On the complexity of color-avoiding site and bond percolation

The mathematical analysis of robustness and error-tolerance of complex networks has been in the center of research interest. On the other hand, little work has been done when the attack-tolerance of the vertices or edges are not independent but certain classes of vertices or edges share a mutual vulnerability. In this study, we consider a graph and we assign colors to the vertices or edges, where the color-classes correspond to the shared vulnerabilities. An important problem is to find robustly connected vertex sets: nodes that remain connected to each other by paths providing any type of error (i.e. erasing any vertices or edges of the given color). This is also known as color-avoiding percolation. In this paper, we study various possible modeling approaches of shared vulnerabilities, we analyze the computational complexity of finding the robustly (color-avoiding) connected components. We find that the presented approaches differ significantly regarding their complexity.Comment: 14 page

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

Observation of B+c → D0K+ decays

Using proton-proton collision data corresponding to an integrated luminosity of 3.0 fb−1, recorded by the LHCb detector at center-of-mass energies of 7 and 8 TeV, the B+ c → D0K+ decay is observed with a statistical significance of 5.1 standard deviations. By normalizing to B+ → D¯ 0π+ decays, a measurement of the branching fraction multiplied by the production rates for B+ c relative to B+ mesons in the LHCb acceptance is obtained, R D 0 K = ( f c / f u ) × B ( B + c → D 0 K + ) = ( 9. 3 + 2.8 − 2.5 ± 0.6 ) × 10 − 7, where the first uncertainty is statistical and the second is systematic. This decay is expected to proceed predominantly through weak annihilation and penguin amplitudes, and is the first B+ c decay of this nature to be observed

Measurement of the B_{s}^{0}→μ^{+}μ^{-} Branching Fraction and Effective Lifetime and Search for B^{0}→μ^{+}μ^{-} Decays.

A search for the rare decays B_{s}^{0}→μ^{+}μ^{-} and B^{0}→μ^{+}μ^{-} is performed at the LHCb experiment using data collected in pp collisions corresponding to a total integrated luminosity of 4.4  fb^{-1}. An excess of B_{s}^{0}→μ^{+}μ^{-} decays is observed with a significance of 7.8 standard deviations, representing the first observation of this decay in a single experiment. The branching fraction is measured to be B(B_{s}^{0}→μ^{+}μ^{-})=(3.0±0.6_{-0.2}^{+0.3})×10^{-9}, where the first uncertainty is statistical and the second systematic. The first measurement of the B_{s}^{0}→μ^{+}μ^{-} effective lifetime, τ(B_{s}^{0}→μ^{+}μ^{-})=2.04±0.44±0.05  ps, is reported. No significant excess of B^{0}→μ^{+}μ^{-} decays is found, and a 95% confidence level upper limit, B(B^{0}→μ^{+}μ^{-})<3.4×10^{-10}, is determined. All results are in agreement with the standard model expectations

Test of lepton universality in b→sℓ+ℓ−b \rightarrow s \ell^+ \ell^- decays

The first simultaneous test of muon-electron universality using $B^{+}\rightarrow K^{+}\ell^{+}\ell^{-}$ and $B^{0}\rightarrow K^{*0}\ell^{+}\ell^{-}$ decays is performed, in two ranges of the dilepton invariant-mass squared, $q^{2}$. The analysis uses beauty mesons produced in proton-proton collisions collected with the LHCb detector between 2011 and 2018, corresponding to an integrated luminosity of 9 $\mathrm{fb}^{-1}$. Each of the four lepton universality measurements reported is either the first in the given $q^{2}$ interval or supersedes previous LHCb measurements. The results are compatible with the predictions of the Standard Model.Comment: All figures and tables, along with any supplementary material and additional information, are available at https://cern.ch/lhcbproject/Publications/p/LHCb-PAPER-2022-046.html (LHCb public pages

Precision measurement of CP\it{CP} violation in the penguin-mediated decay Bs0→ϕϕB_s^{0}\rightarrow\phi\phi

A flavor-tagged time-dependent angular analysis of the decay $B_s^{0}\rightarrow\phi\phi$ is performed using $pp$ collision data collected by the LHCb experiment at % at $\sqrt{s}=13$ TeV, the center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 6 fb^{-1}. The $\it{CP}$-violating phase and direct $\it{CP}$-violation parameter are measured to be $\phi_{s\bar{s}s} = -0.042 \pm 0.075 \pm 0.009$ rad and $|\lambda|=1.004\pm 0.030 \pm 0.009$, respectively, assuming the same values for all polarization states of the $\phi\phi$ system. In these results, the first uncertainties are statistical and the second systematic. These parameters are also determined separately for each polarization state, showing no evidence for polarization dependence. The results are combined with previous LHCb measurements using $pp$ collisions at center-of-mass energies of 7 and 8 TeV, yielding $\phi_{s\bar{s}s} = -0.074 \pm 0.069$ rad and $|lambda|=1.009 \pm 0.030$. This is the most precise study of time-dependent $\it{CP}$ violation in a penguin-dominated $B$ meson decay. The results are consistent with $\it{CP}$ symmetry and with the Standard Model predictions.Comment: All figures and tables, along with any supplementary material and additional information, are available at https://cern.ch/lhcbproject/Publications/p/LHCb-PAPER-2023-001.html (LHCb public pages

