Tensor meson transition form factors in holographic QCD and the muon $g-2$

Despite the prominence of tensor mesons in photon-photon collisions, until recently their contribution to the hadronic light-by-light (HLbL) scattering part of the anomalous magnetic moment of the muon has been estimated to be at the level of only a few $10^{-12}$. A recent reanalysis within the dispersive approach has found that after resolving the issue of kinematic singularities in previous approaches, a larger result is obtained, a few $10^{-11}$, and with opposite sign as in previous results, when a simple quark model for the transition form factors is employed. In this paper, we present the first complete evaluation of tensor meson contributions within a hard-wall model in holographic QCD, which reproduces surprisingly well mass, two-photon width, and the observed singly virtual transition form factors of the dominant $f_2(1270)$. Due to a second structure function that is absent in the quark model and in lowest-order resonance chiral theory, the result for $a_\mu$ turns out to be positive instead of negative, and also with a magnitude of a few $10^{-11}$. We find that the infinite tower of tensor mesons permits to fill the gap in the symmetric longitudinal short-distance constraint on the HLbL amplitude left by the contribution of axial vector mesons. Matching the corresponding leading-order OPE result leads to two-photon couplings consistent with the observed combined effects of the ground-state $f_2,a_2,f_2'$ multiplet and a total $a_\mu^\mathrm{Tensor}$ contribution of $+12.4\times 10^{-11}$; with an $F_\rho$ fit this is reduced slightly to $+11.1\times 10^{-11}$. A contribution of this size from the tensor sector could explain the tension between the most recent dispersive and lattice results for $a_\mu^\mathrm{HLbL}$.