Synchronization Problems in Automata without Non-trivial Cycles

We study the computational complexity of various problems related to synchronization of weakly acyclic automata, a subclass of widely studied aperiodic automata. We provide upper and lower bounds on the length of a shortest word synchronizing a weakly acyclic automaton or, more generally, a subset of its states, and show that the problem of approximating this length is hard. We investigate the complexity of finding a synchronizing set of states of maximum size. We also show inapproximability of the problem of computing the rank of a subset of states in a binary weakly acyclic automaton and prove that several problems related to recognizing a synchronizing subset of states in such automata are NP-complete.Comment: Extended and corrected version, including arXiv:1608.00889. Conference version was published at CIAA 2017, LNCS vol. 10329, pages 188-200, 201

Search for lepton-flavour-violating decays of Higgs-like bosons.

A search is presented for a Higgs-like boson with mass in the range 45 to 195 GeV/c2 decaying into a muon and a tau lepton. The dataset consists of proton-proton interactions at a centre-of-mass energy of 8 TeV , collected by the LHCb experiment, corresponding to an integrated luminosity of 2 fb-1 . The tau leptons are reconstructed in both leptonic and hadronic decay channels. An upper limit on the production cross-section multiplied by the branching fraction at 95% confidence level is set and ranges from 22 pb for a boson mass of 45 GeV/c2 to 4 pb for a mass of 195 GeV/c2

Superhard CrN/MoN films with multilayer architecture

Main regularities of the formation of microstructure and properties ofmultilayer nanostructured CrN/MoN films with periodically changing architecture of layers were considered. Coatings were fabricated by vacuum-arc evaporation of the cathodes (Arc-PVD) in nitrogen atmosphere (pN was 0.4, 0.09 and 0.03 Pa). CrN and γ-Mo2N nitride phases with fcc lattices and a small volume of metastable MoNx cubic phase were formed in the films at pN = 0.4 Pa. The decrease of pN to 0.09 Pa causes the formation of β-Cr2N hexagonal phase. Preferential crystallographic orientation changes from [311] to [111] and [200] when bias voltage Ub is −20, −150 and −300 V respectively. The nanocrystallites size in coatings with bilayer thickness λ = 44 nm decreases to 5.8 nm. The microdeformation grows from 0.4 to 2.3% when Ub changes to −20 V. Coatings show high hardness of 38–42 GPa and H/E = 0.107. In a couple with results of tribological tests, coatings demonstrate strong wear resistance, which makes them appropriate and promising for industrial applications as protective ones. The effect of deposition conditions (pN, Ub, λ) on composition, structure, hardness, toughness and wear resistance was studied to achieve superior mechanical and physical properties of coatings with long lifetime in harsh environment.State budget programs of Ukraine, grant numbers 0116U002621, 0115U000682, 0116U006816; SFRH/BD/ 129614/2017; NORTE-01-0145-FEDER-022096info:eu-repo/semantics/publishedVersio

Observation of two new Ξb−\Xi_b^- baryon resonances

Two structures are observed close to the kinematic threshold in the $\Xi_b^0 \pi^-$ mass spectrum in a sample of proton-proton collision data, corresponding to an integrated luminosity of 3.0 fb$^{-1}$ recorded by the LHCb experiment. In the quark model, two baryonic resonances with quark content $bds$ are expected in this mass region: the spin-parity $J^P = \frac{1}{2}^+$ and $J^P=\frac{3}{2}^+$ states, denoted $\Xi_b^{\prime -}$ and $\Xi_b^{*-}$. Interpreting the structures as these resonances, we measure the mass differences and the width of the heavier state to be $m(\Xi_b^{\prime -}) - m(\Xi_b^0) - m(\pi^{-}) = 3.653 \pm 0.018 \pm 0.006$ MeV$/c^2$, $m(\Xi_b^{*-}) - m(\Xi_b^0) - m(\pi^{-}) = 23.96 \pm 0.12 \pm 0.06$ MeV$/c^2$, $\Gamma(\Xi_b^{*-}) = 1.65 \pm 0.31 \pm 0.10$ MeV, where the first and second uncertainties are statistical and systematic, respectively. The width of the lighter state is consistent with zero, and we place an upper limit of $\Gamma(\Xi_b^{\prime -}) < 0.08$ MeV at 95% confidence level. Relative production rates of these states are also reported.Comment: 17 pages, 2 figure

