We compute the tensor meson pole contributions to the Hadronic Light-by-Light piece of aμ in the purely hadronic region, using Resonance Chiral Theory. Given the differences between the dispersive and holographic groups determinations and the resulting discussion of the corresponding uncertainty estimate for the Hadronic Light-by-Light section of the muon g − 2 theory initiative second White Paper, we consider timely to present an alternative evaluation. In our approach, in addition to the lightest tensor meson nonet, two vector meson resonance nonets are considered, in the chiral limit. Disregarding operators with derivatives, only the form factor \({\mathcal{F}}_{1}^{T}\) is non-vanishing, as assumed in the dispersive study. All parameters are determined by imposing a set of short-distance QCD constraints, and the radiative tensor decay widths. In this case, we obtain the following results for the different contributions (in units of 10−11): \({a}_{\mu }^{{\text{a}}_{2}-{\text{pole}}}=-\left(1.02{\left(10\right)}_{\text{stat}}{{(}_{-0.12}^{+0.00})}_{\text{syst}}\right)\) , \({a}_{\mu }^{{\text{f}}_{2}-{\text{pole}}}=-\left(3.2{\left(3\right)}_{\text{stat}}{{(}_{-0.4}^{+0.0})}_{\text{syst}}\right)\) and \({a}_{\mu }^{{\text{f}}_{2}{\prime}-{\text{pole}}}=-\left(0.042{\left(13\right)}_{\text{stat}}\right)\) , which add up to \({a}_{\mu }^{{\text{a}}_{2}+{f}_{2}+{f}_{2}{\prime}-{\text{pole}}}=-\left({4.3}_{-0.5}^{+0.3}\right)\) , in close agreement with the holographic result when truncated to \({\mathcal{F}}_{1}^{T}\) only. However, with an ad-hoc extended Lagrangian, that also generates \({\mathcal{F}}_{3}^{T}\) , as in the holographic approach, we have found: \({a}_{\mu }^{{\text{a}}_{2}-{\text{pole}}}=+0.47{\left(1.43\right)}_{\text{norm}}{\left(3\right)}_{\text{stat}}{{(}_{-0.00}^{+0.06})}_{\text{syst}}\) , \({a}_{\mu }^{{\text{f}}_{2}-{\text{pole}}}=+1.18{\left(4.18\right)}_{\text{norm}}{\left(12\right)}_{\text{stat}}{{(}_{-0.00}^{+0.24})}_{\text{syst}}\) and \({a}_{\mu }^{{\text{f}}_{2}{\prime}-{\text{pole}}}=+0.040{\left(78\right)}_{\text{norm}}{\left(2\right)}_{\text{stat}}\) , summing to \({a}_{\mu }^{{{a}_{2}+{f}_{2}+f}_{2}{\prime}-{\text{pole}}}=+1.7(4.4)\) , which agree with these recent determinations within uncertainties (dominated by the \({\mathcal{F}}_{3}^{T}\) normalization). We point out that RχT generates all five form factors, differently to previous approaches. The contributions to aμ of \({\mathcal{F}}_{\text{2,4},5}\) cannot be evaluated in the current basis, preventing for the moment a complete calculation of \({a}_{\mu }^{\text{T}-{\text{pole}}{\text{s}}}\) within our framework.
