https://www.zora.uzh.ch/id/eprint/191493/1/1-s2.0-S0370157320302556-main.pdf

The anomalous magnetic moment of the muon in the Standard Model

A Call for New Physics : The Muon Anomalous Magnetic Moment and Lepton Flavor Violation

Motivated by additional experimental hints of Lepton Flavour Universality violation in B decays, both in charged- and in neutral-current processes, we analyse the ingredients necessary to provide a combined description of these phenomena. By means of an Effective Field Theory (EFT) approach, based on the hypothesis of New Physics coupled predominantly to the third generation of left-handed quarks and leptons, we show how this is possible. We demonstrate, in particular, how to solve the problems posed by electroweak precision tests and direct searches with a rather natural choice of model parameters, within the context of a U(2)q ×U(2)l flavour symmetry. We further exemplify the general EFT findings by means of simplified models with explicit mediators in the TeV range: coloured scalar or vector leptoquarks and colour-less vectors. Among these, the case of an SU(2)L-singlet vector leptoquark emerges as a particularly simple and successful framework.

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B -physics anomalies: a guide to combined explanations

We address the contribution of the $3\pi$ channel to hadronic vacuum polarization (HVP) using a dispersive representation of the $e^+e^-\to 3\pi$ amplitude. This channel gives the second-largest individual contribution to the total HVP integral in the anomalous magnetic moment of the muon $(g-2)_\mu$, both to its absolute value and uncertainty. It is largely dominated by the narrow resonances $\omega$ and $\phi$, but not to the extent that the off-peak regions were negligible, so that at the level of accuracy relevant for $(g-2)_\mu$ 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 $\gamma^*\to3\pi$ amplitude and its normalization from a chiral low-energy theorem, which, in particular, allows us to check the internal consistency of the various $e^+e^-\to 3\pi$ data sets. Overall, we obtain $a_\mu^{3\pi}|_{\leq 1.8\,\text{GeV}}=46.2(6)(6)\times 10^{-10}$ as our best estimate for the total $3\pi$ contribution consistent with all (low-energy) constraints from QCD. In combination with a recent dispersive analysis imposing the same constraints on the $2\pi$ channel below $1\,\text{GeV}$, this covers nearly $80\%$ of the total HVP contribution, leading to $a_\mu^\text{HVP}=692.3(3.3)\times 10^{-10}$ when the remainder is taken from the literature, and thus reaffirming the $(g-2)_\mu$ anomaly at the level of at least $3.4\sigma$. As side products, we find for the vacuum-polarization-subtracted masses $M_\omega=782.63(3)(1)\,\text{MeV}$ and $M_\phi=1019.20(2)(1)\,\text{MeV}$, confirming the tension to the $\omega$ mass as extracted from the $2\pi$ channel.

/pdf/three-pion-contribution-to-hadronic-vacuum-polarization-3iaox9z950.pdf

Three-pion contribution to hadronic vacuum polarization

Following updates in the compilation of ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\text{hadrons}$ data, this work presents reevaluations of the hadronic vacuum polarization contributions to the anomalous magnetic moments of the electron (${a}_{e}$), muon (${a}_{\ensuremath{\mu}}$) and tau lepton (${a}_{\ensuremath{\tau}}$), to the ground-state hyperfine splitting of muonium and also updates the hadronic contributions to the running of the QED coupling at the mass scale of the $Z$ boson, $\ensuremath{\alpha}({M}_{Z}^{2})$. Combining the results for the hadronic vacuum polarization contributions with recent updates for the hadronic light-by-light corrections, the electromagnetic and the weak contributions, the deviation between the measured value of ${a}_{\ensuremath{\mu}}$ and its Standard Model prediction amounts to $\mathrm{\ensuremath{\Delta}}{a}_{\ensuremath{\mu}}=(28.02\ifmmode\pm\else\textpm\fi{}7.37)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, corresponding to a muon $g\ensuremath{-}2$ discrepancy of $3.8\ensuremath{\sigma}$.

g − 2 of charged leptons, α ( M Z 2 ) , and the hyperfine splitting of muonium

We present a unified explanation for the $B$-decay anomalies in ${R}_{{D}^{(*)}}$ and ${R}_{K}$ together with the anomalous muon magnetic moment, consistent with the constraints from the current measurements of leptonic decay rates and ${D}^{0}\ensuremath{-}{\overline{D}}^{0}$, ${B}_{s}^{0}\ensuremath{-}{\overline{B}}_{s}^{0}$ mixings, within the framework of a minimal left-right symmetric gauge theory motivated by one of the low-energy subgroups of ${E}_{6}$ naturally accommodating leptoquarks.

Towards a unified explanation of R D (*) , R K and (g -2 ) μ anomalies in a left-right model with leptoquarks

The LHCb has measured the ratios of $B\ensuremath{\rightarrow}{K}^{*}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ to $B\ensuremath{\rightarrow}{K}^{*}{e}^{+}{e}^{\ensuremath{-}}$ branching fractions in two dilepton invariant mass squared bins, which deviate from the standard model predictions by approximately $25\ensuremath{\sigma}$ These new measurements strengthen the hint of lepton flavor universality breaking which was observed earlier in $B\ensuremath{\rightarrow}K{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ decays In this work we explore the possibility of explaining these anomalies within the framework of $R$-parity violating interactions In this framework, $b\ensuremath{\rightarrow}s{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ transitions are generated through tree and one loop diagrams involving exchange of down-type right-handed squarks, up-type left-handed squarks and left-handed sneutrinos We find that the tree level contributions are not enough to explain the anomalies, but at one loop, simultaneous explanation of the deviations in $B\ensuremath{\rightarrow}{K}^{*}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ and $B\ensuremath{\rightarrow}K{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ is feasible for a parameter space of the Yukawa couplings that is consistent with the bounds coming from $B\ensuremath{\rightarrow}{K}^{(*)}\ensuremath{\nu}\overline{\ensuremath{\nu}}$ and ${D}^{0}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ decays and ${B}_{s}\ensuremath{-}{\overline{B}}_{s}$ mixing

