Scalar resonances in the hadronic light-by-light contribution to the muon $(g-2)$

Abstract

We evaluate the contribution of scalar mesons to the hadronic light-by-light piece of the muon anomalous magnetic moment, using a warped five-dimensional model and holographic methods. We assess the contribution of the lightest, sub-GeV scalars σ(500), a0(980) and f0(990) together with their associated towers of excited states, which the model generates automatically. Our results point at a clearly negative contribution, overwhelmingly dominated by the σ(500) meson, that we estimate at a HLbL,S µ = −9(2) • 10 −11 . This number is in very good agreement with the most recent determinations from dispersive analyses.

Holographic QCD and the muon anomalous magnetic moment

“…Recently, also the contribution of scalar mesons has been worked out [108] in a variant of the HW model where the scalar X has additional interaction terms |X| 2 F 2 which can be fitted to match phenomenological input on the decay widths of f 0 (500), f 0 (990), and the a 0 (980), albeit by using a different set of parameters for each of them. Here the holographic result for the sum of their contribution to a µ is…”

$π^0, η, η^\prime$ two-photon transition form factors in the holographic soft-wall model and contributions to $(g-2)_μ$

“…The HLbL pole contribution of different mesons to a µ has been computed by various holographic models [8,9,10,12,14]. Scalar mesons have been considered in [13], axial-vector mesons…”

“…The HLbL pole contribution of the various hadrons represents a fraction of the total hadronic contribution dominated by the hadronic vacuum polarization (HVP), as discussed in the White Paper of the Muon (g − 2) Theory Initiative [7], however it is affected by a sizeable error. The contribution of light pseudoscalar mesons, after past analyses in holographic approaches which also considered axial-vector and scalar mesons [8,9,10,11,12,13,14], has been recently evaluated in an updated model [15]: the comparison with the results obtained here will strenghten the confidence on the precision achieved by such models. 2 This is an important issue, due to the role played by the lepton anomalous magnetic moments as powerful tests of the SM.…”

Prospects for precise predictions of $a_μ$ in the Standard Model

“…For this reason uncertainties in this panel were added linearly, as the errors in this category are potentially strongly correlated. Ongoing work is aimed at improving estimates of these subleading contributions, including SDCs at higher orders [184,185], the implementation of these SDCs [183,[186][187][188][189][190], and the evaluation of narrow resonances [182,[191][192][193].…”