Angular distributions of the decay B$^+$$\to$ K$^*$(892)$^+\mu^+\mu^-$ are studied using events collected with the CMS detector in $\sqrt{s} =$ 8 TeV proton-proton collisions at the LHC, corresponding to an integrated luminosity of 20.0 fb$^{-1}$. The forward-backward asymmetry of the muons and the longitudinal polarization of the K$^*$(892)$^+$ meson are determined as a function of the square of the dimuon invariant mass. These are the first results from this exclusive decay mode and are in agreement with a standard model prediction.

Measurements are presented of the lifetimes of the B$^0$, B$^0_\mathrm{s}$, $\Lambda^0_\mathrm{b}$, and B$_\mathrm{c}^+$ hadrons using the decay channels B$^0\to$ J/$\psi$K*(892)$^0$, B$^0\to$J/$\psi$K$^0_\mathrm{S}$, B$^0_\mathrm{s}\to$J/$\psi \pi^+\pi^-$, B$^0_\mathrm{s}\to$J/$\psi\phi$(1020), $\Lambda^0_\mathrm{b}\to$J/$\psi\Lambda^0$, and B$_\mathrm{c}\to$J/$\psi\pi^+$. The data sample, corresponding to an integrated luminosity of 19.7 fb$^{-1}$, was collected by the CMS detector at the LHC in proton-proton collisions at $\sqrt{s}=$ 8 TeV. The B$^0$ lifetime is measured to be 453.0 $\pm$ 1.6 (stat) $\pm$ 1.8 (syst) $\mu$m in J/$\psi$K*(892)$^0$ and 457.8 $\pm$ 2.7 (stat) $\pm$ 2.8 (syst) $\mu$m in J/$\psi$K$^0_\mathrm{S}$, which results in a combined measurement of $c\tau_{\mathrm{B}^0} =$ 454.1 $\pm$ 1.4 (stat) $\pm$ 1.7 (syst) $\mu$m. The effective lifetime of the B$^0_\mathrm{s}$ meson is measured in two decay modes, with contributions from different amounts of the heavy and light eigenstates. This results in two different measured lifetimes: $c\tau_{\mathrm{B}^0_\mathrm{s} \to \mathrm{J}/\psi \pi^+\pi^-} =$ 502.7 $\pm$ 10.2 (stat) $\pm$ 3.4 (syst) $\mu$m and $c\tau_{\mathrm{B}^0_\mathrm{s} \to \mathrm{J}/\psi\phi(1020)} =$ 443.9 $\pm$ 2.0 (stat) $\pm$ 1.5 (syst) $\mu$m. The $\Lambda^0_\mathrm{b}$ lifetime is found to be 443.9 $\pm$ 8.2 (stat) $\pm$ 2.8 (syst) $\mu$m. The precision from each of these channels is as good as or better than previous measurements. The B$_\mathrm{c}^+$ lifetime, measured with respect to the B$^+$ to reduce the systematic uncertainty, is 162.3 $\pm$ 7.8 (stat) $\pm$ 4.2 (syst) $\pm$ 0.1 $(\tau_{\mathrm{B}^+})$ $\mu$m. All results are in agreement with current world-average values.

An analysis of the decay $\Lambda_b \to J/\psi(\to\mu^+\mu^-)\Lambda(\to p \pi^-)$ decay is performed to measure the $\Lambda_b$ polarization and three angular parameters in data from pp collisions at $\sqrt{s} =$ 7 and 8 TeV, collected by the CMS experiment at the LHC. The $\Lambda_b$ polarization is measured to be 0.00 $\pm$ 0.06 (stat) $\pm$ 0.06 (syst) and the parity-violating asymmetry parameter is determined to be 0.14 $\pm$ 0.14 (stat) $\pm$ 0.10 (syst). The measurements are compared to various theoretical predictions, including those from perturbative quantum chromodynamics.

Measurements are presented of the B$^0_\mathrm{S}$$\to$$\mu^+\mu^-$ branching fraction and effective lifetime, as well as results of a search for the B$^0$$\to$$\mu^+\mu^-$ decay in proton-proton collisions at $\sqrt{s}$ = 13 TeV at the LHC. The analysis is based on data collected with the CMS detector in 2016-2018 corresponding to an integrated luminosity of 140 fb$^{-1}$. The branching fraction of the B$^0_\mathrm{S}$$\to$$\mu^+\mu^-$ decay and the effective B$^0_\mathrm{S}$ meson lifetime are the most precise single measurements to date. No evidence for the B$^0$$\to$$\mu^+\mu^-$ decay has been found. All results are found to be consistent with the standard model predictions and previous measurements.

In this erratum we report changes on the $D^0$ $p_T$ spectra and nuclear modification factor ($R_{AA}$) in Au+Au collisions at $\sqrt{s_{_{\mathrm{NN}}}}$ = 200 GeV by fixing the errors in the efficiency and selection criteria that affected the Au+Au results. The p+p reference spectrum has changed as well and is updated with new fragmentation parameters.

