaon-to-vacuum weak amplitude is discussed using the QCD finite energy sum rule approach. Its structure in terms of quark masses and other parameters of the theory is elucidated. Numerical estimates are also given.     

A comprehensive revisit of the ρ meson with improved Monte-Carlo based QCD sum rules

We improve the Monte-Carlo based QCD sum rules by introducing the rigorous H¨older-inequalitydetermined sum rule window and a Breit-Wigner type parametrization for the phenomenological spectral function.In this improved sum rule analysis methodology, the sum rule analysis window can be determined without any assumptions on OPE convergence or the QCD continuum. Therefore, an unbiased prediction can be obtained for the phenomenological parameters(the hadronic mass and width etc.). We test the new approach in the ρ meson channel with re-examination and inclusion of α_s corrections to dimension-4 condensates in the OPE. We obtain results highly consistent with experimental values. We also discuss the possible extension of this method to some other channels.     

夸克的横向性分布与核子张量荷

夸克的横向性分布的一次矩定义了核子张量荷. 核子张量荷也可用张量流算符在核子态的矩阵元定义,由此用量子色动力学求和规则、有效理论和模型计算了核子张量荷. 对研究核子性质及强子物理的自洽非微扰途径问题也作了简要讨论. The first moment of quark transversity distribution defines the tensor charge of nucleon. The tensor charge of nucleon can also be defined as the forward matrix element of the tensor current in the nucleon state，which is used to study the nucleon’s tensor charge in terms of quantum color dynamics(QCD) sum rule approach， the effective theory and model. A consistent nonperturbative approach to study nucleon property and hadronic physics is also discussed.     

On the applicability of perturbative QCD to exclusive processes at currently available momentum transfer

We re-examine the problems connected with the end-point dominance in the calculation of exclusive processes in perturbative QCD. In a re-analysis we construct nucleon quark distribution amplitudes from the respective moments obtained from a QCD sum rule approach. These functions lead to acceptable values for the e.m. Dirac form factorsF ₁ ^p,n of the nucleon if effective gluon masses of ca. 300–600 MeV are included into the hard-scattering amplitude. In addition we also find a reasonable Q₂ — dependence of the proton form factor. The results point at the importance of the end-point k-dependence of distribution amplitude and hard-scattering amplitude in the calculation of exclusive processes.Work is supported by Deutsche Forschungsgemeinschaft (Ga 153-13-1) and partially by NATO (0581/87)     

Understanding light scalar meson by color-magnetic wave function in QCD sum rule

In this paper, we study the 0⁺ nonet mesons as tetraquark states with interpolating currents inspired by the color-magnetic wave function. This wave function is the eigenfunction of an effective color-magnetic Hamiltonian with the lowest eigenvalue, meaning that the state depicted by this wave function is the most stable one and is the most probable to be observed in experiments. We perform an OPE calculation up to dimension-eight condensates and find that the best QCD sum rule is achieved when the current inspired by the color-magnetic wave function is a proper mixture of the tensor and pseudoscalar diquark-antidiquark bound states. Compared with previous results, to sigma(600) and kappa(800), our results appear better, due to larger pole contribution. The direct instanton contributions are also considered, which yields a consistent result with previous OPE results. Finally, we also discuss the h￠ \eta{^\prime} problem as a possible six-quark state.     

Rho Meson Distribution Amplitudes from QCD Sum Rules with Nonlocal Condensates

The leading-twist distribution amplitude for the longitudinal rho-meson was studied using QCD Sum Rules with nonlocal condensates and a spectral density which includes next-to-leading order radiative corrections. The obtained profile is compared with results from standard QCD sum rules, lattice QCD, holographic QCD, a light-front quark model, and the instanton liquid model. Preliminary estimates for the first two moments of the transverse ρ-meson distribution amplitude are also given.     

