Vertex QCD sum rules,quark model and pion wave function

It is shown that the predictions of the QCD sum rules (SR) and the quark model for the low energy pion wave function can be reconciled within the so-called vertex SR in exclusive kinematics. In contrast to the standard procedure, non-singular terms asx→0 in correlation functions are summed up by means of the conformal symmetry arguments. The soft contribution into the pion form factor is argued to dominate at least up toQ ²～4–6 GeV²     

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     

QCD sum rules for heavy quark systems

In this paper we present in a detailed and coherent fashion our work on QCD sum rules for equal mass heavy quark meson states. We discuss the technical procedures used to calculate the perturbative and non-perturbative contributions to the vacuum polarization, which have been calculated for all currents up to and including spin 2⁺⁺. Using dispersion relations, sum rules are derived. Extensive applications are made to the lowest lying states of the charmonium and upsilon systems. The masses of the S- and P-wave charmonium levels are reproduced to a high degree of accuracy, and the mass of the ¹P₁ level is predicted at 3.51 GeV. For the upsilon system it only appears to be possible to predict the γ-η_b splitting which gives 60 MeV. Very accurate values are given for the current quark masses at p² = ?m_q²: m_c = 1.28 GeV and m_b = 4.25 GeV.     

New contributions to heavy quark sum rules

We analyze new contributions to the theoretical input in heavy quark sum rules and we show that the general theory of singularities of perturbation theory amplitudes yields the method to handle these specific features. In particular we study the inclusion of heavy quark radiation by light quarks at and of non-symmetric correlators at . Closely related with this is that we also propose a solution to the construction of moments of the spectral densities at where the presence of massless contributions invalidates the standard approach. We circumvent this problem through a new definition of the moments, providing an infrared safe and consistent procedure. Received: 11 February 2002 / Revised version: 14 March 2002 / Published online: 22 May 2002     

The strange quark mass from QCD sum rules

The strange quark mass is calculated from QCD sum rules for the divergence of the vector as well as axialvector current in the next-next-to-leading logarithmic approximation. The determination for the divergence of the axial-vector current is found to be unreliable due to large uncertainties in the hadronic parametrisation of the two-point function.From the sum rule for the divergence of the vector current, we obtain a value of (1 GeV)=189±32 MeV, where the error is dominated by the unknown perturbativeO( _s ³ ) correction. Assuming a continued geometric growth of the perturbation series, we findm _s =178±18 MeV. Using both determinations ofm _s , together with quark-mass ratios from chiral perturbation theory, we also give estimates of the light quark massesm _u andm _d.     

Hadronic corrections to QCD sum rules and light quark masses

A parametrization of theJ ^p =0^? hadronic continuum, in the framework of Extended PCAC, is discussed with emphasis on finite-width effects and on the constraints imposed by the correct threshold behavior of the pion spectral function. As an application light quark masses are calculated using both Hilbert and Laplace transform QCD sum rules. The results for the runing quark masses are: \((\bar m_u + \bar m_d )|_{1 Gev} = 16 \pm 2 MeV,(\bar m_u + \bar m_s )|_{1 Gev} = 199 \pm 27 MeV\) , and a ratio \(R \equiv 2(\bar m_u + \bar m_s )/(\bar m_u + \bar m_d )_{1 Gev} = 25 \pm 4\) .     

Cross-section sum rules and inequalities in a quark model for light and heavy flavour productions

The model for inclusive processes is reformulated to consider the production of heavy flavours (c, b andt) and higher order flavour exchange effects. Predictions are made in terms of sum rules and inequalities for various inclusive cross-sections. Plausible parametrization of flavour symmetry breaking is also suggested.     

The Drell-Hearn-Gerasimov sum rule and the constituent quark model

The helicity structure function of the nucleon has been calculated for the constituent quark model and compared to the prediction of the Drell-Hearn-Gerasimov sum rule. The multipole decomposition of the sum rule shows large cancellations between different resonances. The small isoscalar-isovector contribution is related to the admixture of aD-state (bag deformation) in the nucleon's wave function. The calculations indicate a relatively slow saturation of this part of the sum rule with excitation energy.Work supported by Deutsche Forschungsgemeinschaft and Istituto Nazionale di Fisica Nucleare     

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.     

On the choice of quark currents in the QCD sum rules for baryon masses

The cryteria for the choice of the most suitable quark currents in the QCD sum rules for baryon masses are discussed. The currents used in [1, 2] are preferable comparing with those adopted in [3, 4] since the latters result in large power corrections.     

Nonlocal condensate model for QCD sum rules

We include effects of nonlocal quark condensates into QCD sum rules (QSR) via the Källén–Lehmann representation for a dressed fermion propagator, in which a negative spectral density function manifests their nonperturbative nature. Applying our formalism to the pion form factor as an example, QSR results are in good agreement with data for momentum transfer squared up to Q²≈10 GeV²$Q^2\approx 10{\text{GeV}}^2$. It is observed that the nonlocal quark condensate contribution descends like 1/Q²$1/Q^2$, different from the exponential decrease in Q²$Q^2$ obtained in the literature, and contrary to the linear rise in the local-condensate approximation.