First observation of a doubly charged tetraquark and its neutral partner

A combined amplitude analysis is performed for the decays $B^0 \rightarrow \overline{D}^0 D^+_s\pi^-$ and $B^+\rightarrow D^- D^+_s\pi^+$, which are related by isospin symmetry. The analysis is based on data collected by the LHCb detector in proton-proton collisions at center-of-mass energies of 7, 8 and 13$\,\rm{TeV}$. The full data sample corresponds to an integrated luminosity of 9$\,\rm{fb^{-1}}$. Two new resonant states with masses of $2.908\pm0.011\pm0.020\,\rm{GeV}$ and widths of $0.136\pm0.023\pm0.011\,\rm{GeV}$ are observed, which decay to $D^+_s\pi^+$ and $D^+_s\pi^-$ respectively. The former state indicates the first observation of a doubly charged open-charm tetraquark state with minimal quark content $[c\bar{s}u\bar{d}]$, and the latter state is a neutral tetraquark composed of $[c\bar{s}\bar{u}d]$ quarks. Both states are found to have spin-parity $0^+$, and their resonant parameters are consistent with each other, which suggests that they belong to an isospin triplet.Comment: All figures and tables, along with any supplementary material and additional information, are available at https://cern.ch/lhcbproject/Publications/p/LHCb-PAPER-2022-026.html (LHCb public pages

Measurement of the B0s →J/ψη lifetime

Using a data set corresponding to an integrated luminosity of 3 fb−1, collected by the LHCb experiment in pp collisions at centre-of-mass energies of 7 and 8 TeV, the effective lifetime in the Bs0→J/ψη decay mode, τeff, is measured to be τeff=1.479±0.034 (stat)±0.011 (syst) ps. Assuming CP conservation, τeff corresponds to the lifetime of the light Bs0 mass eigenstate. This is the first measurement of the effective lifetime in this decay mode

Observation of B(s)0→J/ψpp¯ decays and precision measurements of the B(s)0 masses

The first observation of the decays B 0 ( s ) → J / ψ p ¯ p is reported, using proton-proton collision data corresponding to an integrated luminosity of 5.2     fb − 1 , collected with the LHCb detector. These decays are suppressed due to limited available phase space, as well as due to Okubo-Zweig-Iizuka or Cabibbo suppression. The measured branching fractions are B ( B 0 → J / ψ p ¯ p ) = [ 4.51 ± 0.40 ( stat ) ± 0.44 ( syst ) ] × 10 − 7 , B ( B 0 s → J / ψ p ¯ p ) = [ 3.58 ± 0.19 ( stat ) ± 0.39 ( syst ) ] × 10 − 6 . For the B 0 s meson, the result is much higher than the expected value of O ( 10 − 9 ) . The small available phase space in these decays also allows for the most precise single measurement of both the B 0 mass as 5279.74 ± 0.30 ( stat ) ± 0.10 ( syst )     MeV and the B 0 s mass as 5366.85 ± 0.19 ( stat ) ± 0.13 ( syst )     MeV

Observation of a resonant structure near the Ds+Ds−D_s^+ D_s^- threshold in the B+→Ds+Ds−K+B^+\to D_s^+ D_s^- K^+ decay

An amplitude analysis of the $B^+\to D_s^+ D_s^- K^+$ decay is carried out to study for the first time its intermediate resonant contributions, using proton-proton collision data collected with the LHCb detector at centre-of-mass energies of 7, 8 and 13 TeV. A near-threshold peaking structure, referred to as $X(3960)$, is observed in the $D_s^+ D_s^-$ invariant-mass spectrum with significance greater than 12 standard deviations. The mass, width and the quantum numbers of the structure are measured to be $3956\pm5\pm10$ MeV, $43\pm13\pm8$ MeV and $J^{PC}=0^{++}$, respectively, where the first uncertainties are statistical and the second systematic. The properties of the new structure are consistent with recent theoretical predictions for a state composed of $c\bar{c}s\bar{s}$ quarks. Evidence for an additional structure is found around 4140 MeV in the $D_s^+ D_s^-$ invariant mass, which might be caused either by a new resonance with the $0^{++}$ assignment or by a $J/\psi \phi\leftrightarrow D_s^+ D_s^-$ coupled-channel effect.Comment: All figures and tables, along with any supplementary material and additional information, are available at https://cern.ch/lhcbproject/Publications/p/LHCb-PAPER-2022-018.html (LHCb public pages