Abstract
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)μ 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 π0, η, η′. 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 π0 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 varDelta {a}_{mu}^{mathrm{LSDC}}=13(6) × 10-11. This number does not include the contribution from the charm quark, for which we find {a}_{mu}^{c- quark} = 3(1) × 10−11.
Highlights
Current Standard Model (SM) evaluations of the anomalous magnetic moment of the muon, aμ = (g − 2)μ/2, differ from the value measured at the Brookhaven National Laboratory [1]aeμxp = 116 592 089(63) × 10−11, (1.1)by around 3.5 σ
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 operator product expansion (OPE), and phenomenology
Since the form (2.16) of the pseudoscalar poles is a direct consequence of the dispersion relation for the hadronic light-by-light (HLbL) tensor, which we suggested in refs. [31,32,33,34,35] for the case of general four-point kinematics, this modification is not compatible with the description of other intermediate states in the same framework
Summary
Our model is only needed for the low-energy part of the (g − 2)μ integral: above the energy where the matching occurs, we calculate the integral with the quark loop This strategy ensures that the estimate of the asymptotic region still applies in the chiral limit, in which the excited pseudoscalar states decouple, see section 5.3, while at low energies phenomenological input is needed either way to account for the effect of quark-mass corrections. All this leads to a more reliable estimate for the impact of the OPE constraints on the total HLbL contribution. Technical details and alternative evaluations that are used to estimate the systematic uncertainty are collected in the appendices
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