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 K\"uhn-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 $a_{\mu}^{\mathrm{HVP,\; LO}}(\pi^{+} \pi^{-} \leq 1\ \text{GeV}) = (497.76\pm3.15) \times 10^{-10}$. Our results are consistent with the other works.
Highlights
The muon magnetic moment is an important and long historical issue in particle physics [1,2,3,4,5,6,7]
In order to reduce the uncertainties of the calculation of two-pion contribution to the muon anomalous magnetic moment, we try to get the best fit for the two-pion cross sections with several theoretical models of the pion vector form factor (PVFF), combined with a polynomial description
Since the polynomial description is valid up to 1 GeV, we only take into account all the experimental data below 1 GeV, which is below the significant inelastic threshold and contributes almost more than 70% of the hadronic contribution to the muon anomalous magnetic moment
Summary
The muon magnetic moment is an important and long historical issue in particle physics [1,2,3,4,5,6,7]. Δaμ 1⁄4 aeμxp − aSμM 1⁄4 ð26.0 Æ 7.9Þ × 10−10; ð3Þ where one can see that there is a discrepancy of about 3.3σ between the measured value and the full standard model prediction This discrepancy has been updated with the recent results in both theory calculations and experimental measurements. To solve the inverse problem to the dispersion relation, a value for the HVP contribution was obtained as aHμ VP 1⁄4 ð641þ−6635Þ × 10−10 in Ref. 73% of the LO hadronic contribution and about 60% of the total uncertainty are given by the cross section of eþe− annihilated to the πþπ−ðγÞ final states, which are dominated by the ρð770Þ resonance. The LO HVP contribution to the aSμM can be calculated via a dispersion relation using the measured cross sections of eþe− → hadrons [82]. The two-pion contribution to the anomalous magnetic moment of the muon can be written as aHμ VP;LOðπþπ−Þ α 12π
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
