ρ0–γ mixing in the neutral channel pion form factor $F^{(e)}_{\pi}(s)$ and its role in comparing e+e− with τ spectral functions

By F. Jegerlehner, R. Szafron. 2011

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We study the effect of ρ0–γ mixing in e+e−→π+π− and its relevance for the comparison of the square modulus of the pion from-factor $|F_{\pi }^{(e)}(s)|^{2}$, as measured in e+e− annihilation experiments, and $|F_{\pi }^{(\tau )}(s)|^{2}$  the corresponding quantity obtained after accounting for known isospin breaking effects by an isospin rotation from the τ-decay spectra. After correcting the τ data for the missing ρ–γ mixing contribution, besides the other known isospin symmetry violating corrections, the ππI=1 part of the hadronic vacuum polarization contribution to the muon g−2 are fully compatible between τ based and e+e− based evaluations. τ data thus confirm result obtained with e+e− data. Our evaluation of the leading order vacuum polarization contribution, based on all e+e− data including more recent BaBar and KLOE data, yields $a_{\mu}^{\mathrm{had,LO}}[e]=690.75(4.72)\times 10^{-10}$ (e+e− based), while including τ data we find $a_{\mu}^{\mathrm{had,LO}}[e,\tau]=690.96(4.65)\times 10^{-10}$ (e+e−+τ based). This backs the ∼3σ deviation between $a_{\mu}^{\mathrm{experiment}}$ and $a_{\mu}^{\mathrm{theory}}$. For the τ di-pion branching fraction we find $B^{\mathrm{CVC}}_{\pi\pi^{0}}=25.20\pm0.17\pm0.28$ from e+e−+CVC, while $B_{\pi\pi^{0}}=25.34\pm0.06\pm0.08$ is evaluated directly from the τ spectra.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/2bf6a6d8331089c38e7fcbe70c53d07dbee8b68f

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In Nuclear and High Energy Physics

  1. David M. Straub
  2. Aoife Bharucha
  3. R. Zwicky
  4. S. Descotes-Genon
  5. W. Altmannshofer
  6. Andrzej Buras
  7. T. Hurth
  8. D. London

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