The Pion-Photon Transition Form Factor and New Physics in the Tau Sector

Abstract

Recent measurement of the $γγ^\ast$ form factor of the neutral pion in the high $Q^2$ region disagrees with {\em a priori} predictions of QCD-based calculations. We comment on existing explanations, and analyze a possibility that this discrepancy is not due to poorly understood QCD effects, but is a result of some new physics beyond the standard model (SM). We show that such physics would necessarily involve a new neutral light state with mass close to the mass of $π^0$, and with stronger than $π^0$ couplings to heavier SM flavors such as $c$, $τ$, and $b$. It is found that only the coupling to the $τ$ lepton can survive the existing constraints and lead to the observed rise of the pion form factor relative to $Q^{-2}$ at high $Q^2$. We perform numerical fits to data and determine the allowed range of masses and couplings for such new particles. This range of masses and couplings could also reduce or eliminate the tension between the $e^+e^-$ and $τ$ decay determinations of the hadronic vacuum polarization. Dedicated experimental analysis of $τ$ pair production in association with such new states should provide a conclusive test of the new physics hypothesis as an explanation to the pion form factor rise. We also comment on the calculations of the pion form factor in the chiral quark model, and point out a possible dynamical origin of the quark mass scale inferred from the form factor measurement.