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 Limits on Lepton-Flavor-Violating Decays of Light Pseudoscalars via Spin-Dependent µâ†’e Conversion in Nuclei.

Lepton-flavor-violating decays of light pseudoscalars, P=π^{0},η,η^{'}→µe, are stringently suppressed in the standard model up to tiny contributions from neutrino oscillations, so that their observation would be a clear indication for physics beyond the standard model. However, in effective field theory such decays proceed via axial-vector, pseudoscalar, or gluonic operators, which are, at the same time, probed in spin-dependent µâ†’e conversion in nuclei. We derive master formulas that connect both processes in a model-independent way in terms of Wilson coefficients and study the implications of current µâ†’e limits in titanium for the P→µe decays. We find that these indirect limits surpass direct ones by many orders of magnitude.

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.

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.

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.

Mixed Leptonic and Hadronic Corrections to the Anomalous Magnetic Moment of the Muon.

Higher-order hadronic corrections to the anomalous magnetic moment of the muon have been evaluated including next-to-next-to-leading-order insertions of hadronic vacuum polarization and next-to-leading-order corrections to hadronic light-by-light scattering. This leaves a set of mixed leptonic and hadronic corrections in the form of double-bubble topologies as the only remaining hadronic effect at O(α^{4}). Here, we estimate these contributions by analyzing the respective cuts of the diagrams, suggesting that the impact is limited to ≲1×10^{-11} and thus negligible at the level of the final precision of the Fermilab g-2 experiment.

Pion-Nucleon Sigma Term from Lattice QCD.

We present an analysis of the pion-nucleon σ-term σ_{πN} using six ensembles with 2+1+1-flavor highly improved staggered quark action generated by the MILC Collaboration. The most serious systematic effect in lattice calculations of nucleon correlation functions is the contribution of excited states. We estimate these using chiral perturbation theory (χPT) and show that the leading contribution to the isoscalar scalar charge comes from Nπ and Nππ states. Therefore, we carry out two analyses of lattice data to remove excited-state contamination, the standard one and a new one including Nπ and Nππ states. We find that the standard analysis gives σ_{πN}=41.9(4.9) MeV, consistent with previous lattice calculations, while our preferred χPT-motivated analysis gives σ_{πN}=59.6(7.4) MeV, which is consistent with phenomenological values obtained using πN scattering data. Our data on one physical pion mass ensemble were crucial for exposing this difference, therefore, calculations on additional physical mass ensembles are needed to confirm our result and resolve the tension between lattice QCD and phenomenology.

Hints of lepton flavor universality violations.

Mounting evidence shows where the standard model may be incomplete.

Fermi Constant from Muon Decay Versus Electroweak Fits and Cabibbo-Kobayashi-Maskawa Unitarity.

The Fermi constant G_{F} is extremely well measured through the muon lifetime, defining one of the key fundamental parameters in the standard model (SM). Therefore, to search for physics beyond the SM (BSM) via G_{F}, the constraining power is determined by the precision of the second-best independent determination of G_{F}. The best alternative extractions of G_{F} proceed either via the global electroweak (EW) fit or from superallowed ß decays in combination with the Cabibbo angle measured in kaon, τ, or D decays. Both variants display some tension with G_{F} from muon decay, albeit in opposite directions, reflecting the known tensions within the EW fit and hints for the apparent violation of Cabibbo-Kobayashi-Maskawa unitarity, respectively. We investigate how BSM physics could bring the three determinations of G_{F} into agreement using SM effective field theory and comment on future perspectives.

Toward Complete Leading-Order Predictions for Neutrinoless Double ß Decay.

The amplitude for the neutrinoless double ß (0νßß) decay of the two-neutron system nn→ppe^{-}e^{-} constitutes a key building block for nuclear-structure calculations of heavy nuclei employed in large-scale 0νßß searches. Assuming that the 0νßß process is mediated by a light-Majorana-neutrino exchange, a systematic analysis in chiral effective field theory shows that already at leading order a contact operator is required to ensure renormalizability. In this Letter, we develop a method to estimate the numerical value of its coefficient (in analogy to the Cottingham formula for electromagnetic contributions to hadron masses) and validate the result by reproducing the charge-independence-breaking contribution to the nucleon-nucleon scattering lengths. Our central result, while derived in dimensional regularization, is given in terms of the renormalized amplitude A_{ν}(|p|,|p^{'}|), matching to which will allow one to determine the contact-term contribution in regularization schemes employed in nuclear-structure calculations. Our results thus greatly reduce a crucial uncertainty in the interpretation of searches for 0νßß decay.

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.

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.

ß Decays as Sensitive Probes of Lepton Flavor Universality.

