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تسجيل مستخدم جديدA note on the anomalous magnetic moment of the muon
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Davor Palle
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The anomalous magnetic moment of the muon is an important observable that tests radiative corrections of all three observed local gauge forces: electromagnetic, weak and strong interactions. High precision measurements reveal some discrepancy with the most accurate theoretical evaluations of the anomalous magnetic moment. We show in this note that the UV finite theory cannot resolve this discrepancy. We believe that more reliable estimate of the nonperturbative hadronic contribution and the new measurements can resolve the problem.
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A new QCD sum rule determination of the leading order hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon, $a_{mu}^{rm hvp}$, is proposed. This approach combines data on $e^{+}e^{-}$ annihilation into hadrons, pertu
rbative QCD and lattice QCD results for the first derivative of the electromagnetic current correlator at zero momentum transfer, $Pi_{rm EM}^prime(0)$. The idea is based on the observation that, in the relevant kinematic domain, the integration kernel $K(s)$, entering the formula relating $a_{mu}^{rm hvp}$ to $e^{+}e^{-}$ annihilation data, behaves like $1/s$ times a very smooth function of $s$, the squared energy. We find an expression for $a_{mu}$ in terms of $Pi_{rm EM}^prime(0)$, which can be calculated in lattice QCD. Using recent lattice results we find a good approximation for $a_{mu}^{rm hvp}$, but the precision is not yet sufficient to resolve the discrepancy between the $R(s)$ data-based results and the experimentally measured value.
We review the present status of the Standard Model calculation of the anomalous magnetic moment of the muon. This is performed in a perturbative expansion in the fine-structure constant $alpha$ and is broken down into pure QED, electroweak, and hadro
nic contributions. The pure QED contribution is by far the largest and has been evaluated up to and including $mathcal{O}(alpha^5)$ with negligible numerical uncertainty. The electroweak contribution is suppressed by $(m_mu/M_W)^2$ and only shows up at the level of the seventh significant digit. It has been evaluated up to two loops and is known to better than one percent. Hadronic contributions are the most difficult to calculate and are responsible for almost all of the theoretical uncertainty. The leading hadronic contribution appears at $mathcal{O}(alpha^2)$ and is due to hadronic vacuum polarization, whereas at $mathcal{O}(alpha^3)$ the hadronic light-by-light scattering contribution appears. Given the low characteristic scale of this observable, these contributions have to be calculated with nonperturbative methods, in particular, dispersion relations and the lattice approach to QCD. The largest part of this review is dedicated to a detailed account of recent efforts to improve the calculation of these two contributions with either a data-driven, dispersive approach, or a first-principle, lattice-QCD approach. The final result reads $a_mu^text{SM}=116,591,810(43)times 10^{-11}$ and is smaller than the Brookhaven measurement by 3.7$sigma$. The experimental uncertainty will soon be reduced by up to a factor four by the new experiment currently running at Fermilab, and also by the future J-PARC experiment. This and the prospects to further reduce the theoretical uncertainty in the near future-which are also discussed here-make this quantity one of the most promising places to look for evidence of new physics.
The Goldberger-Treiman relation $M=2pi/sqrt{3}f^{rm cl}_pi$ where $M$ is the constituent quark mass in the chiral limit (cl) and $f^{rm cl}_pi$ the pion decay constant in the chiral limit predicts constituent quark masses of $m_u=328.8pm 1.1$ MeV and
$m_d=332.3pm 1.1$ MeV for the up and down quark, respectively, when $f^{rm cl}_pi=89.8pm 0.3$ MeV is adopted. Treating the constituent quarks as bare Dirac particles the following zero order values $mu^{(0)}}_p=2.850pm 0.009$ and $mu^{(0)}}_n= -1.889pm 0.006$ are obtained for the proton and neutron magnetic moments, leading to deviations from the experimental data of 2.0% and 1.3%, respectively. These unavoidable deviations are discussed in terms of contributions to the magnetic moments proposed in previous work.
The latest measurement of the muon anomalous magnetic moment $a^{}_{mu} equiv (g^{}_mu - 2)/2$ at the Fermi Laboratory has found a $4.2,sigma$ discrepancy with the theoretical prediction of the Standard Model (SM). Motivated by this exciting progress
, we investigate in the present paper the general one-loop contributions to $a^{}_mu$ within the SM and beyond. First, different from previous works, the analytical formulae of relevant loop functions after integration are now derived and put into compact forms with the help of the Passarino-Veltman functions. Second, given the interactions of muon with new particles running in the loop, we clarify when the one-loop contribution to $a^{}_mu$ could take the correct positive sign as desired. Third, possible divergences in the zero- and infinite-mass limits are examined, and the absence of any divergences in the calculations leads to some consistency conditions for the construction of ultraviolet complete models. Applications of our general formulae to specific models, such as the SM, seesaw models, $Z^prime$ and leptoquark models, are also discussed.
We compute the leading hadronic contribution to the anomalous magnetic moment of the muon a_mu^HLO using two dynamical flavours of non-perturbatively O(a) improved Wilson fermions. By applying partially twisted boundary conditions we are able to impr
ove the momentum resolution of the vacuum polarisation, an important ingredient for the determination of the leading hadronic contribution. We check systematic uncertainties by studying several ensembles, which allows us to discuss finite size effects and lattice artefacts. The chiral behavior of a_mu^HLO turns out to be non-trivial, especially for small pion masses.
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