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

Abstract

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. Second, we have implemented the on-shell 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 π 0 → γγ at NLO. With additional input from experiment and theory, we reproduce recent estimates for the decay width Γ(π 0 → γγ). 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 HLbL;π 0 µ = (59.7 ± 3.6) × 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 HLbL;π 0 µ = (62.3 ± 2.3) × 10 −11 .

Pseudoscalar transition form factors and the hadronic light-by-light contribution to the anomalous magnetic moment of the muon from holographic QCD

“…With full numerical evaluation, the bottom-up-holographic results span the range a π 0 µ = 5.9(2) · 10 −10 , which turns out to be well in line with the recent result obtained with the DRV interpolator fitted to the world data for π 0 [7] and also with the lattice results of Ref. [15].…”

“…Given that the bottom-up holographic models are all in remarkable agreement with the lowenergy data for single-virtual pion TFF as shown in Fig. 1, while also bracketing the lattice results [15] of double-virtual TFF (Fig. 3), they provide, taken together, an arguably strong prediction for a µ consisting of the range (5.7 .…”

“…In fact, the behavior found in the recent lattice extrapolation of Ref. [15] for the π 0 TFF for generic virtualities is closer to that of the holographic results than that of the DRV interpolator.…”

“…The SS model result drops already above 0.5 GeV 2 , where its incorrect short-distance behavior starts to dominate. Also shown are the various predictions for the dependence on x of the asymmetric double-virtual TFF F ((1 − x)GeV 2 , x GeV 2 )/F (0, 0) at fixed Q 2 1 + Q 2 2 , where all holographic results have a much milder dependence on x than the DRV interpolator, with the lattice result of [15] being closer to the former. Fig.…”

“…Unfortunately, there are not yet experimental data for the double-virtual pion TFF for low values of Q 2 , but these could be provided by BESIII around and below 1 GeV 2 in the future [7]. However, there exists a new lattice QCD calculation [15], which extrapolates its results to arbitrary Q 2 1 and Q 2 2 . This is compared with the holographic results and the DIP1,2 and DRV4 interpolators in Fig.…”