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

B-meson semileptonic form factors on (2+1+1)-flavor HISQ ensembles

We report updates to an ongoing lattice-QCD calculation of the form factors for the semileptonic decays B → π`ν, Bs → K`ν, B → π`+`−, and B → K`+`−. The tree-level decays B(s) → π(K)`ν enable precise determinations of the CKM matrix element |Vub|, while the flavor-changing neutral-current interactions B → π(K)`+`− are sensitive to contributions from new physics. This work uses MILC's (2+1+1)-flavor HISQ ensembles at approximate lattice spacings between 0.057 and 0.15 fm, with physical sea-quark masses on four out of the seven ensembles. The valence sector is comprised of a clover b quark (in the Fermilab interpretation) and HISQ light and s quarks. We present preliminary results for the form factors f0, f+, and fT, including studies of systematic errors. © Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0).Open access journalThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Semileptonic form factors for

We present the first unquenched lattice-QCD calculation of the form factors for the decay $$B\rightarrow D^*\ell \nu$$ at nonzero recoil. Our analysis includes 15 MILC ensembles with $$N_f=2+1$$ flavors of asqtad sea quarks, with a strange quark mass close to its physical mass. The lattice spacings range from $$a\approx 0.15$$ fm down to 0.045 fm, while the ratio between the light- and the strange-quark masses ranges from 0.05 to 0.4. The valence b and c quarks are treated using the Wilson-clover action with the Fermilab interpretation, whereas the light sector employs asqtad staggered fermions. We extrapolate our results to the physical point in the continuum limit using rooted staggered heavy-light meson chiral perturbation theory. Then we apply a model-independent parametrization to extend the form factors to the full kinematic range. With this parametrization we perform a joint lattice-QCD/experiment fit using several experimental datasets to determine the CKM matrix element $$|V_{cb}|$$. We obtain $$\left| V_{cb}\right| = (38.40 \pm 0.68_{\text {th}} \pm 0.34_{\text {exp}} \pm 0.18_{\text {EM}})\times 10^{-3}$$. The first error is theoretical, the second comes from experiment and the last one includes electromagnetic and electroweak uncertainties, with an overall $$\chi ^2\text {/dof} = 126/84$$, which illustrates the tensions between the experimental data sets, and between theory and experiment. This result is in agreement with previous exclusive determinations, but the tension with the inclusive determination remains. Finally, we integrate the differential decay rate obtained solely from lattice data to predict $$R(D^*) = 0.265 \pm 0.013$$, which confirms the current tension between theory and experiment