Target Enumeration via Euler Characteristic Integrals

We solve the problem of counting the total number of observable targets (e.g., persons, vehicles, landmarks) in a region using local counts performed by a network of sensors, each of which measures the number of targets nearby but neither their identities nor any positional information. We formulate and solve several such problems based on the types of sensors and mobility of the targets. The main contribution of this paper is the adaptation of a topological sheaf integration theory — integration with respect to Euler characteristic — to yield complete solutions to these problems

Measurement of the J/ψ pair production cross-section in pp collisions at s=13 \sqrt{s}=13 TeV

The production cross-section of J/ψ pairs is measured using a data sample of pp collisions collected by the LHCb experiment at a centre-of-mass energy of $\sqrt{s}=13$ TeV, corresponding to an integrated luminosity of 279 ±11 pb$^{−1}$. The measurement is performed for J/ψ mesons with a transverse momentum of less than 10 GeV/c in the rapidity range 2.0 < y < 4.5. The production cross-section is measured to be 15.2 ± 1.0 ± 0.9 nb. The first uncertainty is statistical, and the second is systematic. The differential cross-sections as functions of several kinematic variables of the J/ψ pair are measured and compared to theoretical predictions.The production cross-section of $J/\psi$ pairs is measured using a data sample of $pp$ collisions collected by the LHCb experiment at a centre-of-mass energy of $\sqrt{s} = 13 \,{\mathrm{TeV}}$, corresponding to an integrated luminosity of $279 \pm 11 \,{\mathrm{pb^{-1}}}$. The measurement is performed for $J/\psi$ mesons with a transverse momentum of less than $10 \,{\mathrm{GeV}}/c$ in the rapidity range $2.0<y<4.5$. The production cross-section is measured to be $15.2 \pm 1.0 \pm 0.9 \,{\mathrm{nb}}$. The first uncertainty is statistical, and the second is systematic. The differential cross-sections as functions of several kinematic variables of the $J/\psi$ pair are measured and compared to theoretical predictions

Measurement of the B0s→μ+μ− Branching Fraction and Effective Lifetime and Search for B0→μ+μ− Decays

A search for the rare decays Bs0→μ+μ- and B0→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 Bs0→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(Bs0→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 Bs0→μ+μ- effective lifetime, τ(Bs0→μ+μ-)=2.04±0.44±0.05  ps, is reported. No significant excess of B0→μ+μ- decays is found, and a 95% confidence level upper limit, B(B0→μ+μ-)<3.4×10-10, is determined. All results are in agreement with the standard model expectations.A search for the rare decays $B^0_s\to\mu^+\mu^-$ and $B^0\to\mu^+\mu^-$ 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 $B^0_s\to\mu^+\mu^-$ 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 ${\cal B}(B^0_s\to\mu^+\mu^-)=\left(3.0\pm 0.6^{+0.3}_{-0.2}\right)\times 10^{-9}$, where the first uncertainty is statistical and the second systematic. The first measurement of the $B^0_s\to\mu^+\mu^-$ effective lifetime, $\tau(B^0_s\to\mu^+\mu^-)=2.04\pm 0.44\pm 0.05$ ps, is reported. No significant excess of $B^0\to\mu^+\mu^-$ decays is found and a 95 % confidence level upper limit, ${\cal B}(B^0\to\mu^+\mu^-)<3.4\times 10^{-10}$, is determined. All results are in agreement with the Standard Model expectations

Study of the lineshape of the chi(c1) (3872) state

A study of the lineshape of the chi(c1) (3872) state is made using a data sample corresponding to an integrated luminosity of 3 fb(-1) collected in pp collisions at center-of-mass energies of 7 and 8 TeV with the LHCb detector. Candidate chi(c1)(3872) and psi(2S) mesons from b-hadron decays are selected in the J/psi pi(+)pi(-) decay mode. Describing the lineshape with a Breit-Wigner function, the mass splitting between the chi(c1 )(3872) and psi(2S) states, Delta m, and the width of the chi(c1 )(3872) state, Gamma(Bw), are determined to be (Delta m=185.598 +/- 0.067 +/- 0.068 Mev,)(Gamma BW=1.39 +/- 0.24 +/- 0.10 Mev,) where the first uncertainty is statistical and the second systematic. Using a Flatte-inspired model, the mode and full width at half maximum of the lineshape are determined to be (mode=3871.69+0.00+0.05 MeV.)(FWHM=0.22-0.04+0.13+0.07+0.11-0.06-0.13 MeV, ) An investigation of the analytic structure of the Flatte amplitude reveals a pole structure, which is compatible with a quasibound D-0(D) over bar*(0) state but a quasivirtual state is still allowed at the level of 2 standard deviations

