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Dispersion relations for hadronic light-by-light scattering in triangle kinematics
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abstract
We present a new strategy for the dispersive evaluation of the hadronic light-by-light contribution to the anomalous magnetic moment of the muon $a_\mu$. The new approach directly applies in the kinematic limit relevant for $a_\mu$: one of the photons is treated as an external electromagnetic field with vanishing momentum, so that the kinematics corresponds to a triangle. We derive expressions for the relevant single-particle intermediate states, as well as the tensor decompositions of the two-pion sub-processes that appear in addition to those needed in the established dispersive approach. The existing approach is based on a set of dispersion relations for the hadronic light-by-light tensor in four-point kinematics. At present it is not known how to consistently include in this framework resonant intermediate states of spin 2 or larger, due to the appearance of kinematic singularities that can be traced back to the redundancy of the tensor decomposition. We show that our new approach circumvents this problem and enables dispersion relations in the limit of triangle kinematics that are manifestly free from kinematic singularities, paving the way towards a data-driven evaluation of all relevant exclusive hadronic intermediate states.
Forward citations
Cited by 5 Pith papers
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Tensor meson transition form factors in holographic QCD and the muon $g-2$
Holographic QCD predicts a positive tensor-meson contribution of about +11e-11 to the muon g-2, driven by a previously omitted doubly-virtual form factor.
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Longitudinal short-distance constraints on hadronic light-by-light scattering and tensor meson contributions to the muon $g-2$
In hard-wall holographic QCD, the infinite tower of tensor mesons fills most of the missing symmetric longitudinal short-distance constraint and yields a total hadronic light-by-light contribution of about +11 x 10^-1...
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Imposing the absence of complex zeros in the pion vector form factor reduces the dominant systematic uncertainty and makes the tensions between CMD-3 and other e+e- data sets appear sharper, including in the pion char...
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Hadronic vacuum polarization for the muon $g-2$ from lattice QCD: Long-distance and full light-quark connected contribution
The light-quark connected hadronic vacuum polarization contribution to muon g-2 is determined to 0.69% precision, 655.2(4.5) x 10^-10, from lattice QCD.
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Dispersion relation for hadronic light-by-light scattering: $\eta$ and $\eta'$ poles
A dispersive analysis of the eta and eta' transition form factors yields data-driven pole contributions to the muon g-2 of 14.7(9) x 10^-11 and 13.5(7) x 10^-11.
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