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Register a new userHard two photon processes gammagamma --> M_2 M_1 in QCD
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Authors
Victor L. Chernyak
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A short review of leading term QCD predictions vs those of the handbag model for large angle cross sections gammagamma --> P_2 P_1 (P is the pseudoscalar meson pi^{pm,o}, K^{pm,o}, eta), and for gammagamma --> V_2 V_1 (V is the neutral vector meson rho^o, omega, phi), in comparison with Belle Collaboration measuments
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This is a short review of some hard two-photon processes: $ a) ,,gammagammato {overline P}_1 P_2,,, {overline P}_1 P_2= {pi^+pi^-, K^+ K^-, K_S K_S, pi^opi^o, pi^oeta},, b) ,,gammagammato V_1 V_2,,, V_1 V_2={rho^orho^o, phiphi, omegaphi, omegaomega }, c) ,,gammagammato {rm baryon-antibaryon}, d) ,,gamma^*gammato P^o,,, P^o={pi^o, eta, eta^prime, eta_c}$. The available experimental data are presented. A number of theoretical approaches to calculation of these processes is described, both those based mainly on QCD and more phenomenological (the handbag model, the diquark model, etc). Some theoretical questions tightly connected with this subject are discussed, in particular: the applications of various types of QCD sum rules, the endpoint behavior of the leading twist meson wave functions, etc.
We summarize the standard factorization theorems for hard processes in QCD, and describe their proofs.
Using some techniques of conformal field theories, we find a closed expression for the contribution of leading twist operators and their descendants, obtained by adding total derivatives, to the operator product expansion (OPE) of two electromagnetic currents in QCD. Our expression resums contributions of all twists and to all orders in perturbation theory up to corrections proportional to the QCD $beta$-function. At tree level and to twist-four accuracy, our result agrees with the expression derived earlier by a different method. The results are directly applicable to deeply-virtual Compton scattering and, e.g., $gammagamma^ast$ annihilation in two mesons. As a byproduct, we derive a simple representation for the OPE of two scalar currents that is convenient for applications.
We investigate the azimuthal angular correlation between the lepton transverse momentum $P_perp$ and the impact parameter $b_perp$ in non-central heavy-ion collisions, where the leptons are produced through two-photon scattering. Among the Fourier harmonic coefficients, a significant $v_4$ asymmetry is found for the typical kinematics at RHIC and LHC with a mild dependence on the $P_perp$, whereas $v_2$ is power suppressed by the lepton mass over $P_perp$. This unique prediction, if confirmed from the experiments, shall provide crucial information on the production mechanism for the dilepton in two-photon processes.
We discuss some problems concerning the application of perturbative QCD to high energy processes. In particular for hard processes, we analyze higher order and higher twist corrections. It is argued that these effects are of great importance for understanding the behaviour of pion electromagnetic form factor at moderately large momentum transfers. For soft processes, we show that summing the contributions of the lowest twist operators leads to a Regge-like amplitude.
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