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A bstract One of the open issues in evaluations of the contribution from hadronic light- by-light scattering to the anomalous magnetic moment of the muon ( g − 2) μ concerns the role of heavier scalar, axial-vector, and tensor-meson intermediate states. The coupling of axial vectors to virtual photons is suppressed for small virtualities by the Landau-Yang theorem, but otherwise there are few rigorous constraints on the corresponding form factors. In this paper, we first derive the Lorentz decomposition of the two-photon matrix elements into scalar functions following the general recipe by Bardeen, Tung, and Tarrach. Based on this decomposition, we then calculate the asymptotic behavior of the meson transition form factors from a light-cone expansion in analogy to the asymptotic limits for the pseudoscalar transition form factor derived by Brodsky and Lepage. Finally, we compare our results to existing data as well as previous models employed in the literature.

A bstract With the long-standing tension between experiment and Standard-Model (SM) prediction in the anomalous magnetic moment of the muon a μ recently reaffirmed by the Fermilab experiment, the crucial question becomes which other observables could be sensitive to the underlying physics beyond the SM to which a μ may be pointing. While from the effective field theory (EFT) point of view no direct correlations exist, this changes in specific new physics models. In particular, in the case of explanations involving heavy new particles above the electroweak (EW) scale with chiral enhancement, which are preferred to evade exclusion limits from direct searches, correlations with other observables sensitive to EW symmetry breaking are expected. Such scenarios can be classified according to the SU(2) L representations and the hypercharges of the new particles. We match the resulting class of models with heavy new scalars and fermions onto SMEFT and study the resulting correlations with h → μμ and Z → μμ decays, where, via SU(2) L symmetry, the latter process is related to Z → νν and modified W - μ - ν couplings.

A bstract We present a detailed analysis of e + e − → π + π − data up to s = 1 GeV in the framework of dispersion relations. Starting from a family of ππ P -wave phase shifts, as derived from a previous Roy-equation analysis of ππ scattering, we write down an extended Omnès representation of the pion vector form factor in terms of a few free parameters and study to which extent the modern high-statistics data sets can be described by the resulting fit function that follows from general principles of QCD. We find that statistically acceptable fits do become possible as soon as potential uncertainties in the energy calibration are taken into account, providing a strong cross check on the internal consistency of the data sets, but preferring a mass of the ω meson significantly lower than the current PDG average. In addition to a complete treatment of statistical and systematic errors propagated from the data, we perform a comprehensive analysis of the systematic errors in the dispersive representation and derive the consequences for the two-pion contribution to hadronic vacuum polarization. In a global fit to both time- and space-like data sets we find a μ ππ | ≤ 1 GeV  = 495.0(1.5)(2.1) × 10 − 10 and a μ ππ | ≤ 0.63 GeV  = 132.8(0.4)(1.0) × 10 − 10 . While the constraints are thus most stringent for low energies, we obtain uncertainty estimates throughout the whole energy range that should prove valuable in corroborating the corresponding contribution to the anomalous magnetic moment of the muon. As side products, we obtain improved constraints on the ππ P -wave, valuable input for future global analyses of low-energy ππ scattering, as well as a determination of the pion charge radius, 〈 r π 2 〉 = 0 . 429(1)(4) fm 2 .