Scrutinizing R -parity violating interactions in light of R K ( * ) data

We present a determination of the pion charge radius from high precision data on the pion vector form factor from both timelike and spacelike regions, using a novel formalism based on analyticity and unitarity. At low energies, instead of the poorly known modulus of the form factor, we use its phase, known with high accuracy from Roy equations for pi pi elastic scattering via the Fermi-Watson theorem. We use also the values of the modulus at several higher timelike energies, where the data from e(+)e(-) annihilation and tau decay are mutually consistent, as well as the most recent measurements at spacelike momenta. The experimental uncertainties are implemented by Monte Carlo simulations. The results, which do not rely on a specific parametrization, are optimal for the given input information and do not depend on the unknown phase of the form factor above the first inelastic threshold. Our prediction for the charge radius of the pion is r(pi) = (0.657 +/- 0.003) fm, which amounts to an increase in precision by a factor of about 2.7 compared to the Particle Data Group average.

Electromagnetic Charge Radius of the Pion at High Precision

The two-pion low-energy contribution to the anomalous magnetic moment of the muon, ${a}_{\ensuremath{\mu}}\ensuremath{\equiv}(g\ensuremath{-}2{)}_{\ensuremath{\mu}}/2$, expressed as an integral over the modulus squared of the pion electromagnetic form factor, brings a relatively large contribution to the theoretical error, since the low accuracy of experimental measurements in this region is amplified by the drastic increase of the integration kernel. We derive stringent constraints on the two-pion contribution by exploiting analyticity and unitarity of the pion electromagnetic form factor. To avoid the poor knowledge of the modulus of this function, we use instead its phase, known with high precision in the elastic region from Roy equations for pion-pion scattering via the Fermi-Watson theorem. Above the inelastic threshold we adopt a conservative integral condition on the modulus, determined from data and perturbative QCD. Additional high precision data on the modulus in the range 0.65--0.71 GeV, obtained from ${e}^{+}{e}^{\ensuremath{-}}$ annihilation and $\ensuremath{\tau}$-decay experiments, are used to improve the predictions on the modulus at lower energies by means of a parametrization-free analytic extrapolation. The results are optimal for a given input and do not depend on the unknown phase of the form factor above the inelastic threshold. The present work improves a previous analysis based on the same technique, including more experimental data and employing better statistical tools for their treatment. We obtain for the contribution to ${a}_{\ensuremath{\mu}}$ from below 0.63 GeV the value $(133.258\ifmmode\pm\else\textpm\fi{}0.723)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, which amounts to a reduction of the theoretical error by about $6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$.

Precise determination of the low-energy hadronic contribution to the muon g-2 from analyticity and unitarity: An improved analysis

The rare decay $B\ensuremath{\rightarrow}{K}^{*}(\ensuremath{\rightarrow}K\ensuremath{\pi})\ensuremath{\nu}\overline{\ensuremath{\nu}}$ is expected to play an important role in searches for physics beyond the Standard Model at the near future $B$-physics experiments. We investigate resonant and nonresonant backgrounds that arise beyond the narrow-width approximation for the ${K}^{*}$. Nonresonant $B\ensuremath{\rightarrow}K\ensuremath{\pi}\ensuremath{\nu}\overline{\ensuremath{\nu}}$ decays are analyzed in the region of low hadronic recoil, where $B\ensuremath{\rightarrow}K\ensuremath{\pi}$ form factors from the heavy-hadron-chiral-perturbation theory are available. In a Breit-Wigner--type model interference-induced effects in the ${K}^{*}$ signal region are found to be sizable, as large as 20% in the branching ratio. Corresponding effects in the longitudinal polarization fraction ${F}_{L}$ are smaller, at most around a few percent. Effects of the broad scalar states ${K}_{0}^{*}$ and $\ensuremath{\kappa}$ are at the level of percent in the branching fraction in the ${K}^{*}$ signal region and negligible in ${F}_{L}$. Since the backgrounds to ${F}_{L}$ are small, this observable constitutes a useful probe of form factor calculations or, alternatively, of right-handed currents in the entire ${q}^{2}$ region. The forward-backward asymmetry in the $K\ensuremath{\pi}$ system, ${A}_{\mathrm{FB}\text{ }\mathrm{L}}^{K}$, with normalization to the longitudinal decay rate probes predominantly $S$, $P$-wave interference free of short-distance coefficients and can therefore be used to control the resonant and nonresonant backgrounds.

Diganta Das

Papers

Towards a unified explanation of R D (*) , R K and (g -2 ) μ anomalies in a left-right model with leptoquarks

Scrutinizing R -parity violating interactions in light of R K ( * ) data

Electromagnetic Charge Radius of the Pion at High Precision

Precise determination of the low-energy hadronic contribution to the muon g-2 from analyticity and unitarity: An improved analysis

Revisiting B → K * ( → K π ) ν ν ¯ decays