Observation of Bc+→D0K+B_{c}^{+} \rightarrow D^{0} K^{+} 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 Bc+→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 Bc+ relative to B+ mesons in the LHCb acceptance is obtained, RD0K=(fc/fu)×B(Bc+→D0K+)=(9.3-2.5+2.8±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 Bc+ decay of this nature to be observed.Using proton-proton collision data corresponding to an integrated luminosity of 3.0 fb$^{-1}$, recorded by the LHCb detector at centre-of-mass energies of 7 and 8 TeV, the $B_{c}^{+} \rightarrow D^{0} K^{+}$ decay is observed with a statistical significance of 5.1 standard deviations. By normalising to $B^{+} \rightarrow \bar{D}^{0} \pi^{+}$ 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} = \frac{f_{c}}{f_{u}}\times\mathcal{B}(B_{c}^{+} \rightarrow D^{0} K^{+}) = (9.3\,^{+2.8}_{-2.5} \pm 0.6) \times 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±B^{\pm} production asymmetry and the CPCP asymmetry in B±→J/ψK±B^{\pm} \to J/\psi K^{\pm} decays

The B± meson production asymmetry in pp collisions is measured using B+→D¯0π+ decays. The data were recorded by the LHCb experiment during Run 1 of the LHC at center-of-mass energies of s=7 and 8 TeV. The production asymmetries, integrated over transverse momenta in the range 2<pT<30  GeV/c, and rapidities in the range 2.1<y<4.5 are measured to be Aprod(B+,s=7  TeV)=(-0.41±0.49±0.10)×10-2, Aprod(B+,s=8  TeV)=(-0.53±0.31±0.10)×10-2, where the first uncertainties are statistical and the second are systematic. These production asymmetries are used to correct the raw asymmetries of B+→J/ψK+ decays, thus allowing a measurement of the CP asymmetry, ACP(B+→J/ψK+)=(0.09±0.27±0.07)×10-2.The $B^{\pm}$ meson production asymmetry in $pp$ collisions is measured using $B^+ \to \bar{D}^0 \pi^+$ decays. The data were recorded by the LHCb experiment during Run 1 of the LHC at centre-of-mass energies of $\sqrt{s}=$ 7 and 8 TeV. The production asymmetries, integrated over transverse momenta in the range $2 < p_{\rm T} < 30$ GeV/$c$, and rapidities in the range $2.1 < y < 4.5$, are measured to be \begin{align*} \mathcal{A}_{\rm prod}(B^+,\sqrt{s}=7~{\rm TeV}) &= (-0.41 \pm 0.49 \pm 0.10) \times 10^{-2},\\ \mathcal{A}_{\rm prod}(B^+,\sqrt{s}=8~{\rm TeV}) &= (-0.53 \pm 0.31 \pm 0.10) \times 10^{-2}, \end{align*} where the first uncertainties are statistical and the second are systematic. These production asymmetries are used to correct the raw asymmetries of $B^{+} \to J/\psi K^{+}$ decays, thus allowing a measurement of the $CP$ asymmetry, \begin{equation*} \mathcal{A}_{CP} = (0.09 \pm 0.27 \pm 0.07) \times 10^{-2}. \end{equation*

