The CORE-MATH Project

International audienceThe CORE-MATH project aims at providing opensource mathematical functions with correct rounding that can be integrated into current mathematical libraries. This article demonstrates the CORE-MATH methodology on two functions: the binary32 power function (powf) and the binary64 cube root function (cbrt). CORE-MATH already provides a full set of correctly rounded C99 functions for single precision (binary32). These functions provide similar or in some cases up to threefold speedups with respect to the GNU libc mathematical library, which is not correctly rounded. This work offers a prospect of the mandatory requirement of correct rounding for mathematical functions in the next revision of the IEEE-754 standard

Implications for the ΔAFB\Delta A_{FB} anomaly in Bˉ0→D∗+ℓ−νˉ{\bar B}^0\to D^{*+}\ell^- {\bar\nu} using a new Monte Carlo Event Generator

Recent experimental results in $B$ physics from Belle, BaBar and LHCb suggest new physics (NP) in the weak $b\to c$ charged-current and the $b\to s$ neutral-current processes. Here we focus on the charged-current case and specifically on the decay modes $\bar{B}^0\to D^{*+}\ell^- \bar{\nu}$ with $\ell = e$ and $\mu$. The world averages of the ratios $R_D$ and $R_D^{*}$ currently differ from the Standard Model (SM) predictions by $3.4\sigma$ while recently a new anomaly has been observed in the forward-backward asymmetry measurement, $A_{FB}$, in $\bar{B}^0\to D^{*+}\mu^- \bar{\nu}$ decay. It is found that $\Delta A_{FB} = A_{FB}(B\to D^{*} \mu\nu) - A_{FB} (B\to D^{*} e \nu)$ is around $4.1\sigma$ away from the SM prediction in an analysis of 2019 Belle data. In this work we explore possible solutions to the $\Delta A_{FB}$ anomaly and point out correlated NP signals in other angular observables. These correlations between angular observables must be present in the case of beyond the Standard Model physics. We stress the importance of $\Delta$ type observables that are obtained by taking the difference of the observable for the muon and the electron mode. These quantities cancel form factor uncertainties in the SM and allow for clean tests of NP. These intriguing results also suggest an urgent need for improved simulation and analysis techniques in $\bar{B}^0\to D^{*+}\ell^- \bar{\nu}$ decays. Here we also describe a new Monte Carlo Event-generator tool based on EVTGEN that we developed to allow simulation of the NP signatures in $\bar{B}^0\to D^{*+}\ell^- \nu$, which arise due to the interference between the SM and NP amplitudes. We then discuss prospects for improved observables sensitive to NP couplings with 1, 5, 50, and 250 ab$^{-1}$ of Belle II data, which seem to be ideally suited for this class of measurements.Comment: 22 pages, 9 figures, Improved version of arXiv:2203.07189, which was submitted to the US Community Summer Study on the Future of Particle Physics (Snowmass2021), withdrawn from final proceedings. Improvements include calculations of correlations between several observables and discussions of prospects for NP-sensitive observables with several benchmark values of Belle II integrated luminosit

A new tool to search for physics beyond the Standard Model in Bˉ→D∗+ℓ−νˉ{\bar B}\to D^{*+}\ell^- {\bar\nu}

