Width effects of broad new resonances in loop observables and application to $(g-2{)}_{\mu }$

Abstract

In the phenomenology of strong interactions most physical states acquire a substantial width, and thus can only be defined in a model-independent way by pole positions and residues of the $S$-matrix. This information is incorporated in the Källén-Lehmann representation, whose spectral function characterizes the shape of the resonance and can be constrained by the dominant decay channels. Here, we argue that similar effects become important whenever beyond-the-Standard-Model particles possess a sizable decay width - as possible for instance in cases with a large branching fraction to a dark sector or strongly coupled scenarios - and show how their widths can be incorporated in the calculation of loop observables. As an application, we consider the anomalous magnetic moment of the muon, including both the direct effect of new physics and the possible indirect impact of a broad light $Z^{\prime }$ on $e^{+}{e}^{-}\to \text{hadrons}$ cross sections. Throughout, we provide results for a general spectral function and its reconstruction from the one-loop imaginary part, where the latter captures the leading two-loop effects.

13 pages, 4 figures; journal version

References in corpus (26)

• Measurement of the Positive Muon Anomalous Magnetic Moment to 0.46 ppm
• The $g-2$ of charged leptons, $\alpha (M_Z^2)$ and the hyperfine splitting of muonium
• Hadronic contribution to the muon anomalous magnetic moment to next-to-next-to-leading order
• Neutrino Trident Production: A Powerful Probe of New Physics with Neutrino Beams
• B-physics anomalies: a guide to combined explanations
• The muon $g$-2 and $\Delta \alpha$ connection
• Measurement of the anomalous precession frequency of the muon in the Fermilab Muon g-2 experiment
• Window observable for the hadronic vacuum polarization contribution to the muon $g-2$ from lattice QCD
• Lattice calculation of the short and intermediate time-distance hadronic vacuum polarization contributions to the muon magnetic moment using twisted-mass fermions
• The K^*_0(800) scalar resonance from Roy-Steiner representations of pi K scattering
• What is the scale of new physics behind the $B$-flavour anomalies?
• The muon g-2 and the bounds on the Higgs boson mass
• Data-driven evaluations of Euclidean windows to scrutinize hadronic vacuum polarization
• A New Light Particle in B Decays?
• Kaon electromagnetic form factors in dispersion theory
• Light-quark connected intermediate-window contributions to the muon $g-2$ hadronic vacuum polarization from lattice QCD
• Radiative resonance couplings in $\gamma \pi \to \pi \pi$
• The hadronic running of the electromagnetic coupling and the electroweak mixing angle from lattice QCD
• Search for new physics in the monophoton final state in proton-proton collisions at sqrt(s) = 13 TeV
• Radiative corrections to the forward-backward asymmetry in $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$
• On Light Resonance Interpretations of the B Decay Anomalies
• Dark photon and dark $Z$ mediated $B$ meson decays
• What is the scale of new physics behind the muon $g-2$?
• A global analysis of $b\to s\ell \ell$ data in heavy and light $Z^{\prime }$ models
• Towards excluding a light $Z^{\prime }$ explanation of $b\to s{\ell }^{+}{\ell }^{-}$
• First direct lattice calculation of the chiral perturbation theory low-energy constant ${\ell }_7$

Cited by in corpus (12)

• Axial-vector transition form factors and $e^{+}{e}^{-}\to f_1{\pi }^{+}{\pi }^{-}$
• A phenomenological estimate of isospin breaking in hadronic vacuum polarization
• Isospin-breaking effects in the three-pion contribution to hadronic vacuum polarization
• Dispersion relation for hadronic light-by-light scattering: $\eta$ and ${\eta }^{\prime }$ poles
• Model Independent Tests of the Hadronic Vacuum Polarization Contribution to the Muon $g$$-$$2$
• Anomalous thresholds in $B\to (P,V){\gamma }^{\ast }$ form factors
• From pole parameters to line shapes and branching ratios
• The semileptonic decays ${\eta }^{(\prime )}\to {\pi }^0{\ell }^{+}{\ell }^{-}$ and ${\eta }^{\prime }\to \eta {\ell }^{+}{\ell }^{-}$ in the standard model
• The Muon Magnetic Moment and Physics Beyond the Standard Model
• Improved Standard-Model prediction for $K_L\to {\ell }^{+}{\ell }^{-}$
• The Hierarchy Problem and the Top Yukawa: An Alternative to Top Partner Solutions
• Charting the new physics through one-loop effects in the muon magnetic dipole moment