Light quark masses from scalar sum rules

In this work, the mass of the strange quark is calculated from QCD sum rules for the divergence of the strangeness-changing vector current. The phenomenological scalar spectral function which enters the sum rule is determined from our previous work on strangeness-changing scalar form factors [1]. For the running strange mass in the scheme, we find . Making use of this result and the light quark mass ratios obtained from chiral perturbation theory, we are also able to extract the masses of the lighter quarks and . We then obtain and . In addition, we present an updated value for the light quark condensate. Received: 18 October 2001 / Revised version: 22 January 2002 / Published online: 12 April 2002     

Heavy-light current correlators at order \alpha_\mathrm{s}^2 in QCD and HQET

The non-diagonal correlators of vector and scalar currents are considered at three-loop order in QCD. The full mass dependence is computed in the case where one of the quarks is massless and the other one carries mass M. We exploit the decoupling relations between the full theory and the heavy quark effective theory (HQET) in order to obtain the logarithmic parts of the leading threshold terms. With the help of conformal mapping and Padé approximation numerical estimates for the non-logarithmic terms are extracted which in turn lead to a prediction of the correlator in HQET at order . As applications of the vector and scalar correlator we consider the single-top-quark production via the process and the decay rate of a charged Higgs boson into hadrons, respectively. In both cases the computed NLO corrections are shown to be numerically much less important than the leading ones. On the contrary, the NLO order QCD corrections to the HQET sum rule for the leptonic decay rate of a heavy-light meson proves to be comparable to the leading one. Received: 19 June 2001 / Published online: 10 August 2001     

Instanton interpolating current for σ-tetraquark

We perform a QCD sum rule analysis for the light scalar meson σ   (f₀(600)$f_0(600)$) with a tetraquark current related to the instanton picture for QCD vacuum. We demonstrate that instanton current, including equal weights of scalar and pseudoscalar diquark–antidiquarks, leads to a strong cancelation between the contributions of high dimension operators in the operator product expansion (OPE). Furthermore, in the case of this current direct instanton contributions do not spoil the sum rules. Our calculation, obtained from the OPE up to dimension 10 operators, gives the mass of σ-meson around 780 MeV.     

The second moments of quark and gluon distribution functions in nucleon

The second moments of quark and gluon distribution functions in proton are calculated on the basis of the QCD sum rule approach. The results obtained are in a good agreement with the experimental data.     

Bc（B）→DIv^- Form Factors in Light-Cone Sum Rules and the D-Meson Distribution Amplitude

We calculate the weak form factors of the decays Be（B） → Dlv^- by using the chiral current correlator within the framework of the QCD light-cone sum rules （LCSRs）. The expressions of the form factors only depend on the leading twist distribution amplitude （DA） of the D meson. Three models of the D-meson distribution amplitude are employed. Our prediction, by using the D-meson distribution amplitude with the exponential suppression at the end points, favours the three-points sum rule （3PSR） approach with the Coulomb corrections included, and is compatible with other approaches.     

Parity Projected QCD Sum Rule of the Nucleon with MEM

The nucleon and its negative-parity excited states are examined in a maximum entropy method analysis of QCD sum rules. We derive the parity projected nucleon sum rules with all known first order α _s corrections to the Wilson coefficients of the operator product expansion (OPE). As these corrections have turned out to be large, we suppress them by using a phase-rotated Gaussian kernel. This phase rotation strongly suppresses the continuum contribution and improves the convergence of the OPE. The resulting sum rule has the interesting feature that it is dominated by the term containing the chiral condensate of dimension 3. Analyzing this sum rule by the maximum entropy method, we are able to extract information of both the positive and negative parity states.     

Techniques of dimensional regularization and the two-point functions of QCD and QED

The necessary and useful tools of dimensional regularization (and renormalization), the so-called ?-scheme, are reviewed. A survey on a comparison of various renormalization schemes is done. The applications of the ?-scheme to the two-point funtions of quantum chromodynamics (QCD) and quantum electrodynamics (QED) are given. In these applications it is shown explicitly how to compute Feynman diagrams and how to use the renormalization group equation (RGE) for the prediction of some terms induced by higher order diagrams. Some phenomenological uses of the two-point functions are briefly discussed. These include the quark mass, the spectral function sum rules in QCD and the control of the asymptotic SU(n)×SU(n) flavour chiral symmetry, the proton-neutron electromagnetic mass difference in the light of QCD and the running electromagnetic charge of QED. We also confront the operator product expansion (OPE) results of the anomalous dimension of non-singlet operators to the result obtained from the method of factorization of mass singularities.     