A bstract In this third paper of a series dedicated to a dispersive treatment of the hadronic light-by-light (HLbL) tensor, we derive a partial-wave formulation for two-pion intermediate states in the HLbL contribution to the anomalous magnetic moment of the muon ( g − 2) μ , including a detailed discussion of the unitarity relation for arbitrary partial waves. We show that obtaining a final expression free from unphysical helicity partial waves is a subtle issue, which we thoroughly clarify. As a by-product, we obtain a set of sum rules that could be used to constrain future calculations of γ ∗ γ ∗ → ππ . We validate the formalism extensively using the pion-box contribution, defined by two-pion intermediate states with a pion-pole left-hand cut, and demonstrate how the full known result is reproduced when resumming the partial waves. Using dispersive fits to high-statistics data for the pion vector form factor, we provide an evaluation of the full pion box, a μ π  − box  = − 15.9(2) × 10 − 11 . As an application of the partial-wave formalism, we present a first calculation of ππ -rescattering effects in HLbL scattering, with γ ∗ γ ∗ → ππ helicity partial waves constructed dispersively using ππ phase shifts derived from the inverse-amplitude method. In this way, the isospin-0 part of our calculation can be interpreted as the contribution of the f 0 (500) to HLbL scattering in ( g − 2) μ . We argue that the contribution due to charged-pion rescattering implements corrections related to the corresponding pion polarizability and show that these are moderate. Our final result for the sum of pion-box contribution and its S -wave rescattering corrections reads a μ π  ‐ box  +  a μ , J  = 0 ππ , π  ‐ pole LHC  = − 24(1) × 10 − 11 .

A bstract New-physics (NP) constraints on first-generation quark-lepton interactions are particularly interesting given the large number of complementary processes and observables that have been measured. Recently, first hints for such NP effects have been observed as an apparent deficit in first-row CKM unitarity, known as the Cabibbo angle anomaly, and the CMS excess in q q ¯ → e + e − . Since the same NP would inevitably enter in searches for low-energy parity violation, such as atomic parity violation, parity-violating electron scattering, and coherent neutrino-nucleus scattering, as well as electroweak precision observables, a combined analysis is required to assess the viability of potential NP interpretations. In this article we investigate the interplay between LHC searches, the Cabibbo angle anomaly, electroweak precision observables, and low-energy parity violation by studying all simplified models that give rise to tree-level effects related to interactions between first-generation quarks and leptons. Matching these models onto Standard Model effective field theory, we derive master formulae in terms of the respective Wilson coefficients, perform a complete phenomenological analysis of all available constraints, point out how parity violation can in the future be used to disentangle different NP scenarios, and project the constraints achievable with forthcoming experiments.

A bstract While the low-energy part of the hadronic light-by-light (HLbL) tensor can be constrained from data using dispersion relations, for a full evaluation of its contribution to the anomalous magnetic moment of the muon ( g − 2) μ also mixed- and high-energy regions need to be estimated. Both can be addressed within the operator product expansion (OPE), either for configurations where all photon virtualities become large or one of them remains finite. Imposing such short-distance constraints (SDCs) on the HLbL tensor is thus a major aspect of a model-independent approach towards HLbL scattering. Here, we focus on longitudinal SDCs, which concern the amplitudes containing the pseudoscalar-pole contributions from π 0 , η , η′ . Since these conditions cannot be fulfilled by a finite number of pseudoscalar poles, we consider a tower of excited pseudoscalars, constraining their masses and transition form factors from Regge theory, the OPE, and phenomenology. Implementing a matching of the resulting expressions for the HLbL tensor onto the perturbative QCD quark loop, we are able to further constrain our calculation and significantly reduce its model dependence. We find that especially for the π 0 the corresponding increase of the HLbL contribution is much smaller than previous prescriptions in the literature would imply. Overall, we estimate that longitudinal SDCs increase the HLbL contribution by Δ a μ LSDC = 13 6 × 10 -11 . This number does not include the contribution from the charm quark, for which we find a μ c − quark = 3(1) × 10 − 11 .

