Pion pole light-by-light contribution tog−2of the muon in a nonlocal chiral quark model

Abstract

We calculate the pion pole term of the light-by-light contribution to the g − 2 of the muon in the framework of an effective chiral quark model with instanton-like nonlocal quark-quark interaction. The full kinematic dependence of the pion-photon transition form factors is taken into account. The dependence of form factors on the pion virtuality decreases the result by about 15% in comparison to the calculation where this dependence is neglected. Further, it is demonstrated that the QCD constraints suggested by Melnikov and Vainshtein are satisfied within the model. The corresponding contributions originate from the box diagram as well from the pion-pole term. Our chiral nonlocal model result for the pion-pole light-by-light contribution to (g−2)/2 of the muon is (6.3 − 6.7)·10 −10 , which is in the ball park of other effective-model calculations.

$\eta$ and $\eta '$ transition form factors from rational approximants

“…This result, which for the first time contains a systematic error, is in nice agreement with most of the recent phenomenological calculations for such quantity [78], but smaller than those determinations that model an offshell TFF [75,76,85,86], pointing towards a positive impact of the off-shellness of the pseudoscalar in such computation. Indeed, assuming U (3) and chiral symmetries (neglecting the effect of nonzero quark masses, the η −η mixing and the possible gluonic contribution to the axial anomaly coming from the η ), one can parameterize the off-shellness of the η and η in the TFF through the quark condensate magnetic susceptibility χ as done for the π 0 contribution in Refs.…”

“…The TFF should be considered to be off shell (see Refs. [75,76,79,85,86] where this point is addressed). Since such effects for the η and η , which are expected to be small, are not known, we should keep the pseudoscalar-pole simplifications in our calculations.…”

“…The latter cannot be directly related to any measurable cross section and requires the knowledge of QCD contributions at all energy scales. Since this is not known yet, one relies on hadronic models to compute it [69][70][71][72][73][74][75][76][77][78][79][80][81][82][83]. Indeed, the theoretical value of a µ is currently limited by uncertainties from the HLBL scattering contribution leading to an uncertainty in a µ of (2.6-4.0)×10 −10 [84][85][86] as well as the one from hadronic vacuum polarization (4.2-4.9)×10 −10 [87,88].…”

Hadronic light-by-light contribution toaμ: extended Nambu-Jona-Lasinio, chiral quark models and chiral Lagrangians

“…The above behaviour of the four-point function must be obeyed in a full calculation, however whether one implements it via π 0 -exchange is a choice. Models incorporating a short-distance quark-loop contribution have the short-distance part of this included [10,27]. One can see this when comparing quark-loop plus pseudo-scalar exchange of [14] with pseudo-scalar exchange of [34].…”

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.…”