Gluon distributions in real and virtual photon and the photon structure function

Gluon distributions in real and virtual photons are calculated using evolution equations in the NLO approximation. The quark distributions in the photon determined on the basis of the QCD sum rule approach in [1] are taken as an input. It is shown that gluon distribution in the photon can be reliably determined up tox=0.03÷0.05, much lower than the corresponding values in the case of quark distributions. Two variants of the calculations are considered: (1) it is assumed that there are no intrinsic gluons in the photon at some low normalization pointQ ²=Q ₀ ² ∼1GeV²; (2) it is assumed that gluonic content of the photon at lowQ ₀ ² is described by gluonic content of vector mesonsρ, ω, ϕ. The gluon distributions in these two variants appear to be different. This fact permits one to clarify the origin of nonperturbative gluonic content of the photon by comparing the results with experiment. Structure functionsF ₂(x) for real and virtual photon are calculated and it is shown that in the regionx≥0.2 where QCD approach is valid, there is a good agreement with experiment.     

Moments of the heavy-quark parton distribution function from QCD sum rules

The moments of the heavy-quark parton distribution functions in a heavy pseudoscalar meson are calculated from QCD sum rules. Expanding these sum rules in the inverse heavy-quark mass we obtain the heavy-mass limits of the moments. Comparison with the finite-mass results reveals that while the heavy-mass expansion works reasonably well for the b quark, one has to take into account terms of higher order than (1/m _c )² for the c quark. This result can provide a quantitative assessment of c- and b-quark fragmentation models based on the heavy-quark mass limit. The text was submitted by the authors in English.     

OPE, charm-quark mass, and decay constants of D and Ds mesons from QCD sum rules

We present a sum-rule extraction of the decay constants of the charmed mesons D and Ds from the two-point correlator of pseudoscalar currents. First, we compare the perturbative expansion for the correlator and the decay constant performed in terms of the pole and the running MSˉ masses of the charm quark. The perturbative expansion in terms of the pole mass shows no signs of convergence whereas reorganizing this very expansion in terms of the MSˉ mass leads to a distinct hierarchy of the perturbative expansion. Furthermore, the decay constants extracted from the pole-mass correlator turn out to be considerably smaller than those obtained by means of the MSˉ-mass correlator. Second, making use of the OPE in terms of the MSˉ mass, we determine the decay constants of both D and Ds mesons with an emphasis on the uncertainties in these quantities related both to the input QCD parameters and to the limited accuracy of the method of sum rules.     

A perturbative QCD estimate of the η1-Mass

Using perturbative QCD expansions for the two-point correlation function of the U_A(1) current in a properly constructed dispersion sum rule, and using a previously obtained estimate for the strange quark mass, we obtain a realistic upper bound on the η₁-mass.     

OPE and sum rules for correlators of pseudoscalar and axial currents

We study the operator product expansion (OPE) and quark-hadron duality for two-and three-point correlators of the axial (A) and pseudoscalar (P) currents of the light quarks. In the chiral limit, these correlators are often dominated by nonperturbative power corrections leading to subtleties of quark-hadron duality relations and of the extraction of properties of light pseudoscalars. For the two-point correlators, we show the sum rule for 〈PP〉 to be sensitive to the excited light pseudoscalar. For the three-point correlators, we derive the Ward identities which provide the normalization of the pion electromagnetic form factor at zero momentum transfer. For large momentum transfer, we demonstrate the way the correct behavior of the pion form factor in agreement with perturbative QCD emerges from condensate terms in the OPE for the 〈PV P〉 and 〈AV P〉 correlators. The local-duality sum rule for 〈AV A〉 is shown to lead to the pion form factor with the required properties for all values of the momentum transfer. The text was submitted by the authors in English. On leave from Institute of Nuclear Physics, Moscow State University, Moscow, Russia.