Nuclear ß decays as well as the decay of the neutron are well-established low-energy probes of physics beyond the standard model (SM). In particular, with the axial-vector coupling of the nucleon g_{A} determined from lattice QCD, the comparison between experiment and SM prediction is commonly used to derive constraints on right-handed currents. Further, in addition to the CKM element V_{us} from kaon decays, V_{ud} from ß decays is a critical input for the test of CKM unitarity. Here, we point out that the available information on ß decays can be reinterpreted as a stringent test of lepton flavor universality (LFU). In fact, we find that the ratio of V_{us} from kaon decays over V_{us} from ß decays (assuming CKM unitarity) is extremely sensitive to LFU violation (LFUV) in W-µ-ν couplings thanks to a CKM enhancement by (V_{ud}/V_{us})^{2}∼20. From this perspective, recent hints for the violation of CKM unitarity can be viewed as further evidence for LFUV, fitting into the existing picture exhibited by semileptonic B decays and the anomalous magnetic moments of muon and electron. Finally, we comment on the future sensitivity that can be reached with this LFU violating observable and discuss complementary probes of LFU that may reach a similar level of precision, such as Γ(π→µν)/Γ(π→eν) at the PEN and PiENu experiments or even direct measurements of W→µν at an FCC-ee.

Hadronic Vacuum Polarization: (g-2)_{µ} versus Global Electroweak Fits.

Hadronic vacuum polarization (HVP) is not only a critical part of the standard model (SM) prediction for the anomalous magnetic moment of the muon (g-2)_{µ}, but also a crucial ingredient for global fits to electroweak (EW) precision observables due to its contribution to the running of the fine-structure constant encoded in Δα_{had}^{(5)}. We find that with modern EW precision data, including the measurement of the Higgs mass, the global fit alone provides a competitive, independent determination of Δα_{had}^{(5)}|_{EW}=270.2(3.0)×10^{-4}. This value actually lies below the range derived from e^{+}e^{-}→hadrons cross section data, and thus goes into the opposite direction as would be required if a change in HVP were to bring the SM prediction for (g-2)_{µ} into agreement with the Brookhaven measurement. Depending on the energy where the bulk of the changes in the cross section occurs, reconciling experiment and SM predictions for (g-2)_{µ} by adjusting HVP would thus not necessarily weaken the case for physics beyond the SM (BSM), but to some extent shift it from (g-2)_{µ} to the EW fit. We briefly explore some options of BSM scenarios that could conceivably explain the ensuing tension.

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.

CP Violation in Higgs-Gauge Interactions: From Tabletop Experiments to the LHC.

We investigate the interplay between the high- and low-energy phenomenology of CP-violating interactions of the Higgs boson with gauge bosons. For this purpose, we use an effective field theory approach and consider all dimension-six operators arising in so-called universal theories. We compute their loop-induced contributions to electric dipole moments and the CP asymmetry in B→X_{s}γ and compare the resulting current and prospective constraints to the projected sensitivity of the LHC. Low-energy measurements are shown to generally have a far stronger constraining power, which results in highly correlated allowed regions in coupling space-a distinctive pattern that could be probed at the high-luminosity LHC.

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}.

No-Go Theorem for Nonstandard Explanations of the τ→K_{S}πν_{τ} CP Asymmetry.

The CP asymmetry in τ→K_{S}πν_{τ}, as measured by the BABAR collaboration, differs from the standard model prediction by 2.8σ. Most nonstandard interactions do not allow for the required strong phase needed to produce a nonvanishing CP asymmetry, leaving only new tensor interactions as a possible mechanism. We demonstrate that, contrary to previous assumptions in the literature, the crucial interference between vector and tensor phases is suppressed by at least 2 orders of magnitude due to Watson's final-state-interaction theorem. Furthermore, we find that the strength of the relevant CP-violating tensor interaction is strongly constrained by bounds from the neutron electric dipole moment and D-D[over ¯] mixing. These observations together imply that it is extremely difficult to explain the current τ→K_{S}πν_{τ} measurement in terms of physics beyond the standard model originating in the ultraviolet.

Improved Limits for Higgs-Portal Dark Matter from LHC Searches.

Searches for invisible Higgs decays at the Large Hadron Collider constrain dark matter Higgs-portal models, where dark matter interacts with the standard model fields via the Higgs boson. While these searches complement dark matter direct-detection experiments, a comparison of the two limits depends on the coupling of the Higgs boson to the nucleons forming the direct-detection nuclear target, typically parametrized in a single quantity f_{N}. We evaluate f_{N} using recent phenomenological and lattice-QCD calculations, and include for the first time the coupling of the Higgs boson to two nucleons via pion-exchange currents. We observe a partial cancellation for Higgs-portal models that makes the two-nucleon contribution anomalously small. Our results, summarized as f_{N}=0.308(18), show that the uncertainty of the Higgs-nucleon coupling has been vastly overestimated in the past. The improved limits highlight that state-of-the-art nuclear physics input is key to fully exploiting experimental searches.