Hadronic Light-by-Light Contributions to the Muong−2

Abstract

In the calculation of the contribution of the second diagram in Fig. 2(b), a global normalization factor was erroneously applied twice. Unfortunately, this changes the conclusions of our Letter rather significantly. Full details of this work and this Erratum will be given in a forthcoming publication. Below is Table I corrected.

Hadronic light-by-light corrections to the muong−2:The pion-pole contribution

“…Our purpose here is not to intervene in this ongoing debate [11,12,13,14,15,16,17], but rather to have a closer look at the remaining item on the list, namely, the hadronic effects in the so-called light-by-light scattering contribution. There exist several estimates of the latter [18,19,20,21,22]. The latest to date, obtained by two different groups (see also [23]), give values that are consistent within the quoted errors, On the other hand, both groups have changed their value of a LbyL; had µ , and even its sign, at some stage, and for reasons that are not very easy to follow -partly because both analyses The three topologies involving hadronic contributions to the anomalous magnetic moment of the muon: from left to right, vacuum polarization insertion in the vertex, light-bylight scattering, and two-loop electroweak contributions.…”

What does Holographic QCD predict for anomalous (g− 2)μ?

“…Another caveat is that, although large values of the magnetic susceptibility χ 0 are disfavored, in the absence of stronger bounds on χ 0 , an additional (10 − 15)% systematic uncertainty on the previous value for a π 0 μ cannot be excluded. Modified ENJL [26][27][28] 59(9) VMD/HLS [29][30][31][32] 57(4) VMD+V (h 2 = 0) [33] 58(10) VMD+V (h 2 = −10 GeV 2 ) [33] 63(10) VMD+V (const.F π 0 γ * γ ) [37] 77(7) DSE [34,36] 58(7) Non local χQM [38] 65(2) AdS/QCD [21,39] 69 AdS/QCD/DIP [2] 65.4(2.5) RχT [40] 65.8(1.2) CχQM [41] 68(3) Table 3 shows a partial list of values of a π 0 μ obtained using different models, some of them discussed in other talks at this conference. Our numerical analysis showed also that the values of χ 0 hovered around 2 GeV −2 , as in the case shown in (18), with higher values disfavored although not definitely excluded.…”

Future Muon Dipole Moment Measurements

“…[32] investigation. [33,34,35,36,37] Unlike the lowestorder contribution, it can only be calculated from a model, and this contribution is likely to provide the ultimate limit to the precision of the standard-model value of a µ . One of the very useful roles the measurements of a µ have played in the past is placing serious restrictions on physics beyond the standard model.…”

“…The standard model value of a µ has measurable contributions from three types of radiative processes: QED loops containing leptons (e, µ, τ ) and photons; [8] hadronic loops containing hadrons in vacuum polarization loops; [26,27,28,29,30,31,32,33,34,35,36,37] and weak loops involving the W and Z weak gauge bosons (the standard model Higgs contribution is negligible), [26] a µ (SM) = a µ (QED) + a µ (Had) + a µ (Weak). (4) A significant difference between the experimental value and the standard model prediction would signify the presence of new physics.…”