**Authors:** Matti Pitkänen

The recent discovery of CDF anomaly suggest the existence of a new long-lived particle which means a dramatic deviation from standard model. This article summarizes the quantum model of CDF anomaly. The anomaly is interpreted in terms of production of τ-pions which can be regarded as pion like bound states of color octet excitations of τ-leptons and corresponding neutrinos. Colored leptons are one of the basic predictions of TGD distinguishing it from standard model and for 18 years ago were applied to explain the anomalous production of electron-positron pairs in heavy ion collisions near Coulomb wall. First it is shown that the model explains the basic characteristics of the anomaly. Then various alternatives generalizing the earlier model for electro-pion production are discussed and a general formula for differential cross section is deduced. Three alternatives inspired by eikonal approximation generalizing the earlier model inspired by Born approximation to a perturbation series in the Coulomb interaction potential of the colliding charges. The requirement of manifest relativistic invariance for the formula of differential cross section leaves only two options, call them I and II. The production cross section for τ-pion is estimated and found to be consistent with the reported cross section of order 100 pb for option I using same energy cutoff for lepto-pions as in the model for electro-pion production. For option II the production cross section is by several orders of magnitude too small under these assumptions. Since the model involves only fundamental coupling constants, the result can be regarded as a further success of the τ-pion model of CDF anomaly. Analytic expressions for the production amplitude are deduced in the Appendix as a Fourier transform for the inner product of the non-orthogonal magnetic and electric fields of the colliding charges in various kinematical situations. This allows to reduce numerical integrations to an integral over the phase space of lepto-pion and gives a tight analytic control over the numerics.

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[v1] 9 Dec 2008

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