On Wings of the Minimum Induced Drag: Spanload Implications for Aircraft and Birds

For nearly a century Ludwig Prandtl's lifting-line theory remains a standard tool for understanding and analyzing aircraft wings. The tool, said Prandtl, initially points to the elliptical spanload as the most efficient wing choice, and it, too, has become the standard in aviation. Having no other model, avian researchers have used the elliptical spanload virtually since its introduction. Yet over the last half-century, research in bird flight has generated increasing data incongruous with the elliptical spanload. In 1933 Prandtl published a little-known paper presenting a superior spanload: any other solution produces greater drag. We argue that this second spanload is the correct model for bird flight data. Based on research we present a unifying theory for superior efficiency and coordinated control in a single solution. Specifically, Prandtl's second spanload offers the only solution to three aspects of bird flight: how birds are able to turn and maneuver without a vertical tail; why birds fly in formation with their wingtips overlapped; and why narrow wingtips do not result in wingtip stall. We performed research using two experimental aircraft designed in accordance with the fundamentals of Prandtl's second paper, but applying recent developments, to validate the various potentials of the new spanload, to wit: as an alternative for avian researchers, to demonstrate the concept of proverse yaw, and to offer a new method of aircraft control and efficiency

Bs→KℓνB_s \to K \ell\nu form factors with 2+1 flavors

Using the MILC 2+1 flavor asqtad quark action ensembles, we are calculating the form factors $f_0$ and $f_+$ for the semileptonic $B_s \rightarrow K \ell\nu$ decay. A total of six ensembles with lattice spacing from $\approx0.12$ to 0.06 fm are being used. At the coarsest and finest lattice spacings, the light quark mass $m'_l$ is one-tenth the strange quark mass $m'_s$. At the intermediate lattice spacing, the ratio $m'_l/m'_s$ ranges from 0.05 to 0.2. The valence $b$ quark is treated using the Sheikholeslami-Wohlert Wilson-clover action with the Fermilab interpretation. The other valence quarks use the asqtad action. When combined with (future) measurements from the LHCb and Belle II experiments, these calculations will provide an alternate determination of the CKM matrix element $|V_{ub}|$.Comment: 8 pages, 6 figures, to appear in the Proceedings of Lattice 2017, June 18-24, Granada, Spai

Bs → Klν decay from lattice QCD

We use lattice QCD to calculate the form factors f+(q2) and f0(q2) for the semileptonic decay Bs→Kℓν. Our calculation uses six MILC asqtad 2+1 flavor gauge-field ensembles with three lattice spacings. At the smallest and largest lattice spacing the light-quark sea mass is set to 1/10 the strange-quark mass. At the intermediate lattice spacing, we use four values for the light-quark sea mass ranging from 1/5 to 1/20 of the strange-quark mass. We use the asqtad improved staggered action for the light valence quarks, and the clover action with the Fermilab interpolation for the heavy valence bottom quark. We use SU(2) hard-kaon heavy-meson rooted staggered chiral perturbation theory to take the chiral-continuum limit. A functional z expansion is used to extend the form factors to the full kinematic range. We present predictions for the differential decay rate for both Bs→Kμν and Bs→Kτν. We also present results for the forward-backward asymmetry, the lepton polarization asymmetry, ratios of the scalar and vector form factors for the decays Bs→Kℓν and Bs→Dsℓν. Our results, together with future experimental measurements, can be used to determine the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element |Vub|.This project was supported in part by the URA Visiting Scholar Award 12-S-15 (Y. L.); by the U.S. Department of Energy under Grants No. DE-FG02-91ER40628 (C. B.), No. DE-FC02-12ER41879 (C. D.), No. DE-FG02- 13ER42001 (A. X. K.), No. DE-SC0015655 (A. X. K., Z.G.), No. DE-SC0010120 (S. G.), No. DE-FG02- 91ER40661 (S. G.), No. DE-SC0010113 (Y. M.), No. DESC0010005 (E. T. N.), No. DE-FG02-13ER41976 (D. T.); by the U.S. National Science Foundation under Grants No. PHY14-14614 and No. PHY17-19626 (C. D.), and No. PHY14-17805 (J. L.); by the MINECO (Spain) under Grants No. FPA2013-47836-C-1-P and No. FPA2016- 78220-C3-3-P (E. G.); by the Junta de Andalucía (Spain) under Grant No. FQM-101 (E. G.); by the Fermilab Distinguished Scholars program (A. X. K.); by the German Excellence Initiative and the European Union Seventh Framework Program under Grant Agreement No. 291763 as well as the European Union’s Marie Curie COFUND program (A. S. K.)

The anomalous magnetic moment of the muon in the Standard Model

194 pages, 103 figures, bib files for the citation references are available from: https://muon-gm2-theory.illinois.eduWe review the present status of the Standard Model calculation of the anomalous magnetic moment of the muon. This is performed in a perturbative expansion in the fine-structure constant $\alpha$ and is broken down into pure QED, electroweak, and hadronic contributions. The pure QED contribution is by far the largest and has been evaluated up to and including $\mathcal{O}(\alpha^5)$ with negligible numerical uncertainty. The electroweak contribution is suppressed by $(m_\mu/M_W)^2$ and only shows up at the level of the seventh significant digit. It has been evaluated up to two loops and is known to better than one percent. Hadronic contributions are the most difficult to calculate and are responsible for almost all of the theoretical uncertainty. The leading hadronic contribution appears at $\mathcal{O}(\alpha^2)$ and is due to hadronic vacuum polarization, whereas at $\mathcal{O}(\alpha^3)$ the hadronic light-by-light scattering contribution appears. Given the low characteristic scale of this observable, these contributions have to be calculated with nonperturbative methods, in particular, dispersion relations and the lattice approach to QCD. The largest part of this review is dedicated to a detailed account of recent efforts to improve the calculation of these two contributions with either a data-driven, dispersive approach, or a first-principle, lattice-QCD approach. The final result reads $a_\mu^\text{SM}=116\,591\,810(43)\times 10^{-11}$ and is smaller than the Brookhaven measurement by 3.7$\sigma$. The experimental uncertainty will soon be reduced by up to a factor four by the new experiment currently running at Fermilab, and also by the future J-PARC experiment. This and the prospects to further reduce the theoretical uncertainty in the near future-which are also discussed here-make this quantity one of the most promising places to look for evidence of new physics