Phenomenological Estimate of Isospin Breaking in Hadronic Vacuum Polarization.

Puzzles in the determination of the hadronic-vacuum-polarization contribution currently impede a conclusive interpretation of the precision measurement of the anomalous magnetic moment of the muon at the Fermilab experiment. One such puzzle concerns tensions between evaluations in lattice QCD and using e^{+}e^{-}→hadrons cross-section data. In lattice QCD, the dominant isospin-symmetric part and isospin-breaking (IB) corrections are calculated separately, with very different systematic effects. Identifying these two pieces in a data-driven approach provides an opportunity to compare them individually and trace back the source of the discrepancy. Here, we estimate the IB component of the lattice-QCD calculations from phenomenology, based on a comprehensive study of exclusive contributions that can be enhanced via infrared singularities, threshold effects, or hadronic resonances, including, for the first time, in the e^{+}e^{-}→3π channel. We observe sizable cancellations among different channels, with a sum that even suggests a slightly larger result for the QED correction than obtained in lattice QCD. We conclude that the tensions between lattice QCD and e^{+}e^{-} data therefore cannot be explained by the IB contributions in the lattice-QCD calculations.

Improved Standard-Model Prediction for π

We present an improved standard-model (SM) prediction for the dilepton decay of the neutral pion. The loop amplitude is determined by the pion transition form factor for π^{0}→γ^{*}γ^{*}, for which we employ a dispersive representation that incorporates both spacelike and timelike data as well as short-distance constraints. The resulting SM branching fraction, Br[π^{0}→e^{+}e^{-}]=6.25(3)×10^{-8}, sharpens constraints on physics beyond the SM, including pseudoscalar and axial-vector mediators.

Two-Loop Analysis of the Pion Mass Dependence of the ρ Meson.

Analyzing the pion mass dependence of ππ scattering phase shifts beyond the low-energy region requires the unitarization of the amplitudes from chiral perturbation theory. In the two-flavor theory, unitarization via the inverse-amplitude method (IAM) can be justified from dispersion relations, which is therefore expected to provide reliable predictions for the pion mass dependence of results from lattice QCD calculations. In this work, we provide compact analytic expression for the two-loop partial-wave amplitudes for J=0, 1, 2 required for the IAM at subleading order. To analyze the pion mass dependence of recent lattice QCD results for the P wave, we develop a fit strategy that for the first time allows us to perform stable two-loop IAM fits and assess the chiral convergence of the IAM approach. While the comparison of subsequent orders suggests a breakdown scale not much below the ρ mass, a detailed understanding of the systematic uncertainties of lattice QCD data is critical to obtain acceptable fits, especially at larger pion masses.

Where Is the Lightest Charmed Scalar Meson?

The lightest charmed scalar meson is known as the D_{0}^{*}(2300), which is one of the earliest new hadron resonances observed at modern B factories. We show here that the parameters assigned to the lightest scalar D meson are in conflict with the precise LHCb data of the decay B^{-}→D^{+}π^{-}π^{-}. On the contrary, these data can be well described by an unitarized chiral amplitude containing a much lighter charmed scalar meson, the D_{0}^{*}(2100). We also extract the low-energy S-wave Dπ phase of the decay B^{-}→D^{+}π^{-}π^{-} from the data in a model-independent way, and show that its difference from the Dπ scattering phase shift can be traced back to an intermediate ρ^{-} exchange. Our work highlights that an analysis of data consistent with chiral symmetry, unitarity, and analyticity is mandatory in order to extract the properties of the ground-state scalar mesons in the singly heavy sector correctly, in analogy to the light scalar mesons f_{0}(500) and K_{0}^{*}(700).

Erratum: Nucleon Matrix Elements of the Antisymmetric Quark Tensor [Phys. Rev. Lett. 122, 122001 (2019)].

This corrects the article DOI: 10.1103/PhysRevLett.122.122001.

Nucleon Matrix Elements of the Antisymmetric Quark Tensor.

If physics beyond the standard model enters well above the electroweak scale, its low-energy effects are described by standard model effective field theory. Already, at dimension 6, many operators involve the antisymmetric quark tensor q[over ¯]σ^{µν}q, whose matrix elements are difficult to constrain from experiment, Ward identities, or low-energy theorems, in contrast to the corresponding vector and axial-vector or even scalar and pseudoscalar currents. However, with normalizations determined from lattice QCD, analyticity and unitarity often allow one to predict the momentum dependence in a large kinematic range. Starting from recent results in the meson sector, we extend this method to the nucleon case and, in combination with pole dominance, provide a comprehensive assessment of the current status of the nucleon form factors of the quark tensor.

Pion-Pole Contribution to Hadronic Light-By-Light Scattering in the Anomalous Magnetic Moment of the Muon.

