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Register a new userChiral symmetry breaking corrections to the pseudoscalar pole contribution of the Hadronic Light-by-Light piece of $a_mu$
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We have studied the $Ptogamma^stargamma^star$ form factor in Resonance Chiral Theory, with $P = pi^0etaeta$, to compute the contribution of the pseudoscalar pole to the hadronic light-by-light piece of the anomalous magnetic moment of the muon. In this work we allow the leading $U(3)$ chiral symmetry breaking terms, obtaining the most general expression for the form factor up to $mathcal{O}(m_P^2)$. The parameters of the Effective Field Theory are obtained by means of short distance constraints on the form factor and matching with the expected behavior from QCD. Those parameters that cannot be fixed in this way are fitted to experimental determinations of the form factor within the spacelike region. Chiral symmetry relations among the transition form factors for $pi^0,eta$ and $eta$ allow for a simultaneous fit to experimental data for the three mesons. This shows an inconsistency between the BaBar $pi^0$ data and the rest of the experimental inputs. Thus, we find a total pseudoscalar pole contribution of $a_mu^{P,HLbL}=(8.47pm 0.16)cdot 10^{-10}$ for our best fit (that neglecting the BaBar $pi^0$ data). Also, a preliminary rough estimate of the impact of NLO in $1/N_C$ corrections and higher vector multiplets (asym) enlarges the uncertainty up to $a_mu^{P,HLbL}=(8.47pm 0.16_{rm stat}pm 0.09_{N_C}{}^{+0.5}_{-0.0_{rm asym}})10^{-10}$.
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In this work we study the axial contributions to the hadronic light-by-light piece of the muon anomalous magnetic moment using the framework of resonance chiral theory. As a result, we obtain $a_{mu}^{textrm{HLbL};A} = left(0.8^{+3.5}_{-0.1}right)cdot 10^{-11}$, that might suggest a smaller value than most recent calculations, underlining the need of future work along this direction. In particular, we find that our results depend critically on the asymptotic behavior of the form factors, and as such, emphasizes the relevance of future experiments for large photon virtualities. In addition, we present general results regarding the involved axial form factors description, comprehensively examining (and relating) the current approaches, that shall be of general interest.
The evaluation of the numerically dominant pseudoscalar-pole contribution to hadronic light-by-light scattering in the muon g-2 involves the pseudoscalar-photon transition form factor F_{P gamma^* gamma^*}(-Q_1^2, -Q_2^2) with P = pi^0, eta, eta^prime and, in general, two off-shell photons with spacelike momenta Q_{1,2}^2. We determine which regions of photon momenta give the main contribution for hadronic light-by-light scattering. Furthermore, we analyze how the precision of future measurements of the single- and double-virtual form factor impacts the precision of a data-driven estimate of this contribution to hadronic light-by-light scattering.
The evaluation of the numerically dominant pseudoscalar-pole contribution to hadronic light-by-light scattering in the muon g-2 involves the pseudoscalar-photon transition form factor F_{P gamma^* gamma^*}(-Q_1^2, -Q_2^2) with P = pi^0, eta, eta^prime and, in general, two off-shell photons with spacelike momenta Q_{1,2}^2. We show, in a largely model-independent way, that for pi^0 (eta, eta^prime) the region of photon momenta below about 1 (1.5) GeV gives the main contribution to hadronic light-by-light scattering. We then discuss how the precision of current and future measurements of the single- and double-virtual transition form factor in different momentum regions impacts the precision of a data-driven estimate of this contribution to hadronic light-by-light scattering. Based on Monte Carlo simulations for a planned first measurement of the double-virtual form factor at BESIII, we find that for the pi^0, eta, eta^prime-pole contributions a precision of 14%, 23%, 15% seems feasible. Further improvements can be expected from other experimental data and also from the use of dispersion relations for the different form factors themselves.
The $pi^0$ pole constitutes the lowest-lying singularity of the hadronic light-by-light (HLbL) tensor, and thus provides the leading contribution in a dispersive approach to HLbL scattering in the anomalous magnetic moment of the muon $(g-2)_mu$. It is unambiguously defined in terms of the doubly-virtual pion transition form factor, which in principle can be accessed in its entirety by experiment. We demonstrate that, in the absence of a direct measurement, the full space-like doubly-virtual form factor can be reconstructed very accurately based on existing data for $e^+e^-to 3pi$, $e^+e^-to e^+e^-pi^0$, and the $pi^0togammagamma$ decay width. We derive a representation that incorporates all the low-lying singularities of the form factor, matches correctly onto the asymptotic behavior expected from perturbative QCD, and is suitable for the evaluation of the $(g-2)_mu$ loop integral. The resulting value, $a_mu^{pi^0text{-pole}}=62.6^{+3.0}_{-2.5}times 10^{-11}$, for the first time, represents a complete data-driven determination of the pion-pole contribution with fully controlled uncertainty estimates. In particular, we show that already improved singly-virtual measurements alone would allow one to further reduce the uncertainty in $a_mu^{pi^0text{-pole}}$.
Using an effective sigma/f_0(500) resonance, which describes the pipi-->pipi and gammagamma-->pipi scattering data, we evaluate its contribution and the ones of the other scalar mesons to the the hadronic light-by-light (HLbL) scattering component of the anomalous magnetic moment a_mu of the muon. We obtain the conservative range of values: sum_S~a_mu^{lbl}vert_S = -(4.51+- 4.12) 10^{-11}, which is dominated by the sigma/f_0(500) contribution ( 50%~98%), and where the large error is due to the uncertainties on the parametrisation of the form factors. Considering our new result, we update the sum of the different theoretical contributions to a_mu within the standard model, which we then compare to experiment. This comparison gives (a_mu^{rm exp} - a_mu^{SM})= +(312.1+- 64.3) 10^{-11}, where the theoretical errors from HLbL are dominated by the scalar meson contributions.
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