Upper Bound on the Hadronic Light-By-Light Contribution to the Muong−2

Abstract

There are indications that hadronic loops in some electroweak observables are almost saturated by parton level effects. Taking this as the hypothesis for this work, we propose a genuine parton level estimate of the hadronic light-by-light contribution to the anomalous magnetic moment of the muon, a LBL µ (had). Our quark mass definitions and values are motivated in detail, and the simplicity of our approach allows for a transparent error estimate. For infinitely heavy quarks our treatment is exact, while for asymptotically small quark masses a LBL µ (had) is overestimated. Interpolating, this suggests to quote an upper bound. We obtain a LBL µ (had) < 1.59 × 10 −9 (95% CL).PACS numbers: 13.40. Em, 14.60.Ef, 12.20.Ds, 12.38.Bx.The E-821 Collaboration at BNL [1] has measured the anomalous magnetic moment of the muon, a µ ≡ (g µ − 2)/2, with an uncertainty of ∆a µ = ±0.63 × 10 −9 . This would provide sensitivity to new physics scales, Λ, as large as Λ ∼ m µ / ∆a µ = 4.2 TeV, where m µ is the mass of the muon [2]. A new experiment [3] at BNL is approved aiming at even greater (±0.2 ppm) precision and implying a reach up to 7 TeV. Unfortunately, the interpretation of a µ is compromised by large theoretical uncertainties introduced by hadronic effects diluting the new physics sensitivity. These mainly arise from two-loop vacuum polarization (VP) effects, a VP µ (2, had), and from the three-loop contribution of light-by-light type, a LBL µ (had). The calculations of a LBL µ (had) based on chiral perturbation theory [4,5] are the only ones to date solidly based on a systematic expansion. However, the estimated uncertainty, > ∼ ±10 −9 , is significantly larger [5] than the measurement error. There is a variety of model estimates, all supplementing the dominant π 0 -exchange contribution with other resonance exchanges and π ± -loops. Current analyzes [6,7] agree reasonably well on the magnitude (where residual differences are largely understood) and the sign of a LBL µ (had). They have reached a high level of sophistication, but the error estimates remain rough guesses. There is also an estimate [8] based on the instanton liquid model with a small (< 10%) quoted error.In this work we offer a complementary way to estimate a LBL µ (had), with no need to commit to the dominance of any particular type of contribution. It is a naïve parton level estimate which is solid in the heavy quark limit where it matches onto perturbative QCD, but overestimates the light-by-light contribution in the chiral limit. Therefore, our approach naturally implies an upper bound for a LBL µ (had), which is very useful in view of the a µ measurement lying above the Standard Model prediction. It can also be applied to a VP µ (had), which serves as a reference case and allows for a transparent error estimate.Attempting to obtain a LBL µ (had) directly at the parton level seems hopeless at first since perturbative QCD cannot be applied except for the heavy c and b quarks. Moreover, in the chiral limit, in which the bulk of the effect arises from light...

Electron, muon and tau magnetic moments: a theoretical update

“…The upper bounds found in Refs. [88] are consistent with this higher value. Further independent calculations would provide an important check of these results for a HHO µ (lbl) (see [89] for a recent critical comparison of these evaluations), a contribution whose uncertainty may become the ultimate limitation of the SM prediction of the muon g−2.…”

The muon g−2

“…[255] in terms of a series expansion in δ = (m Finally, the EFT analysis shows that the modeling of hadronic light-by-light scattering by a constituent quark loop, as suggested in Refs. [301,302] (see also [303]), is not consistent with QCD. 32 The latter has a priori nothing to do with the full "quark loop" in QCD which is dual to the corresponding contribution in terms of hadronic degrees of freedom.…”

(g− 2)μand α(M2Z) re-evaluated using new precise data

“…the leading contributions, and that both have cancellations in the subleading parts, thus strengthening our confidence in the reliability of these estimates. Also note that these predictions of a had, l−by−l µ are below the estimated upper bound a had, l−by−l µ < 15.9 · 10 −10 based on parton hadron duality [53]. For our prediction of a SM µ we will use the result from [50], which has been obtained as a 'best estimate' for a had, l−by−l µ after reviewing different approaches.…”