A bstract We address the contribution of the 3 π channel to hadronic vacuum polarization (HVP) using a dispersive representation of the e + e − → 3 π amplitude. This channel gives the second-largest individual contribution to the total HVP integral in the anomalous magnetic moment of the muon ( g − 2) μ , both to its absolute value and uncertainty. It is largely dominated by the narrow resonances ω and ϕ , but not to the extent that the off-peak regions were negligible, so that at the level of accuracy relevant for ( g − 2) μ an analysis of the available data as model independent as possible becomes critical. Here, we provide such an analysis based on a global fit function using analyticity and unitarity of the underlying γ ∗ → 3 π amplitude and its normalization from a chiral low-energy theorem, which, in particular, allows us to check the internal consistency of the various e + e − → 3 π data sets. Overall, we obtain a μ 3 π | ≤1.8 GeV = 46 . 2(6)(6) × 10 −10 as our best estimate for the total 3 π contribution consistent with all (low-energy) constraints from QCD. In combination with a recent dispersive analysis imposing the same constraints on the 2 π channel below 1 GeV, this covers nearly 80% of the total HVP contribution, leading to a μ HVP = 692 . 3(3 . 3) × 10 −10 when the remainder is taken from the literature, and thus reaffirming the ( g −2) μ anomaly at the level of at least 3 . 4 σ . As side products, we find for the vacuum-polarization-subtracted masses M ω = 782 . 63(3)(1) MeV and M ϕ = 1019 . 20(2)(1) MeV, confirming the tension to the ω mass as extracted from the 2 π channel.

A bstract Isospin-breaking (IB) effects in the two-pion contribution to hadronic vacuum polarization (HVP) can be resonantly enhanced, if related to the interference of the ρ (770) and ω (782) resonances. This particular IB contribution to the pion vector form factor and thus the line shape in e + e − → π + π − can be described by the residue at the ω pole — the ρ - ω mixing parameter ϵ ω . Here, we argue that while in general analyticity requires this parameter to be real, the radiative channels π 0 γ , ππγ , ηγ can induce a small phase, whose size we estimate as δ ϵ = 3 . 5(1 . 0) ° by using a narrow-width approximation for the intermediate-state vector mesons. We then perform fits to the e + e − → π + π − data base and study the consequences for the two-pion HVP contribution to the anomalous magnetic moment of the muon, its IB part due to ρ - ω mixing, and the mass of the ω resonance. We find that the global fit does prefer a non-vanishing value of δ ϵ = 4 . 5(1 . 2) ° , close to the narrow-resonance expectation, but with a large spread among the data sets, indicating systematic differences in the ρ - ω region.

A bstract We propose a formalism to extract the γπ → ππ chiral anomaly F 3 π from calculations in lattice QCD performed at larger-than-physical pion masses. To this end, we start from a dispersive representation of the γ (*) π → ππ amplitude, whose main quark-mass dependence arises from the ππ scattering phase shift and can be derived from chiral perturbation theory via the inverse-amplitude method. With parameters constrained by lattice calculations of the P -wave phase shift, we use this combination of dispersion relations and effective field theory to extrapolate two recent γ (*) π → ππ calculations in lattice QCD to the physical point. Our formalism allows us to extract the radiative coupling of the ρ (770) meson and, for the first time, the chiral anomaly F 3 π = 38(16)(11) GeV − 3 . The result is consistent with the chiral prediction albeit within large uncertainties, which will improve in accordance with progress in future lattice-QCD computations.

A bstract In this work, we present an evaluation of subleading effects in the hadronic light-by-light contribution to the anomalous magnetic moment of the muon. Using a recently derived optimized basis, we first study the matching of axial-vector contributions to short-distance constraints at the level of the scalar basis functions, finding that also the tails of the pseudoscalar poles and tensor mesons play a role. We then develop a matching strategy that allows for a combined evaluation of axial-vector and short-distance constraints, supplemented by an estimate of tensor-meson contributions based on simplified assumptions for their transition form factors. Uncertainties are primarily propagated from the axial-vector transition form factors and the variation of the matching scale, but we also consider estimates of the low-energy effect of hadronic states not explicitly included. In total, we obtain a μ HLbL subleading = 33 . 2(7 . 2) × 10 −11 , which in combination with previously evaluated contributions in the dispersive approach leads to a μ HLbL total = 101 . 9(7 . 9) × 10 −11 .