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Register a new userThe gamma(*) pi(0) -> gamma form factor
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The gamma(*) pi(0) -> gamma form factor is obtained within the Lagrangian quark model with separable interaction known to provide a good description of the pion observables at low energies. The pion-quarks vertex is chosen in a Gaussian form. The form factor obtained is close to the available experimental data and reaches smoothly the Brodsky-Lepage limit at Q2 = 10 GeV2.
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An intrinsic form factor has benn found and the slope of the form factor has been predicted.
The calculation of the hadronic light-by-light scattering contribution to the muon g-2 currently relies entirely on models. Measurements of the form factors which describe the interactions of hadrons with photons can help to constrain the models and reduce the uncertainty in a_{mu}(had. LbyL) = (116 pm 40) x 10^{-11}. In the dominant pion-exchange contribution, the form factor F_{{pi^0}^*gamma^*gamma^*}((q_1 + q_2)^2, q_1^2, q_2^2) with an off-shell pion enters. In general, measurements of the transition form factor F(Q^2) = F_{{pi^0}^*gamma^*gamma^*}(m_{pi}^2, -Q^2, 0) are only sensitive to a subset of the model parameters. Thus, having a good description for F(Q^2) is only necessary, not sufficient, to determine a_{mu}(LbyL; pi^0). Simulations have shown that measurements at KLOE-2 should be able to determine the (pi^0 -> gamma gamma) decay width to 1% statistical precision and the transition form factor for small space-like momenta, 0.01 GeV^2 < Q^2 < 0.1 GeV^2, to 6% precision. In the two-loop integral for the pion-exchange contribution the relevant regions of momenta are in the range 0 - 1.5 GeV. With the (pi^0 -> gamma gamma) decay width from the PDG [PrimEx] and current data for the transition form factor, the error on a_{mu}(LbyL; pi^0) is (pm 4 x 10^{-11}) [pm 2 x 10^{-11}], not taking into account the uncertainty related to the off-shellness of the pion. Including the simulated KLOE-2 data reduces the error to (pm (0.7 - 1.1) x 10^{-11}). For models like VMD, which have only few parameters that are completely determined by measurements of F(Q^2), this represents the total error. But maybe such models are too simplistic. In other models, e.g. those based on large-N_c QCD, parameters describing the off-shell pion dominate the uncertainty in a_{mu; large-N_c}(LbyL; pi^0) = (72 pm 12) x 10^{-11}.
We discuss, how planned measurements at KLOE-2 of the (pi^0 -> gamma gamma) decay width and the (gamma^* gamma -> pi^0) transition form factor can improve estimates for the numerically dominant pion-exchange contribution to hadronic light-by-light scattering in the muon g-2 and what are the limitations related to the modelling of the off-shellness of the pion.
The ratio R_{eta}=Gamma(eta -> pi^+pi^-gamma)/Gamma(eta -> pi^+pi^-pi^0) has been measured by analyzing 22 million phi to eta gamma decays collected by the KLOE experiment at DAPhiNE, corresponding to an integrated luminosity of 558 pb^{-1}. The eta to pi^+pi^-gamma proceeds both via the rho resonant contribution, and possibly a non-resonant direct term, connected to the box anomaly. Our result, R_{eta}= 0.1856pm 0.0005_{stat} pm 0.0028_{syst}, points out a sizable contribution of the direct term to the total width. The di-pion invariant mass for the eta -> pi^+pi^-gamma decay could be described in a model-independent approach in terms of a single free parameter, alpha. The determined value of the parameter alpha is alpha = (1.32 pm 0.08_{stat} +0.10/-0.09_{syst}pm 0.02_{theo}) GeV^{-2}
We have resummed all the (-b_0 alpha_s)^n contributions to the photon-meson transition form factor F_{gamma pi}. To do this, we have used the assumption of `naive nonabelianization (NNA). Within NNA, a series in (N_f alfa_s)^n is interpreted as a series in (-b_0 alpha_S)^n by means of the restoration of the full first QCD beta-function coefficient -b_0 by hand. We have taken into account corrections to the leading order coefficient function and to the evolution of the distribution function. Due to conformal constraints, it is possible to find the eigenfunctions of the evolution kernel. It turns out that the nondiagonal corrections are small, and neglecting them we obtained a representation for the distribution function with multiplicatively renormalized moments. For a simple shape of the distribution function, which is close to the asymptotic shape, we find that the radiative correction decrease the LO by 30 % and the uncertainty in the resummation lies between 10 % and 2 % for Q^2 between 2 and 10 GeV^2.
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