Recent experimental results in $B$ physics from Belle, BaBar and LHCb suggest new physics (NP) in the weak $b\to c$ charged-current and the $b\to s$ neutral-current processes. Here we focus on the charged-current case and specifically on the decay modes $B\to D^{*+}\ell^- \bar{\nu}$ with $\ell = e, \mu,$ and $\tau$. The world averages of the ratios $R_D$ and $R_D^{*}$ currently differ from the Standard Model (SM) by $3.4\sigma$ while $\Delta A_{FB} = A_{FB}(B\to D^{*} \mu\nu) - A_{FB} (B\to D^{*} e \nu)$ is found to be $4.1\sigma$ away from the SM prediction in an analysis of 2019 Belle data. These intriguing results suggest an urgent need for improved simulation and analysis techniques in $B\to D^{*+}\ell^- \bar{\nu}$ decays. Here we describe a Monte Carlo Event-generator tool based on EVTGEN developed to allow simulation of the NP signatures in $B\to D^*\ell^- \nu$, which arise due to the interference between the SM and NP amplitudes. As a demonstration of the proposed approach, we exhibit some examples of NP couplings that are consistent with current data and could explain the $\Delta A_{FB}$ anomaly in $B\to D^*\ell^- \nu$ while remaining consistent with other constraints. We show that the $\Delta$-type observables such as $\Delta A_{FB}$ and $\Delta S_5$ eliminate most QCD uncertainties from form factors and allow for clean measurements of NP. We introduce correlated observables that improve the sensitivity to NP. We discuss prospects for improved observables sensitive to NP couplings with the expected 50 ab$^{-1}$ of Belle II data, which seems to be ideally suited for this class of measurements.Comment: 19 pages, 5 figures, Submitted to the Proceedings of the US Community Study on the Future of Particle Physics (Snowmass 2021), typos correcte

Measurement of the Ωc0\Omega_c^0 lifetime at Belle II

We report on a measurement of the $\Omega_c^0$ lifetime using $\Omega_c^0 \to \Omega^-\pi^+$ decays reconstructed in $e^+e^-\to c\bar{c}$ data collected by the Belle II experiment and corresponding to $207~{\rm fb^{-1}}$ of integrated luminosity. The result, $\rm\tau(\Omega_c^0)=243\pm48( stat)\pm11(syst)~fs$, agrees with recent measurements indicating that the $\Omega_c^0$ is not the shortest-lived weakly decaying charmed baryon

Measurement of the Ωc0\Omega_c^0 lifetime at Belle II

We report on a measurement of the $\Omega_c^0$ lifetime using $\Omega_c^0 \to \Omega^-\pi^+$ decays reconstructed in $e^+e^-\to c\bar{c}$ data collected by the Belle II experiment and corresponding to $207~{\rm fb^{-1}}$ of integrated luminosity. The result, $\rm\tau(\Omega_c^0)=243\pm48( stat)\pm11(syst)~fs$, agrees with recent measurements indicating that the $\Omega_c^0$ is not the shortest-lived weakly decaying charmed baryon

Measurement of the Ωc0\Omega_c^0 lifetime at Belle II

We report on a measurement of the $\Omega_c^0$ lifetime using $\Omega_c^0 \to \Omega^-\pi^+$ decays reconstructed in $e^+e^-\to c\bar{c}$ data collected by the Belle II experiment and corresponding to $207~{\rm fb^{-1}}$ of integrated luminosity. The result, $\rm\tau(\Omega_c^0)=243\pm48( stat)\pm11(syst)~fs$, agrees with recent measurements indicating that the $\Omega_c^0$ is not the shortest-lived weakly decaying charmed baryon

Test of light-lepton universality in τ\tau decays with the Belle II experiment

International audienceWe present a measurement of the ratio $R_\mu = \mathcal{B}(\tau^-\to \mu^-\bar\nu_\mu\nu_\tau) / \mathcal{B}(\tau^-\to e^-\bar\nu_e\nu_\tau)$ of branching fractions $\mathcal{B}$ of the $\tau$ lepton decaying to muons or electrons using data collected with the Belle II detector at the SuperKEKB $e^+e^-$ collider. The sample has an integrated luminosity of 362 fb$^{-1}$ at a centre-of-mass energy of 10.58 GeV. Using an optimised event selection, a binned maximum likelihood fit is performed using the momentum spectra of the electron and muon candidates. The result, $R_\mu = 0.9675 \pm 0.0007 \pm 0.0036$, where the first uncertainty is statistical and the second is systematic, is the most precise to date. It provides a stringent test of the light-lepton universality, translating to a ratio of the couplings of the muon and electron to the $W$ boson in $\tau$ decays of $0.9974 \pm 0.0019$, in agreement with the standard model expectation of unity