Measurement of the mass and lifetime of the Ωb−\Omega_b^- baryon

A proton-proton collision data sample, corresponding to an integrated luminosity of 3 fb$^{-1}$ collected by LHCb at $\sqrt{s}=7$ and 8 TeV, is used to reconstruct $63\pm9$ $\Omega_b^-\to\Omega_c^0\pi^-$, $\Omega_c^0\to pK^-K^-\pi^+$ decays. Using the $\Xi_b^-\to\Xi_c^0\pi^-$, $\Xi_c^0\to pK^-K^-\pi^+$ decay mode for calibration, the lifetime ratio and absolute lifetime of the $\Omega_b^-$ baryon are measured to be \begin{align*} \frac{\tau_{\Omega_b^-}}{\tau_{\Xi_b^-}} &= 1.11\pm0.16\pm0.03, \\ \tau_{\Omega_b^-} &= 1.78\pm0.26\pm0.05\pm0.06~{\rm ps}, \end{align*} where the uncertainties are statistical, systematic and from the calibration mode (for $\tau_{\Omega_b^-}$ only). A measurement is also made of the mass difference, $m_{\Omega_b^-}-m_{\Xi_b^-}$, and the corresponding $\Omega_b^-$ mass, which yields \begin{align*} m_{\Omega_b^-}-m_{\Xi_b^-} &= 247.4\pm3.2\pm0.5~{\rm MeV}/c^2, \\ m_{\Omega_b^-} &= 6045.1\pm3.2\pm 0.5\pm0.6~{\rm MeV}/c^2. \end{align*} These results are consistent with previous measurements.Comment: 11 pages, 5 figures, All figures and tables, along with any supplementary material and additional information, are available at https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2016-008.htm

Study of B−→DK−π+π−B^{-}\to DK^-\pi^+\pi^- and B−→Dπ−π+π−B^-\to D\pi^-\pi^+\pi^- decays and determination of the CKM angle γ\gamma

We report a study of the suppressed $B^-\to DK^-\pi^+\pi^-$ and favored $B^-\to D\pi^-\pi^+\pi^-$ decays, where the neutral $D$ meson is detected through its decays to the $K^{\mp}\pi^{\pm}$ and CP-even $K^+K^-$ and $\pi^+\pi^-$ final states. The measurement is carried out using a proton-proton collision data sample collected by the LHCb experiment, corresponding to an integrated luminosity of 3.0~fb$^{-1}$. We observe the first significant signals in the CP-even final states of the $D$ meson for both the suppressed $B^-\to DK^-\pi^+\pi^-$ and favored $B^-\to D\pi^-\pi^+\pi^-$ modes, as well as in the doubly Cabibbo-suppressed $D\to K^+\pi^-$ final state of the $B^-\to D\pi^-\pi^+\pi^-$ decay. Evidence for the ADS suppressed decay $B^{-}\to DK^-\pi^+\pi^-$, with $D\to K^+\pi^-$, is also presented. From the observed yields in the $B^-\to DK^-\pi^+\pi^-$, $B^-\to D\pi^-\pi^+\pi^-$ and their charge conjugate decay modes, we measure the value of the weak phase to be $\gamma=(74^{+20}_{-19})^{\rm o}$. This is one of the most precise single-measurement determinations of $\gamma$ to date.Comment: 22 pages, 9 figures; All figures and tables, along with any supplementary material and additional information, are available at https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2015-020.htm

