Study of pion vector form factor and its contribution to the muon $(g-2)$

Abstract

In the present work, we investigate several theoretical models of the pion vector form factor and aim at getting the best fit for the two-pion cross sections to reduce the uncertainties of the calculation of two-pion contribution to the muon anomalous magnetic moment. Combined with a polynomial description to the pion vector form factor, we obtain the best fit from the Gounaris-Sakurai (or Kühn-Santamaria) model for the experimental data up to 1 GeV. By product, the branching ratio of $\omega \to \pi \pi$ can be extracted as $\text{Br}(\omega \to \pi \pi )=(1.52\pm 0.06)\%$, which is consistent with the one of Particle Data Group. With the best fit of the data, we obtain the muon anomalous magnetic moment from two-pion contribution as $a_{\mu }^{\mathrm{HVP},\mathrm{LO}}({\pi }^{+}{\pi }^{-}\le 1\text{GeV})=(497.76\pm 3.15)\times 10^{-10}$. Our results are consistent with the other works.

Comments: Updated with more references. More discussions can be referred to the published one