%0 Generic %1 li2020vacuum %A Li, Hsiang-nan %A Umeeda, Hiroyuki %D 2020 %K g-2 %T Vacuum polarization contribution to muon $g-2$ as an inverse problem %U http://arxiv.org/abs/2004.06451 %X We analyze the electromagnetic current correlator at an arbitrary photon invariant mass $q^2$ by exploiting its associated dispersion relation. The dispersion relation is turned into an inverse problem, via which the involved vacuum polarization function $\Pi(q^2)$ at low $q^2$ is solved with the perturbative input of $\Pi(q^2)$ at large $q^2$. It is found that the result for $\Pi(q^2)$, including its first derivative $\Pi^\prime(q^2=0)$, agrees with those from lattice QCD, and its imaginary part accommodates the $e^+e^-$ annihilation data. The corresponding hadronic vacuum polarization contribution $a^HVP_\mu= (687^+64_-56)10^-10$ to the muon anomalous magnetic moment $g-2$, where the uncertainty arises from the variation of the perturbative input, also agrees with those obtained in other phenomenological and theoretical approaches. We point out that our formalism is equivalent to imposing the analyticity constraint to the phenomenological approach solely relying on experimental data, and provides a self-consistent framework for determining $a^HVP_\mu$ in the Standard Model with higher precision.

@misc{li2020vacuum, abstract = {We analyze the electromagnetic current correlator at an arbitrary photon invariant mass $q^2$ by exploiting its associated dispersion relation. The dispersion relation is turned into an inverse problem, via which the involved vacuum polarization function $\Pi(q^2)$ at low $q^2$ is solved with the perturbative input of $\Pi(q^2)$ at large $q^2$. It is found that the result for $\Pi(q^2)$, including its first derivative $\Pi^\prime(q^2=0)$, agrees with those from lattice QCD, and its imaginary part accommodates the $e^+e^-$ annihilation data. The corresponding hadronic vacuum polarization contribution $a^{\rm HVP}_\mu= (687^{+64}_{-56})\times 10^{-10}$ to the muon anomalous magnetic moment $g-2$, where the uncertainty arises from the variation of the perturbative input, also agrees with those obtained in other phenomenological and theoretical approaches. We point out that our formalism is equivalent to imposing the analyticity constraint to the phenomenological approach solely relying on experimental data, and provides a self-consistent framework for determining $a^{\rm HVP}_\mu$ in the Standard Model with higher precision.}, added-at = {2020-04-15T10:29:34.000+0200}, author = {Li, Hsiang-nan and Umeeda, Hiroyuki}, biburl = {https://www.bibsonomy.org/bibtex/2adf5568e7caa92e6682c82f643b5743a/cmcneile}, description = {Vacuum polarization contribution to muon $g-2$ as an inverse problem}, interhash = {97caed934a7eb90dcfc912b44fdce0d5}, intrahash = {adf5568e7caa92e6682c82f643b5743a}, keywords = {g-2}, note = {cite arxiv:2004.06451Comment: 9 pages, 5 figures}, timestamp = {2020-04-15T10:29:34.000+0200}, title = {Vacuum polarization contribution to muon $g-2$ as an inverse problem}, url = {http://arxiv.org/abs/2004.06451}, year = 2020 }