Abstract
Some short-distance properties of the fourth-rank hadronic vacuum polarization tensor are re-examined. Their consequences are critically discussed in the context of the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon.
Highlights
Some short-distance properties of the fourth-rank hadronic vacuum polarization tensor are re-examined. Their consequences are critically discussed in the context of the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon
In the first serious attempts [20,21,22,23,24,25,26] to perform a complete evaluation of the HLxL contribution to aμ, it so occurred that the final result was almost completely given by the contribution due to the pion pole, the other contributions cancelling almost exactly among themselves
I have discussed the two kinematic limits that are currently considered in applications to the anomalous magnetic moment of the muon, for both the contribution from the pion pole or from narrow non-Goldstone pseudoscalar states
Summary
As mentioned in the introduction, the central object of interest is the connected four-point QCD correlator. I have written this correlator as a function of four variables, but only three momenta are independent, since invariance under translations requires that the condition q1 + q2 + q3 + q4 = 0. Where p and m stand for the momentum and the mass of the muon, respectively, and ΓHLxL στ (p, p) is the limit of the vertex function. When the momentum difference k = p − p vanishes. This definition involves the derivative of the four-point function,. I recall some properties of this four-point function relevant for the present discussion
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