Qcd Sum Rule Calculation Ofsup Transition Form Factor

The authors develop a QCD sum rule analysis of the form factor F{sub?{sup *}?{sup *}?°}(q2, Q2) in the region where virtuality of one of the spacelike photons is small q2 ≪ 1 GeV2 while another is large: Q2 ≳ 1 GeV2. They construct the operator product expansion suitable for this kinematic situation and obtain a QCD sum rule for F{sub?{sup *}{gamma}{sup *}?°}(0, Q2). Their results confirm expectation that the momentum transfer dependence of F{sub {gamma}{sup *}{gamma}{sup *}?°}(0,Q2) is close to interpolation between its Q2=0 value fixed by the axial anomaly and Q−2 pQCD behavior for large Q2. Their approach, in contrast to pQCD, does not require additional assumptions about the shape of the pion distribution amplitude {var_phi}{sub {pi}}(x). The absolute value of the 1/Q2 term obtained in this paper favors {var_phi}{sub {pi}}(x) close to the asymptotic form {var_phi}{sub {pi}}{sup as}(x) = 6f{sub {pi}}x(1-x).

Within the QCD sum rule approach, we develop a formalism that enables one to calculate the form factors of the heavy-light mesons in the m(sub)Q -> infinity limit. It is shown that the behaviour of the universal Isgur-Wise form factor is determined by the quark propagation function in imaginary time.

In this talk the author reports on recent progress in a few areas closely related to the virtual Compton scattering studies. In particular, he discusses the quark-hadron duality estimate of the[gamma][sup*]p[r-arrow][Delta][sup+] transition, QCD sum rule calculation of the[gamma][gamma][sup*][r-arrow][pi][sup 0] form factor, and application of perturbative QCD to deeply virtual Compton scattering at small t.

The shape of hadronic distribution amplitudes (DAs) is a critical issue for the perturbative QCD of hard exclusive processes. Recent CLEO data on [gamma][gamma]{sup *} → [pi]° form factor clearly favor a pion DA close to the asymptotic form. The author argues that QCD sum rules for the moments of the pion DA {var_phi}{sub [pi]}(x) are unreliable, so that the humpy shape of {var_phi}{sub {pi}}(x) obtained by Chernyak and Zhitnitsky is a result of model assumptions rather than an unambiguous consequence of QCD sum rules. This conclusion is also supported by a direct QCD sum rule calculation of the [gamma][gamma]{sup *} → {pi}° form factor which gives a result very close to the CLEO data.

In this paper the authors present the result of a direct QCD sum rule calculation of the transition form factor??{sup *} →?° in the region of moderately large invariant momentum Q2> 1GeV2 of the virtual photon. In contrast to pQCD, they make no assumptions about the shape of the pion distribution amplitude {var_phi}{sub?}(x). Their results agree with the Brodsky-Lepage proposal that the Q2-dependence of this form factor is given by an interpolation between its Q2=0 value fixed by the axial anomaly and 1/Q2 pQCD behavior for large Q2, with normalization corresponding to the asymptotic form {var_phi}{sub pi}{sup as}(x)=6 f{sub {pi}}x(1-x) of the pion distribution amplitude. Their prediction for the from factor F{sub?}{sup *}{gamma}{sup *}{pi}°(q12 = 0,q22 = -Q2) is in good agreement with new CLEO data.

Within the QCD sum rule approach, we develop a formalism that enables one to calculate the form factors of the heavy-light mesons in the m{sub Q} --> (infinity) limit. It is shown that the behavior of the universal Isgur-Wise form factor is determined by the quark propagation function in imaginary time.

We extend the QCD sum rule analysis of the pion electromagnetic form factor F(sub)pi(Q^2) into the region of moderately large momentum transfers 3GeV^2