Signals consistent with the B$^+_\mathrm{c}$(2S) and B$^{*+}_\mathrm{c}$(2S) states are observed in proton-proton collisions at $\sqrt{s} =$ 13 TeV, in an event sample corresponding to an integrated luminosity of 140 fb$^{-1}$, collected by the CMS experiment during the 2016, 2017, and 2018 LHC running periods. These excited $\bar{\mathrm{b}}$c states are observed in the B$^+_\mathrm{c}\pi^+\pi^-$ invariant mass spectrum, with the ground state B$^+_\mathrm{c}$ reconstructed through its decay to J/$\psi\,\pi^+$. The two states are well resolved from each other and are observed with a significance exceeding five standard deviations. The mass of the B$^+_\mathrm{c}$(2S) meson is measured to be 6871.0 $\pm$ 1.2 (stat) $\pm$ 0.8 (syst) $\pm$ 0.8 (B$^+_\mathrm{c}$) MeV, where the last term corresponds to the uncertainty in the world-average B$^+_\mathrm{c}$ mass.

The observation of the $\Lambda_\mathrm{b}^0 \to$J/$\psi \Lambda \phi$ decay is reported using proton-proton collision data collected at $\sqrt{s} =$ 13 TeV by the CMS experiment at the LHC in 2018, corresponding to an integrated luminosity of 60 fb$^{-1}$. The ratio of the branching fractions $\mathcal{B}(\Lambda_\mathrm{b}^0 \to$J/$\psi \Lambda \phi)/\mathcal{B}(\Lambda_\mathrm{b}^0\to\psi \Lambda)$ is measured to be (8.26$\pm$0.90 (stat) $\pm$ 0.68 (syst) $\pm$ 0.11 $(\mathcal{B}))\times $10$^{-2}$, where the first uncertainty is statistical, the second is systematic, and the last uncertainty reflects the uncertainties in the world-average branching fractions of $\phi$ and $\psi$(2S) decays to the reconstructed final states.

The J/$\psi$$\to$$\mu^+\mu^-\mu^+\mu^-$ decay has been observed with a statistical significance in excess of five standard deviations. The analysis is based on an event sample of proton-proton collisions at a center-of-mass energy of 13 TeV, collected by the CMS experiment in 2018 and corresponding to an integrated luminosity of 33.6 fb${-1}$. Normalizing to the J/$\psi$$\to$$\mu^+\mu^-$ decay mode leads to a branching fraction [10.1$^{+3.3}_{-2.7}$ (stat) $\pm$ 0.4 (syst) ]$\times$ 10$^{-7}$, a value that is consistent with the standard model prediction.

The leptonic and inclusive hadronic decay branching fractions of the W boson are measured using proton-proton collision data collected at $\sqrt{s} =$ 13 TeV by the CMS experiment at the CERN LHC, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. Events characterized by the production of one or two W bosons are selected and categorized based on the multiplicity and flavor of reconstructed leptons, the number of jets, and the number of jets identified as originating from the hadronization of b quarks. A binned maximum likelihood estimate of the W boson branching fractions is performed simultaneously in each event category. The measured branching fractions of the W boson decaying into electron, muon, and tau lepton final states are (10.83 $\pm$ 0.10)%, (10.94 $\pm$ 0.08)%, and (10.77 $\pm$ 0.21)%, respectively, consistent with lepton flavor universality for the weak interaction. The average leptonic and inclusive hadronic decay branching fractions are estimated to be (10.89 $\pm$ 0.08)% and (67.32 $\pm$ 0.23)%, respectively. Based on the hadronic branching fraction, three standard model quantities are subsequently derived: the sum of squared elements in the first two rows of the Cabibbo-Kobayashi-Maskawa (CKM) matrix $\sum_{ij}\vert V_{ij}\vert^{2}$ = 1.984 $\pm$ 0.021, the CKM element $\vert V_\mathrm{cs}\vert$ = 0.967 $\pm$ 0.011, and the strong coupling constant at the W boson mass scale, $\alpha_\mathrm{S}(m^2_\mathrm{W})$ = 0.095 $\pm$ 0.033.

The ${\rm B_c^+(2S)}$ to ${\rm B_c^+}$ and ${\rm B_c^{*+}(2S)}$ to ${\rm B_c^+}$ cross section ratios, as well as the ${\rm B_c^{*+}(2S)}$ to ${\rm B_c^+(2S)}$ cross section ratio, are measured in proton-proton collisions at $\sqrt{s} = 13$ TeV, using a data sample collected by the CMS experiment, corresponding to an integrated luminosity of 143 fb$^{-1}$. The three measurements are made in the ${\rm B_c^+}$ phase space window defined by transverse momentum $p_{\rm T} > 15$ GeV and absolute rapidity $|y| < 2.4$, with the excited ${\rm B_c^{(*)+}(2S)}$ states reconstructed in their ${\rm B_c^+} \pi^+ \pi^-$ decay. The ${\rm B_c^+(2S)}$ to ${\rm B_c^+}$, ${\rm B_c^{*+}(2S)}$ to ${\rm B_c^+}$, and ${\rm B_c^{*+}(2S)}$ to ${\rm B_c^+(2S)}$ cross section ratios, including the (unknown) ${\rm B_c^{(*)+}(2S) \to B_c^+}\pi^+\pi^-$ branching fractions, are ${\rm (3.57 \pm 0.69~(stat) \pm 0.32~(syst))\,\%}$, ${\rm (4.91 \pm 0.69~(stat) \pm 0.57~(syst))\,\%}$, and ${\rm 1.39 \pm 0.35~(stat) \pm 0.09~(syst)}$, respectively, where the first uncertainty is statistical and the second is systematic. None of these ratios shows a significant dependence on the $p_{\rm T}$ or $|y|$ of the ${\rm B_c^+}$. The shape of the invariant mass distribution of the dipions emitted in the ${\rm B_c^{(*)+}(2S) \to B_c^+}\pi^+\pi^-$ decays is also reported.