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

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 $ω\to ππ$ can be extracted as $\text{Br}(ω\toππ)=(1.52\pm 0.06) \%$, 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 $a_μ^{\mathrm{HVP,\; LO}}(π^{+} π^{-} \leq 1\ \text{GeV}) = (497.76\pm3.15) \times 10^{-10}$. Our results are consistent with the other works.

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