Lattice calculation of the pion transition form factor with Nf=2+1 Wilson quarks

By A. G'erardin, Harvey B. Meyer, A. Nyffeler. Physical Review D, 2019

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We present a lattice QCD calculation of the double-virtual neutral pion transition form factor, with the goal to cover the kinematic range relevant to hadronic light-by-light scattering in the muon $g-2$. Several improvements have been made compared to our previous work. First, we take into account the effects of the strange quark by using the $N_f=2+1$ CLS gauge ensembles. Secondly, we have implemented the on-shell $\mathcal{O}(a)$-improvement of the vector current to reduce the discretization effects associated with Wilson quarks. Finally, in order to have access to a wider range of photon virtualities, we have computed the transition form factor in a moving frame as well as in the pion rest-frame. After extrapolating the form factor to the continuum and to physical quark masses, we compare our results with phenomenology. We extract the normalization of the form factor with a precision of 3.5\% and confirm within our uncertainty previous somewhat conflicting estimates for a low-energy constant that appears in chiral perturbation theory for the decay $\pi^0 \to \gamma\gamma$ at NLO. With additional input from experiment and theory, we reproduce recent estimates for the decay width $\Gamma(\pi^0 \to \gamma\gamma)$. We also study the asymptotic large-$Q^2$ behavior of the transition form factor in the double-virtual case. Finally, we provide as our main result a more precise model-independent lattice estimate of the pion-pole contribution to hadronic light-by-light scattering in the muon $g-2$: $a_{\mu}^{\mathrm{HLbL}; \pi^0} = (59.7 \pm 3.6) \times 10^{-11}$. Using in addition the normalization of the form factor obtained by the PrimEx experiment, we get the lattice and data-driven estimate $a_{\mu}^{\mathrm{HLbL}; \pi^0} = (62.3 \pm 2.3) \times 10^{-11}$.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/af9b38243078a067f5f3119551dac78cb3f83503

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Citations in the corpus

Measurement of the anomalous precession frequency of the muon in the Fermilab Muon g−2 Experiment (2021, background): “[28] A.”
Dispersion relation for hadronic light-by-light scattering: pion pole (2018, methodology): “In the absence of experimental measurements, our result given in the form Q(2)Fπ0γ∗γ∗(−Q(2),−Q(2)) in figure 10 is compared to an LMD+V (lowest meson dominance + vector [140]) resonance model fit to lattice data extrapolated to the physical pion mass [88].”