Toward testing the magnetic moment of the tau at one part per million

If physics beyond the Standard Model (BSM) explains the 4.2 σ difference between the Standard Model and measured muon anomalous magnetic moment a μ , minimal flavor violation predicts a shift in the analog quantity for the τ lepton a τ at the 10 − 6 level, and even larger effects are possible in generic BSM scenarios such as leptoquarks. We show that this produces equivalent BSM deviations in the Pauli form factor F 2 ( s ) at s = ( 10  GeV ) 2 and report the first complete two-loop prediction of Re F eff 2 ( 100 GeV 2 ) = − 268.77 ( 50 ) × 10 − 6 for resonant τ -pair production in e + e − → Υ ( n S ) → τ + τ − , = 1 , 2, 3. Re  F eff 2 can be measured from e − -helicity-dependent transverse and longitudinal asymmetries in τ -pair events, which requires a longitudinally polarized e − beam. We discuss how Belle II asymmetry measurements could probe a BSM τ at 10 − 6 , assuming such a polarization upgrade of the SuperKEKB e + e − collider, and conclude by outlining the next steps to be taken in theory and experiment along this new avenue for exploring realistic BSM effects in a τ

Coherent elastic neutrino-nucleus scattering: EFT analysis and nuclear responses

The cross section for coherent elastic neutrino-nucleus scattering (CEνNS) depends on the response of the target nucleus to the external current, in the Standard Model (SM) mediated by the exchange of a Z boson. This is typically subsumed into an object called the weak form factor of the nucleus. Here, we provide results for this form factor calculated using the large-scale nuclear shell model for a wide range of nuclei of relevance for current CEνNS experiments, including cesium, iodine, argon, fluorine, sodium, germanium, and xenon. In addition, we provide the responses needed to capture the axial-vector part of the cross section, which does not scale coherently with the number of neutrons, but may become relevant for the SM prediction of CEνNS on target nuclei with nonzero spin. We then generalize the formalism allowing for contributions beyond the SM. In particular, we stress that in this case, even for vector and axial-vector operators, the standard weak form factor does not apply anymore, but needs to be replaced by the appropriate combination of the underlying nuclear structure factors. We provide the corresponding expressions for vector, axial-vector, but also (pseudo)scalar, tensor, and dipole effective operators, including two-body-current effects as predicted from chiral effective field theory (EFT). Finally, we update the spin-dependent structure factors for dark matter scattering off nuclei according to our improved treatment of the axial-vector responses

Dynamical Wilson fermions and the problem of the chiral limit in compact lattice QED

We compare the approach to the chiral transition line ~\kappa_c(\bt)~ in quenched and full compact lattice QED with Wilson fermions within the confinement phase, especially in the pseudoscalar sector of the theory. We show that in the strong coupling limit ($\beta =0$) the quenched theory is a good approximation to the full one, in contrast to the case of $\beta =0.8$. At the larger $\beta$-value the transition in the full theory is inconsistent with the zero--mass limit of the pseudoscalar particle, thus prohibiting the definition of a chiral limit.Comment: 13 pages LaTeX (epsf), all figures include

Reconciling threshold and subthreshold expansions for pion-nucleon scattering

Heavy-baryon chiral perturbation theory (ChPT) at one loop fails in relating the pion-nucleon amplitude in the physical region and for subthreshold kinematics due to loop effects enhanced by large low-energy constants. Studying the chiral convergence of threshold and subthreshold parameters up to fourth order in the small-scale expansion, we address the question to what extent this tension can be mitigated by including the $\Delta(1232)$ as an explicit degree of freedom and/or using a covariant formulation of baryon ChPT. We find that the inclusion of the $\Delta$ indeed reduces the low-energy constants to more natural values and thereby improves consistency between threshold and subthreshold kinematics. In addition, even in the $\Delta$-less theory the resummation of $1/m_N$ corrections in the covariant scheme improves the results markedly over the heavy-baryon formulation, in line with previous observations in the single-baryon sector of ChPT that so far have evaded a profound theoretical explanation.Comment: 10 pages, 4 tables, Mathematica notebook with the analytic expressions for threshold and subthreshold parameters included as supplementary material; journal versio

Dark-matter-nucleus scattering in chiral effective field theory

Chiral effective field theory allows one to calculate the response of few-nucleon systems to external currents, both for currents that can be probed in the Standard Model and ones that only exist in Standard-Model extensions. In combination with state-of-the-art many-body methods, the constraints from chiral symmetry can then be implemented in nuclear structure factors that describe the response of atomic nuclei in direct-detection searches for dark matter. We review the present status of this approach, including the role of coherently enhanced two-body currents, the discrimination of dark matter candidates based on the nuclear response functions, and limits on Higgs-portal dark matter

Chiral extrapolation of hadronic vacuum polarization and isospin-breaking corrections

By far the biggest contribution to hadronic vacuum polarization (HVP) arises from the two-pion channel. Its quark-mass dependence can be evaluated by combining dispersion relations with chiral perturbation theory, providing guidance on the functional form of chiral extrapolations, or even interpolations around the physical point. In addition, the approach allows one to estimate in a controlled way the isospin-breaking (IB) corrections that arise from the pion mass difference. As an application, we present an updated estimate of phenomenological expectations for electromagnetic and strong IB corrections to the HVP contribution to the anomalous magnetic moment of the muon. In particular, we include IB effects in the K¯K channel, which are enhanced due to the proximity of the K¯K threshold and the ϕ resonance. The resulting estimates make it unlikely that the current tension between lattice-QCD and data-driven evaluations of the HVP contribution is caused by IB corrections

Quantum Chaos in Compact Lattice QED

Complete eigenvalue spectra of the staggered Dirac operator in quenched $4d$ compact QED are studied on $8^3 \times 4$ and $8^3 \times 6$ lattices. We investigate the behavior of the nearest-neighbor spacing distribution $P(s)$ as a measure of the fluctuation properties of the eigenvalues in the strong coupling and the Coulomb phase. In both phases we find agreement with the Wigner surmise of the unitary ensemble of random-matrix theory indicating quantum chaos. Combining this with previous results on QCD, we conjecture that quite generally the non-linear couplings of quantum field theories lead to a chaotic behavior of the eigenvalues of the Dirac operator.Comment: 11 pages, 4 figure

Spectrum of the U(1) staggered Dirac operator in four dimensions

We compare the low-lying spectrum of the staggered Dirac operator in the confining phase of compact U(1) gauge theory on the lattice to predictions of chiral random matrix theory. The small eigenvalues contribute to the chiral condensate similar as for the SU(2) and SU(3) gauge groups. Agreement with the chiral unitary ensemble is observed below the Thouless energy, which is extracted from the data and found to scale with the lattice size according to theoretical predictions.Comment: 5 pages, 3 figure