Study of the production of Λb0\Lambda_b^0 and B‾0\overline{B}^0 hadrons in pppp collisions and first measurement of the Λb0→J/ψpK−\Lambda_b^0\rightarrow J/\psi pK^- branching fraction

The product of the $\Lambda_b^0$ ($\overline{B}^0$) differential production cross-section and the branching fraction of the decay $\Lambda_b^0\rightarrow J/\psi pK^-$ ($\overline{B}^0\rightarrow J/\psi\overline{K}^*(892)^0$) is measured as a function of the beauty hadron transverse momentum, $p_{\rm T}$, and rapidity, $y$. The kinematic region of the measurements is $p_{\rm T}<20~{\rm GeV}/c$ and $2.0<y<4.5$. The measurements use a data sample corresponding to an integrated luminosity of $3~{\rm fb}^{-1}$ collected by the LHCb detector in $pp$ collisions at centre-of-mass energies $\sqrt{s}=7~{\rm TeV}$ in 2011 and $\sqrt{s}=8~{\rm TeV}$ in 2012. Based on previous LHCb results of the fragmentation fraction ratio, $f_{\Lambda_B^0}/f_d$, the branching fraction of the decay $\Lambda_b^0\rightarrow J/\psi pK^-$ is measured to be \begin{equation*} \mathcal{B}(\Lambda_b^0\rightarrow J/\psi pK^-)= (3.17\pm0.04\pm0.07\pm0.34^{+0.45}_{-0.28})\times10^{-4}, \end{equation*} where the first uncertainty is statistical, the second is systematic, the third is due to the uncertainty on the branching fraction of the decay $\overline{B}^0\rightarrow J/\psi\overline{K}^*(892)^0$, and the fourth is due to the knowledge of $f_{\Lambda_b^0}/f_d$. The sum of the asymmetries in the production and decay between $\Lambda_b^0$ and $\overline{\Lambda}_b^0$ is also measured as a function of $p_{\rm T}$ and $y$. The previously published branching fraction of $\Lambda_b^0\rightarrow J/\psi p\pi^-$, relative to that of $\Lambda_b^0\rightarrow J/\psi pK^-$, is updated. The branching fractions of $\Lambda_b^0\rightarrow P_c^+(\rightarrow J/\psi p)K^-$ are determined.Comment: 29 pages, 19figures. All figures and tables, along with any supplementary material and additional information, are available at https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2015-032.htm

Study of Bc+B_c^+ decays to the K+K−π+K^+K^-\pi^+ final state and evidence for the decay Bc+→χc0π+B_c^+\to\chi_{c0}\pi^+

A study of $B_c^+\to K^+K^-\pi^+$ decays is performed for the first time using data corresponding to an integrated luminosity of 3.0 $\mathrm{fb}^{-1}$ collected by the LHCb experiment in $pp$ collisions at centre-of-mass energies of $7$ and $8$ TeV. Evidence for the decay $B_c^+\to\chi_{c0}(\to K^+K^-)\pi^+$ is reported with a significance of 4.0 standard deviations, resulting in the measurement of $\frac{\sigma(B_c^+)}{\sigma(B^+)}\times\mathcal{B}(B_c^+\to\chi_{c0}\pi^+)$ to be $(9.8^{+3.4}_{-3.0}(\mathrm{stat})\pm 0.8(\mathrm{syst}))\times 10^{-6}$. Here $\mathcal{B}$ denotes a branching fraction while $\sigma(B_c^+)$ and $\sigma(B^+)$ are the production cross-sections for $B_c^+$ and $B^+$ mesons. An indication of $\bar b c$ weak annihilation is found for the region $m(K^-\pi^+)<1.834\mathrm{\,Ge\kern -0.1em V\!/}c^2$, with a significance of 2.4 standard deviations.Comment: All figures and tables, along with any supplementary material and additional information, are available at https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2016-022.html, link to supplemental material inserted in the reference