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Register a new user2-loop short-distance constraints for the $g-2$ HLbL
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The recent experimental measurement of the muon $g-2$ at Fermilab National Laboratory, at a $4.2sigma$ tension with the Standard Model prediction, highlights the need for further improvements on the theoretical uncertainties associated to the hadronic sector. In the framework of the operator product expansion in the presence of a background field, the short-distance behaviour of the hadronic light-by-light contribution was recently studied. The leading term in this expansion is given by the massless quark-loop, which is numerically dominant compared to non-perturbative corrections. Here, we present the perturbative QCD correction to the massless quark-loop and estimate its size numerically. In particular, we find that for scales above 1 GeV it is relatively small, in general roughly $-10%$ the size of the massless quark-loop. The knowledge of these short-distance constraints will in the future allow to reduce the systematic uncertainties in the Standard Model prediction of the hadronic light-by-light contribution to the $g-2$.
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The current $3.7sigma$ discrepancy between the Standard Model prediction and the experimental value of the muon anomalous magnetic moment could be a hint for the existence of new physics. The hadronic light-by-light contribution is one of the pieces requiring improved precision on the theory side, and an important step is to derive short-distance constraints for this quantity containing four electromagnetic currents. Here, we derive such short-distance constraints for three large photon loop virtualities and the external fourth photon in the static limit. The static photon is considered as a background field and we construct a systematic operator product expansion in the presence of this field. We show that the massless quark loop, i.e. the leading term, is numerically dominant over non-perturbative contributions up to next-to-next-to leading order, both those suppressed by quark masses and those that are not.
The short-distance behaviour of the hadronic light-by-light (HLbL) contribution to $(g-2)_{mu}$ has recently been studied by means of an operator product expansion in a background electromagnetic field. The leading term in this expansion has been shown to be given by the massless quark loop, and the non-perturbative corrections are numerically very suppressed. Here, we calculate the perturbative QCD correction to the massless quark loop. The correction is found to be fairly small compared to the quark loop as far as we study energy scales where the perturbative running for the QCD coupling is well-defined, i.e.~for scales $mugtrsim 1, mathrm{GeV}$. This should allow to reduce the large systematic uncertainty associated to high-multiplicity hadronic states.
We derive short-distance constraints for the hadronic light-by-light contribution (HLbL) to the anomalous magnetic moment of the muon in the kinematic region where the three virtual momenta are all large. We include the external soft photon via an external field leading to a well-defined Operator Product Expansion. We establish that the perturbative quark loop gives the leading contribution in a well defined expansion. We compute the first nonzero power correction. It is related to to the magnetic susceptibility of the QCD vacuum. The results can be used as model-independent short-distance constraints for the very many different approaches to the HLbL contribution. Numerically the power correction is found to be small.
We revisit well-known short-distance constraints relating the hadronic light-by light Greens function to the $langle VVA rangle$ one. As a novelty, we identify a previously unnoticed relation among the longitudinal and transverse degrees of freedom that is enforced by the axial anomaly. Such relation allows, among other things, to overcome the problem of basis ambiguities when describing axial-vector mesons transition form factors. It also helps elucidating some caveats of previous models used to describe the short-distance behavior. The new results here presented are model independent and should help paving the way for a better understanding of the, so far, controversial interplay among short-distance constraints and transverse degrees of freedom such as axial-vector mesons.
While the low-energy part of the hadronic light-by-light (HLbL) tensor can be constrained from data using dispersion relations, for a full evaluation of its contribution to the anomalous magnetic moment of the muon $(g-2)_mu$ also mixed- and high-energy regions need to be estimated. Both can be addressed within the operator product expansion (OPE), either for configurations where all photon virtualities become large or one of them remains finite. Imposing such short-distance constraints (SDCs) on the HLbL tensor is thus a major aspect of a model-independent approach towards HLbL scattering. Here, we focus on longitudinal SDCs, which concern the amplitudes containing the pseudoscalar-pole contributions from $pi^0$, $eta$, $eta$. Since these conditions cannot be fulfilled by a finite number of pseudoscalar poles, we consider a tower of excited pseudoscalars, constraining their masses and transition form factors from Regge theory, the OPE, and phenomenology. Implementing a matching of the resulting expressions for the HLbL tensor onto the perturbative QCD quark loop, we are able to further constrain our calculation and significantly reduce its model dependence. We find that especially for the $pi^0$ the corresponding increase of the HLbL contribution is much smaller than previous prescriptions in the literature would imply. Overall, we estimate that longitudinal SDCs increase the HLbL contribution by $Delta a_mu^text{LSDC}=13(6)times 10^{-11}$. This number does not include the contribution from the charm quark, for which we find $a_mu^{ctext{-quark}}=3(1)times 10^{-11}$.
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