Observation of the Ξb−→J/ψΛK−\varXi^{-}_{b}\to J/\psi\varLambda K^{-} decay

The observation of the decay $\varXi_{b}^{-}\to J/\psi\varLambda K^{-}$ is reported, using a data sample corresponding to an integrated luminosity of $3~\mathrm{fb}^{-1}$, collected by the LHCb detector in $pp$ collisions at centre-of-mass energies of $7$ and $8~\mathrm{TeV}$. The production rate of $\varXi_{b}^{-}$ baryons detected in the decay $\varXi_{b}^{-}\to J/\psi\varLambda K^{-}$ is measured relative to that of $\varLambda_{b}^{0}$ baryons using the decay $\varLambda_{b}^{0}\to J/\psi \varLambda$. Integrated over the $b$-baryon transverse momentum $p_{\rm T}<25~\mathrm{GeV/}c$ and rapidity $2.0 < y < 4.5$, the measured ratio is \begin{equation*} \frac{f_{\varXi_{b}^{-}}}{f_{\varLambda_{b}^{0}}}\frac{\mathcal{B}(\varXi_{b}^{-}\to J/\psi\varLambda K^{-})}{\mathcal{B}(\varLambda_{b}^{0}\to J/\psi \varLambda)}=(4.19\pm 0.29~(\mathrm{stat})\pm0.14~(\mathrm{syst}))\times 10^{-2}, \end{equation*}where $f_{\varXi_{b}^{-}}$ and $f_{\varLambda_{b}^{0}}$ are the fragmentation fractions of $b\to\varXi_{b}^{-}$ and $b\to\varLambda_{b}^{0}$ transitions, and $\mathcal{B}$ represents the branching fraction of the corresponding $b$-baryon decay. The mass difference between $\varXi_{b}^{-}$ and $\varLambda_{b}^{0}$ baryons is measured to be \begin{equation*} M(\varXi_{b}^{-})-M(\varLambda_{b}^{0})=177.08\pm0.47~(\mathrm{stat})\pm0.16~(\mathrm{syst} )~\mathrm{MeV/}c^{2}. \end{equation*}The observation of the decay Ξb−→J/ψΛK− is reported, using a data sample corresponding to an integrated luminosity of 3fb−1 , collected by the LHCb detector in pp collisions at centre-of-mass energies of 7 and 8TeV . The production rate of Ξb− baryons detected in the decay Ξb−→J/ψΛK− is measured relative to that of Λb0 baryons using the decay Λb0→J/ψΛ . Integrated over the b -baryon transverse momentum pT<25GeV/c and rapidity 2.0<y<4.5 , the measured ratio is fΞb−fΛb0B(Ξb−→J/ψΛK−)B(Λb0→J/ψΛ)=(4.19±0.29 (stat)±0.15 (syst))×10−2, where fΞb− and fΛb0 are the fragmentation fractions of b→Ξb− and b→Λb0 transitions, and B represents the branching fraction of the corresponding b -baryon decay. The mass difference between Ξb− and Λb0 baryons is measured to be M(Ξb−)−M(Λb0)=177.08±0.47 (stat)±0.16 (syst)MeV/c2.The observation of the decay $\varXi^{-}_{b}\to J/\psi\varLambda K^{-}$ is reported, using a data sample corresponding to an integrated luminosity of $3~\mathrm{fb}^{-1}$, collected by the LHCb detector in $pp$ collisions at centre-of-mass energies of $7$ and $8~\mathrm{TeV}$. The production rate of $\varXi_{b}^{-}$ baryons detected in the decay $\varXi_{b}^{-}\to J/\psi\varLambda K^{-}$ is measured relative to that of $\varLambda_{b}^{0}$ baryons using the decay $\varLambda_{b}^{0}\to J/\psi \varLambda$. Integrated over the $b$-baryon transverse momentum $p_{\rm T}<25~\mathrm{GeV/}c$ and rapidity $2.0<y<4.5$, the measured ratio is \begin{equation*} \frac{f_{\varXi_{b}^{-}}}{f_{\varLambda_{b}^{0}}}\frac{\mathcal{B}(\varXi_{b}^{-}\to J/\psi\varLambda K^{-})}{\mathcal{B}(\varLambda_{b}^{0}\to J/\psi \varLambda)}=(4.19\pm 0.29~(\mathrm{stat})\pm0.15~(\mathrm{syst}))\times 10^{-2}, \end{equation*}where $f_{\varXi_{b}^{-}}$ and $f_{\varLambda_{b}^{0}}$ are the fragmentation fractions of $b\to\varXi_{b}^{-}$ and $b\to\varLambda_{b}^{0}$ transitions, and $\mathcal{B}$ represents the branching fraction of the corresponding $b$-baryon decay. The mass difference between $\varXi_{b}^{-}$ and $\varLambda_{b}^{0}$ baryons is measured to be \begin{equation*} M(\varXi_{b}^{-})-M(\varLambda_{b}^{0})=177.08\pm0.47~(\mathrm{stat})\pm0.16~(\mathrm{syst} )~\mathrm{MeV/}c^{2}. \end{equation*