The π^{0} pole constitutes the lowest-lying singularity of the hadronic light-by-light (HLBL) tensor, and thus, it provides the leading contribution in a dispersive approach to HLBL scattering in the anomalous magnetic moment of the muon (g-2)_{µ}. It is unambiguously defined in terms of the doubly virtual pion transition form factor, which in principle, can be accessed in its entirety by experiment. We demonstrate that, in the absence of a direct measurement, the full spacelike doubly virtual form factor can be reconstructed very accurately based on existing data for e^{+}e^{-}→3π, e^{+}e^{-}→e^{+}e^{-}π^{0}, and the π^{0}→γγ decay width. We derive a representation that incorporates all the low-lying singularities of the form factor, matches correctly onto the asymptotic behavior expected from perturbative QCD, and is suitable for the evaluation of the (g-2)_{µ} loop integral. The resulting value, a_{µ}^{π^{0}-pole}=62.6_{-2.5}^{+3.0}×10^{-11}, for the first time, represents a complete data-driven determination of the pion-pole contribution with fully controlled uncertainty estimates. In particular, we show that already improved singly virtual measurements alone would allow one to further reduce the uncertainty in a_{µ}^{π^{0}-pole}.

Matching Pion-Nucleon Roy-Steiner Equations to Chiral Perturbation Theory.

We match the results for the subthreshold parameters of pion-nucleon scattering obtained from a solution of Roy-Steiner equations to chiral perturbation theory up to next-to-next-to-next-to-leading order, to extract the pertinent low-energy constants including a comprehensive analysis of systematic uncertainties and correlations. We study the convergence of the chiral series by investigating the chiral expansion of threshold parameters up to the same order and discuss the role of the Δ(1232) resonance in this context. Results for the low-energy constants are also presented in the counting scheme usually applied in chiral nuclear effective field theory, where they serve as crucial input to determine the long-range part of the nucleon-nucleon potential as well as three-nucleon forces.

High-Precision Determination of the Pion-Nucleon σ Term from Roy-Steiner Equations.

We present a determination of the pion-nucleon (πN) σ term σ_{πN} based on the Cheng-Dashen low-energy theorem (LET), taking advantage of the recent high-precision data from pionic atoms to pin down the πN scattering lengths as well as of constraints from analyticity, unitarity, and crossing symmetry in the form of Roy-Steiner equations to perform the extrapolation to the Cheng-Dashen point in a reliable manner. With isospin-violating corrections included both in the scattering lengths and the LET, we obtain σ_{πN}=(59.1±1.9±3.0) MeV=(59.1±3.5) MeV, where the first error refers to uncertainties in the πN amplitude and the second to the LET. Consequences for the scalar nucleon couplings relevant for the direct detection of dark matter are discussed.

Addendum: A dispersive analysis of η ' → π + π - γ and η ' → ℓ + ℓ - γ.

In this addendum to Ref. [1] we show that the mismatch between the ρ - ω mixing parameter ϵ ρ ω as extracted from η ' → π + π - γ and e + e - → π + π - can be resolved by including higher orders in the expansion in e 2 in the description of the η ' → π + π - γ decay. We repeat the analysis in this extended framework and update the numerical results accordingly.

A dispersive analysis of η ' → π + π - γ and η ' → ℓ + ℓ - γ.

We present a dispersive representation of the η ' transition form factor that allows one to account, in a consistent way, for the effects of ρ - ω mixing in both the isoscalar and the isovector contributions. Using this formalism, we analyze recent data on η ' → π + π - γ to constrain the isovector part of the form factor, individually and in combination with data for the pion vector form factor, which suggests a tension in the ρ - ω mixing parameter. As a first application, we use our results, in combination with the most recent input for the isoscalar part of the form factor, to predict the corresponding spectrum of η ' → ℓ + ℓ - γ , in particular we find the slope parameter b η ' = 1.455 ( 24 ) GeV - 2 . With forthcoming data on the latter process, our results establish the necessary framework to improve the evaluation of the η ' -pole contribution to the anomalous magnetic moment of the muon using experimental input from both η ' decay channels.

Hadronic vacuum polarization and vector-meson resonance parameters from e + e - → π 0 γ.

We study the reaction e + e - → π 0 γ based on a dispersive representation of the underlying π 0 → γ γ ∗ transition form factor. As a first application, we evaluate the contribution of the π 0 γ channel to the hadronic-vacuum-polarization correction to the anomalous magnetic moment of the muon. We find a µ π 0 γ | ≤ 1.35 GeV = 43.8 ( 6 ) × 10 - 11 , in line with evaluations from the direct integration of the data. Second, our fit determines the resonance parameters of ω and ϕ . We observe good agreement with the e + e - → 3 π channel, explaining a previous tension in the ω mass between π 0 γ and 3 π by an unphysical phase in the fit function. Combining both channels we find M ¯ ω = 782.736 ( 24 ) MeV and M ¯ ϕ = 1019.457 ( 20 ) MeV for the masses including vacuum-polarization corrections. The ϕ mass agrees perfectly with the PDG average, which is dominated by determinations from the K ¯ K channel, demonstrating consistency with 3 π and π 0 γ . For the ω mass, our result is consistent but more precise, exacerbating tensions with the ω mass extracted via isospin-breaking effects from the 2 π channel.