# Axial vector and pseudoscalar hadronic structure in tau- → pi-pi-pi+nutau decays with implications on light quark masses

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- Purdue University
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## Abstract

After a survey of the basic concepts in high energy physics, a model-dependent analysis of the substructure in τ± → π ±π±π∓( ντ/ντ) decays is presented. The analysis is based on 145,000 decays skimmed from a sample of 4.3 × 106 e+e − → τ+τ− events collected by the CLEO II detector operating at the CESR collider. The hadronic transition current in the τ± → π ±π±π∓( ντ/ντ) decay is described by modeling the axial vector a1(1260) and pseudoscalar π ′(1300) primary resonances and their sub-resonances. An unbinned maximum likelihood fit is used to extract the complex amplitude for each sub-resonance, producing a distribution that accounts well for the data. Two model variations are also considered, including one in which corrections due to a more general chiral limit induce pseudoscalar-like terms from the axial vector components and introduce a non-resonant term. All models are found to reasonable describe the data. As expected, the decay is found to be dominated by s-wave a1 → ρπ, which contributed around 70–75% of the τ± → π±π ±π∓(ν τ/ντ) rate, depending on the model used. Statistically significant contributions are also found for d-wave ρπ and ρ′π amplitudes as well as amplitudes involving isoscalars, f2(1270), π, σπ, and f0(1270)π. The isoscalar contributions are particularly prominent, as are interferences involving those terms. As a whole, they contributed around 15–17% to the total τ± → π ±π±π∓( ντ/ντ) rate, depending on the model. Contributions from the pseudoscalar π′ sub-resonances are generally statistically insignificant, though their minimal improvements are shown to lie where one would expect. Upper limits are placed on each of the considered π′ contributions at 90% confidence. The results found for the pseudoscalar contributions are used to place a lower limit on the average of the up and down quark running masses [mˆ ≡ (mu + md)/2] that appear in the QCD Lagrangian [57]. This produced a 90% confidence limit of mˆ(1 GeV2) > 8.3 − 14.2 MeV, depending on the model. Though that result may be higher than expected, it is reasonable given the particulars of the analysis. ^

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