Exclusive processes in position space and the pion distribution amplitude

We suggest to carry out lattice calculations of current correlators in position space, sandwiched between the vacuum and a hadron state (e.g. pion), in order to access hadronic light-cone distribution amplitudes (DAs). In this way the renormalization problem for composite lattice operators is avoided altogether, and the connection to the DA is done using perturbation theory in the continuum. As an example, the correlation function of two electromagnetic currents is calculated to the next-to-next-to-leading order accuracy in perturbation theory and including the twist-4 corrections. We argue that this strategy is fully competitive with direct lattice measurements of the moments of the DA, defined as matrix elements of local operators, and offers new insight in the space-time picture of hard exclusive reactions.Comment: 15 pages, 10 figure

Power corrections to the π0γ\pi^0\gamma transition form factor and pion distribution amplitudes

Employing the standard hard-scattering approach and the running coupling method we calculate a class of power-suppressed corrections $\sim 1/Q^{2n},n=1,2,3,...$ to the electromagnetic $\pi^0\gamma$ transition form factor (FF) $Q^2F_{\pi\gamma}(Q^2)$ arising from the end-point $x \to 0,1$ integration regions. In the investigations we use a hard-scattering amplitude of the subprocess $\gamma+\gamma^{*} \to q +\bar{q}$, symmetrized under exchange $\mu_R^2 \leftrightarrow \bar{\mu}_R^2$ important for exclusive processes containing two external photons. In the computations the pion model distribution amplitudes (DA's) with one and two non-asymptotic terms are employed. The obtained predictions are compared with the CLEO data and constraints on the DA parameters $b_2(\mu_0^2)$ and $b_4(\mu_0^2)$ at the normalization point $\mu_0^2=1 GeV^2$ are extracted. Further restrictions on the pion DA's are deduced from the experimental data on the electromagnetic FF $F_{\pi}(Q^2)$.Comment: 23 pages, 6 figures; the version published in Phys. Rev. D69, 094010 (2004

Pion light cone wave function in the non-local NJL model

We use the simple instanton motivated NJL-type model to calculate the leading twist pion light cone wave function. The model consists in employing the momentum dependent quark mass in the quark loop entering the definition of the wave function. The result is analytical up to a solution of a certain algebraic equation. Various properties including the kT dependence of the pion wave function are discussed. The resulting kT integrated wave function is not asymptotic and is in agreement with recent analysis of the CLEO data.Comment: 9 pages, 12 figures, formulas (23-25) corrected, typos correcte

Unbiased analysis of CLEO data at NLO and pion distribution amplitude

We discuss different QCD approaches to calculate the form factor F^{\gamma^*\gamma\pi}(Q^2) of the \gamma^*\gamma\to\pi^{0} transition giving preference to the light-cone QCD sum rules (LCSR) approach as being the most adequate. In this context we revise the previous analysis of the CLEO experimental data on F^{\gamma^*\gamma\pi}(Q^{2}) by Schmedding and Yakovlev. Special attention is paid to the sensitivity of the results to the (strong radiative) \alpha_s-corrections and to the value of the twist-four coupling \delta^2. We present a full analysis of the CLEO data at the NLO level of LCSRs, focusing particular attention to the extraction of the relevant parameters to determine the pion distribution amplitude, i.e., the Gegenbauer coefficients a_2 and a_4. Our analysis confirms our previous results and also the main findings of Schmedding and Yakovlev: both the asymptotic, as well as the Chernyak--Zhitnitsky pion distribution amplitudes are completely excluded by the CLEO data. A novelty of our approach is to use the CLEO data as a means of determining the value of the QCD vacuum non-locality parameter \lambda^2_q = / =0.4 GeV^2, which specifies the average virtuality of the vacuum quarks.Comment: 25 pages, 5 figures, 4 tables; format and margins corrected to fit page size; small changes in the text and correction of misprint

Spectral quark model and low-energy hadron phenomenology

We propose a spectral quark model which can be applied to low energy hadronic physics. The approach is based on a generalization of the Lehmann representation of the quark propagator. We work at the one-quark-loop level. Electromagnetic and chiral invariance are ensured with help of the gauge technique which provides particular solutions to the Ward-Takahashi identities. General conditions on the quark spectral function follow from natural physical requirements. In particular, the function is normalized, its all positive moments must vanish, while the physical observables depend on negative moments and the so-called log-moments. As a consequence, the model is made finite, dispersion relations hold, chiral anomalies are preserved, and the twist expansion is free from logarithmic scaling violations, as requested of a low-energy model. We study a variety of processes and show that the framework is very simple and practical. Finally, incorporating the idea of vector-meson dominance, we present an explicit construction of the quark spectral function which satisfies all the requirements. The corresponding momentum representation of the resulting quark propagator exhibits only cuts on the physical axis, with no poles present anywhere in the complex momentum space. The momentum-dependent quark mass compares very well to recent lattice calculations. A large number of predictions and relations can be deduced from our approach for such quantities as the pion light-cone wave function, non-local quark condensate, pion transition form factor, pion valence parton distribution function, etc.Comment: revtex, 24 pages, 3 figure

Pion light-cone wave function and pion distribution amplitude in the Nambu-Jona-Lasinio model

We compute the pion light-cone wave function and the pion quark distribution amplitude in the Nambu-Jona-Lasinio model. We use the Pauli-Villars regularization method and as a result the distribution amplitude satisfies proper normalization and crossing properties. In the chiral limit we obtain the simple results, namely phi_pi(x)=1 for the pion distribution amplitude, and = -M / f_pi^2 for the second moment of the pion light-cone wave function, where M is the constituent quark mass and f_pi is the pion decay constant. After the QCD Gegenbauer evolution of the pion distribution amplitude good end-point behavior is recovered, and a satisfactory agreement with the analysis of the experimental data from CLEO is achieved. This allows us to determine the momentum scale corresponding to our model calculation, which is close to the value Q_0 = 313 MeV obtained earlier from the analogous analysis of the pion parton distribution function. The value of is, after the QCD evolution, around (400 MeV)^2. In addition, the model predicts a linear integral relation between the pion distribution amplitude and the parton distribution function of the pion, which holds at the leading-order QCD evolution.Comment: mistake in Eq.(38) correcte

Transverse lattice calculation of the pion light-cone wavefunctions

We calculate the light-cone wavefunctions of the pion by solving the meson boundstate problem in a coarse transverse lattice gauge theory using DLCQ. A large-N_c approximation is made and the light-cone Hamiltonian expanded in massive dynamical fields at fixed lattice spacing. In contrast to earlier calculations, we include contributions from states containing many gluonic link-fields between the quarks.The Hamiltonian is renormalised by a combination of covariance conditions on boundstates and fitting the physical masses M_rho and M_pi, decay constant f_pi, and the string tension sigma. Good covariance is obtained for the lightest 0^{-+} state, which we identify with the pion. Many observables can be deduced from its light-cone wavefunctions.After perturbative evolution,the quark valence structure function is found to be consistent with the experimental structure function deduced from Drell-Yan pi-nucleon data in the valence region x > 0.5. In addition, the pion distribution amplitude is consistent with the experimental distribution deduced from the pi gamma^* gamma transition form factor and diffractive dissociation. A new observable we calculate is the probability for quark helicity correlation. We find a 45% probability that the valence-quark helicities are aligned in the pion.Comment: 27 pages, 9 figure