We report on the computation of the connected light-quark vacuum polarization with $2+1+1$ flavors of highly improved staggered quarks [Follana et al., Phys. Rev. D 75, 054502 (2007).] fermions at the physical point and its contribution to the muon anomalous magnetic moment. Three ensembles, generated by the MILC collaboration, are used to take the continuum limit. The finite-volume correction to this result is computed in the (Euclidean) time-momentum representation to next-to-next-to-leading order (NNLO) in chiral perturbation theory. We find $a_{\mu }^{ll}(\mathrm{HVP})=(659\pm 20\pm 5\pm 5\pm 4)\times {10}^{-10}$, where the errors are statistical and estimates of residual uncertainties from taking the continuum limit, scale setting, and truncation of chiral perturbation theory at NNLO. We compare our results with recent ones in the literature.

We extend our previous work on the light-quark connected part, $a_{\mu }^{\mathrm{HVP},\mathrm{lqc}}$, of the leading-order hadronic-vacuum-polarization (HVP) contribution to the muon anomalous magnetic moment $a_{\mu }$, using staggered fermions, in several directions. We have collected more statistics on ensembles with lattice spacings of 0.06, 0.09 and 0.12 fm, and we added two new ensembles, both with lattice spacing 0.15 fm, but with different volumes. The increased statistics allow us to reduce statistical errors on $a_{\mu }^{\mathrm{HVP},\mathrm{lqc}}$ and related window quantities significantly. We also calculate the current-current correlator from which $a_{\mu }^{\mathrm{HVP},\mathrm{lqc}}$ is obtained to next-to-next-to-leading order (NNLO) in staggered chiral perturbation theory, so that we can correct lattice values for $a_{\mu }^{\mathrm{HVP},\mathrm{lqc}}$ to NNLO for finite-volume, pion-mass mistuning and taste-breaking effects. We discuss the applicability of NNLO chiral perturbation theory to $a_{\mu }^{\mathrm{HVP},\mathrm{lqc}}$ and to the window quantities, emphasizing that it provides a systematic effective-field theory (EFT) approach to $a_{\mu }^{\mathrm{HVP},\mathrm{lqc}}$, but not to short- or intermediate-distance window quantities. This makes it difficult to assess systematic errors on the standard intermediate-distance window quantity that is now widely considered in the literature. In view of this, we investigate a longer-distance window, for which EFT methods should be more reliable. Our most important conclusion is that, especially for staggered fermions, new high-statistics computations at lattice spacings smaller than 0.06 fm are indispensable. Our results are based on configurations provided by the MILC and also by the CalLat collaborations.

Following a recent suggestion by Weinberg, we use the large-$N$ expansion in QCD to discuss the decay amplitudes of tetraquarks into ordinary mesons as well as their mixing properties. We find that the flavor structure of the tetraquark is a crucial ingredient to determine both this mixing as well as the decays. Although in some cases tetraquarks should be expected to be as narrow as ordinary mesons, they may get to be even narrower, depending on this flavor structure.

We combine ALEPH and OPAL results for the spectral distributions measured in $\tau \to {\pi }^{-}{\pi }^0{\nu }_{\tau }$, $\tau \to 2{\pi }^{-}{\pi }^{+}{\pi }^0{\nu }_{\tau }$ and $\tau \to {\pi }^{-}3{\pi }^0{\nu }_{\tau }$ decays with (i) recent BABAR results for the analogous $\tau \to K^{-}{K}^0{\nu }_{\tau }$ distribution and (ii) estimates of the contributions from other hadronic $\tau$-decay modes obtained using CVC and electroproduction data, to obtain a new and more precise nonstrange, inclusive vector, isovector spectral function. The BABAR $K^{-}{K}^0$ and CVC/electroproduction results provide us with alternate, entirely data-based input for the contributions of all exclusive modes for which ALEPH and OPAL employed Monte-Carlo-based estimates. We use the resulting spectral function to determine ${\alpha }_s(m_{\tau })$, the strong coupling at the $\tau$ mass scale, employing finite energy sum rules. Using the fixed-order perturbation theory (FOPT) prescription, we find ${\alpha }_s(m_{\tau })=0.3077\pm 0.0075$, which corresponds to the five-flavor result ${\alpha }_s(M_Z)=0.1171\pm 0.0010$ at the $Z$ mass. While we also provide an estimate using contour-improved perturbation theory (CIPT), we point out that the FOPT prescription is to be preferred for comparison with other ${\alpha }_s$ determinations employing the $\overline{\mathrm{MS}}$ scheme, especially given the inconsistency between CIPT and the standard operator product expansion recently pointed out in the literature. Additional experimental input on the dominant $2\pi$ and $4\pi$ modes would allow for further improvements to the current analysis.