We revisit the procedure for comparing the ππ spectral function measured in τ decays to that obtained in e + e − annihilation. We re-examine the isospin-breaking corrections using new experimental and theoretical input, and find improved agreement between the τ − → π − π 0 ντ branching fraction measurement and its prediction using the isospin-breaking-corrected e + e − → π + π − spectral function, though not resolving all discrepancies. We recompute the lowest order hadronic contributions to the muon g − 2 using e + e − and τ data with the new corrections, and find a reduced difference between the two evaluations. The new tau-based estimate of the muon magnetic anomaly is found to be 1.9 standard deviations lower than the direct measurement.

Monte Carlo simulations of neutron-rich matter of relevance to the inner neutron-star crust are performed for a system of A = 5, 000 nucleons. To determine the proton fraction in the inner crust, numerical simulations are carried out for a variety of densities and proton fractions. We concludeas others have before us using different techniques-that the proton fraction in the inner stellar crust is very small. Given that the purported "nuclear pasta" phase in stellar crusts develops as a consequence of the long-range Coulomb interaction among protons, we question whether pasta formation is possible in such proton-poor environments. To answer this question, we search for physical observables sensitive to the transition between spherical nuclei and exotic pasta structures. Of particular relevance is the static structure factor S(k)-an observable sensitive to density fluctuations. However, no dramatic behavior was observed in S(k). We regard the identification of physical observables sensitive to the existence-or lack-thereof-of a pasta phase in proton-poor environments as an open problem of critical importance.

We evaluate the model-dependent piece of O(α) long-distance radiative corrections to τ − → π − π 0 ντ decays by using a meson dominance model. We find that these corrections to the di-pion invariant mass spectrum are smaller than in previous calculations based on chiral perturbation theory. The corresponding correction to the photon inclusive rate is tiny (−0.15%) but it can be of relevance when new measurements reach better precision.

There are indications that hadronic loops in some electroweak observables are almost saturated by parton level effects. Taking this as the hypothesis for this work, we propose a genuine parton level estimate of the hadronic light-by-light contribution to the anomalous magnetic moment of the muon, a LBL µ (had). Our quark mass definitions and values are motivated in detail, and the simplicity of our approach allows for a transparent error estimate. For infinitely heavy quarks our treatment is exact, while for asymptotically small quark masses a LBL µ (had) is overestimated. Interpolating, this suggests to quote an upper bound. We obtain a LBL µ (had) < 1.59 × 10 −9 (95% CL).PACS numbers: 13.40. Em, 14.60.Ef, 12.20.Ds, 12.38.Bx.The E-821 Collaboration at BNL [1] has measured the anomalous magnetic moment of the muon, a µ ≡ (g µ − 2)/2, with an uncertainty of ∆a µ = ±0.63 × 10 −9 . This would provide sensitivity to new physics scales, Λ, as large as Λ ∼ m µ / ∆a µ = 4.2 TeV, where m µ is the mass of the muon [2]. A new experiment [3] at BNL is approved aiming at even greater (±0.2 ppm) precision and implying a reach up to 7 TeV. Unfortunately, the interpretation of a µ is compromised by large theoretical uncertainties introduced by hadronic effects diluting the new physics sensitivity. These mainly arise from two-loop vacuum polarization (VP) effects, a VP µ (2, had), and from the three-loop contribution of light-by-light type, a LBL µ (had). The calculations of a LBL µ (had) based on chiral perturbation theory [4,5] are the only ones to date solidly based on a systematic expansion. However, the estimated uncertainty, > ∼ ±10 −9 , is significantly larger [5] than the measurement error. There is a variety of model estimates, all supplementing the dominant π 0 -exchange contribution with other resonance exchanges and π ± -loops. Current analyzes [6,7] agree reasonably well on the magnitude (where residual differences are largely understood) and the sign of a LBL µ (had). They have reached a high level of sophistication, but the error estimates remain rough guesses. There is also an estimate [8] based on the instanton liquid model with a small (< 10%) quoted error.In this work we offer a complementary way to estimate a LBL µ (had), with no need to commit to the dominance of any particular type of contribution. It is a naïve parton level estimate which is solid in the heavy quark limit where it matches onto perturbative QCD, but overestimates the light-by-light contribution in the chiral limit. Therefore, our approach naturally implies an upper bound for a LBL µ (had), which is very useful in view of the a µ measurement lying above the Standard Model prediction. It can also be applied to a VP µ (had), which serves as a reference case and allows for a transparent error estimate.Attempting to obtain a LBL µ (had) directly at the parton level seems hopeless at first since perturbative QCD cannot be applied except for the heavy c and b quarks. Moreover, in the chiral limit, in which the bulk of the effect arises from light...

The long-distance electromagnetic radiative corrections to τ − → π − π 0 ντ are re-evaluated. A meson dominance model is used to describe the emission of real photons in this decay. Results obtained for the hadronic spectrum and the decay rate in photon inclusive reactions are compared with previous calculations based on the chiral resonance theory. Independent tests in τ → ππνγ that can help to validate the predictions of one of the two models are briefly discussed.