A bstract We compute the tensor meson pole contributions to the Hadronic Light-by-Light piece of a μ 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 F₁^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 ^{a₂-pole}=- (1. 02 (10) ₒₓ₀ₓ{ (-₀. ₁₂^+0. 00) }ₒₘₒₓ), a ^{f₂-pole}=- (3. 2 (3) ₒₓ₀ₓ{ (-₀. ₄^+0. 0) }ₒₘₒₓ) and a ^{f₂-pole}=- (0. 042 (13) ₒₓ₀ₓ), which add up to a ^{a₂+f₂+f₂-pole}=- (4. 3-₀. ₅^+0. 3), in close agreement with the holographic result when truncated to F₁^T only. However, with an ad-hoc extended Lagrangian, that also generates F₃^T, as in the holographic approach, we have found: a ^{a₂-pole}=+0. 47 (1. 43) ₍₎ₑ₌ (3) ₒₓ₀ₓ{ (-₀. ₀₀^+0. 06) }ₒₘₒₓ, a ^{f₂-pole}=+1. 18 (4. 18) ₍₎ₑ₌ (12) ₒₓ₀ₓ{ (-₀. ₀₀^+0. 24) }ₒₘₒₓ and a ^{f₂-pole}=+0. 040 (78) ₍₎ₑ₌ (2) ₒₓ₀ₓ, summing to a ^{{a₂+f₂+f}₂-pole}=+1. 7 (4. 4), which agree with these recent determinations within uncertainties (dominated by the F₃^T normalization). We point out that RχT generates all five form factors, differently to previous approaches. The contributions to a μ of F₂, ₄, ₅ cannot be evaluated in the current basis, preventing for the moment a complete calculation of a ^T-{poles} within our framework.
Estrada et al. (2026) studied this question.