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Register a new userStudy of the phi-pi0 transition form factor
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Simone Pacetti
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Recently the BaBar Collaboration published new data on the cross section for the annihilation e+e- -> phi pi0, obtained using the initial state radiation technique at a center of mass energy of 10.6 GeV. Such a process represents an interesting test bed for the quark model. Indeed, since the phi-pi0 production via e+e- annihilation proceeds through a mechanism which violates the Okubo-Zweig-Iizuka rule, the corresponding cross section could be characterized by contributions from non-qqbar bound states, like hybrids or tetraquarks. The phi-pi0 cross section is analyzed in connection with other data coming from different processes, that involve the same mesons, using a method which implements the analyticity in the phi-pi0 transition form factor by means of a dispersion relation procedure.
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We report a measurement of the process gamma gamma* --> pi0 with a 759 fb^{-1} data sample recorded with the Belle detector at the KEKB asymmetric-energy e+e- collider. The pion transition form factor, F(Q^2), is measured for the kinematical region 4 GeV^2 <~ Q^2 <~ 40 GeV^2, where -Q^2 is the invariant mass squared of a virtual photon. The measured values of Q^2|F(Q^2)| agree well with the previous measurements below Q^2 ~= 9 GeV^2 but do not exhibit the rapid growth in the higher Q^2 region seen in another recent measurement, which exceeds the asymptotic QCD expectation by as much as 50%.
The eta-photon transition form factor is evaluated in a formalism based on a phenomenological description at low values of the photon virtuality, and a QCD-based description at high photon virtualities, matching at a scale $Q_{0}^{2}$. The high photon virtuality description makes use of a Distribution Amplitude calculated in the Nambu-Jona-Lasinio model with Pauli-Villars regularization at the matching scale $Q_{0}^{2}$, and QCD evolution from $Q_{0}^{2}$ to higher values of $Q^{2}$. A good description of the available data is obtained. The analysis indicates that the recent data from the BaBar collaboration on pion and eta transition form factor can be well reproduced, if a small contribution of twist three at the matching scale $Q_{0}^{2}$ is included.
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.
We provide a theoretical update of the calculations of the pi0-gamma*-gamma form factor in the LCSR framework, including up to six polynomials in the conformal expansion of the pion distribution amplitude and taking into account twist-six corrections related to the photon emission at large distances. The results are compared with the calculations of the B-> pi l nu decay and pion electromagnetic form factors in the same framework. Our conclusion is that the recent BaBar measurements of the pi0-gamma*-gamma form factor at large momentum transfers are consistent with QCD, although they do suggest that the pion DA may have more structure than usually assumed.
A measurement of the vector to pseudoscalar conversion decay $phi to pi^0 e^+e^-$ with the KLOE experiment is presented. A sample of $sim 9500$ signal events was selected from a data set of 1.7 fb$^{-1}$ of $e^+e^-$ collisions at $sqrt{s} sim m_{phi}$ collected at the DA$Phi$NE $e^+e^-$ collider. These events were used to obtain the first measurement of the transition form factor $| F_{phi pi^0}(q^2) |$ and a new measurement of the branching ratio of the decay: $rm{BR},(phi to pi^0 e^+e^-) = (,1.35 pm 0.05^{,,+0.05}_{,,-0.10},) times 10 ^{-5}$. The result improves significantly on previous measurements and is in agreement with theoretical predictions.
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