Pion and Kaon box contribution to $a_μ^{\text{HLbL}}$

Abstract

We present an evaluation of the π ± and K ± box-contributions to the hadronic light-by-light piece of the muon's anomalous magnetic moment, aµ. The calculation of the corresponding electromagnetic form factors (EFFs) is performed within a Dyson-Schwinger equations approach to quantum chromodynamics. These form factors are calculated in the so called rainbow-ladder (RL) truncation, following two different evaluation methods and, subsequently, in a beyond RL truncation that incorporates meson cloud effects. The produced image is quite congruent and indicates that, in the domain of relevance for aµ, the obtained EFFs are practically equivalent, thus yielding the combined estimates of a π ± −box µ = −(15.6 ± 0.5) × 10 −11 and a K ± −box µ = −(0.48 ± 0.04) × 10 −11 , in full agreement with previous results within the DSE formalism and other contemporary estimates.

Kaon electromagnetic form factors in dispersion theory

“…3. The spacelike form factors determine the kaon-box contributions to HLbL scattering in the anomalous magnetic moment of the muon a µ = (g − 2) µ /2, corroborating previous estimates using vector meson dominance (VMD) [34] and Dyson-Schwinger (DS) equations [35,36], see Sec. 4.3.…”

“…Comparison to Eq. (36) shows that this elastic estimate fully agrees with the lattice results, demonstrating that inelastic effects have to be smaller than the precision with which the elastic contributions can currently be evaluated.…”

“…[47,[151][152][153][154][155][156][157][158][159] for recent work in this direction. Meanwhile, KK states prove to be appreciably suppressed compared to their ππ analog, which is true for both the leading box contributions (estimated in VMD [34] or DS equations [35,36]) and rescattering corrections [157], in the latter case despite the strong coupling between the ππ and KK channels via the f 0 (980). While the overall effect is thus known to be small, we can confirm these conclusions by means of our data-driven evaluation of the kaon form factors.…”

Prospects for precise predictions of $a_μ$ in the Standard Model

“…In this part of the evaluation, ongoing work thus mainly concerns a consolidation of the η, η poles, both using dispersion relations [176,177] and lattice QCD [178,179] (see Refs. [155,180] for recent work on the box contributions).…”

Opportunities for precision QCD physics in hadronization at Belle II -- a snowmass whitepaper

“…Compared to the HVP, relating this contribution to data is much more challenging, yet a dispersive approach has been put forward recently that allows to relate unambiguously different hadronic contributions to the HLbL tensor [22]. In particular, the lowest-lying channels, the π 0 , η, and η poles [14,16,17], as well as the ππ and K K [15,38,41,42] channels, have been estimated…”