Measurement of the C ⁣PC\!P violation parameter AΓA_\Gamma in D0→K+K−D^0 \to K^+K^- and D0→π+π−D^0 \to \pi^+\pi^- decays

Asymmetries in the time-dependent rates of D0→K+K- and D0→π+π- decays are measured in a pp collision data sample collected with the LHCb detector during LHC Run 1, corresponding to an integrated luminosity of 3  fb-1. The asymmetries in effective decay widths between D0 and D¯0 decays, sensitive to indirect CP violation, are measured to be AΓ(K+K-)=(-0.30±0.32±0.10)×10-3 and AΓ(π+π-)=(0.46±0.58±0.12)×10-3, where the first uncertainty is statistical and the second systematic. These measurements show no evidence for CP violation and improve on the precision of the previous best measurements by nearly a factor of two.Asymmetries in the time-dependent rates of $D^0 \to K^+K^-$ and $D^0 \to \pi^+\pi^-$ decays are measured in a $pp$ collision data sample collected with the LHCb detector during LHC Run 1, corresponding to an integrated luminosity of $3\,\mathrm{fb}^{-1}$. The asymmetries in effective decay widths between $D^0$ and $\overline{D}^0$ decays, sensitive to indirect $CP$ violation, are measured to be $A_\Gamma(K^+ K^-) = (-0.30 \pm 0.32 \pm 0.10)\times 10^{-3}$ and $A_\Gamma(\pi^+\pi^-) = (0.46 \pm 0.58 \pm 0.12)\times 10^{-3}$, where the first uncertainty is statistical and the second systematic. These measurements show no evidence for $C\!P$ violation and improve on the precision of the previous best measurements by nearly a factor of two

Observation of Bc+→J/ψD(∗)K(∗)B_{c}^{+} \to J/\psi D^{(*)} K^{(*)} decays

A search for the decays Bc+→J/ψD(*)0K+ and Bc+→J/ψD(*)+K*0 is performed with data collected at the LHCb experiment corresponding to an integrated luminosity of 3  fb-1. The decays Bc+→J/ψD0K+ and Bc+→J/ψD*0K+ are observed for the first time, while first evidence is reported for the Bc+→J/ψD*+K*0 and Bc+→J/ψD+K*0 decays. The branching fractions of these decays are determined relative to the Bc+→J/ψπ+ decay. The Bc+ mass is measured, using the J/ψD0K+ final state, to be 6274.28±1.40(stat)±0.32(syst)  MeV/c2. This is the most precise single measurement of the Bc+ mass to date.A search for the decays $B_c^+ \to J/\psi D^{(*)0} K^+$ and $B_c^+ \to J/\psi D^{(*)+} K^{*0}$ is performed with data collected at the LHCb experiment corresponding to an integrated luminosity of 3 fb$^{-1}$. The decays $B_c^+ \to J/\psi D^0 K^+$ and $B_c^+ \to J/\psi D^{*0} K^+$ are observed for the first time, while first evidence is reported for the $B_c^+ \to J/\psi D^{*+} K^{*0}$ and $B_c^+ \to J/\psi D^+ K^{*0}$ decays. The branching fractions of these decays are determined relative to the $B_c^+ \to J/\psi \pi^+$ decay. The $B_c^+$ mass is measured, using the $J/\psi D^0 K^+$ final state, to be $6274.28 \pm 1.40 (stat) \pm 0.32 (syst)$ MeV/$c^2$. This is the most precise single measurement of the $B_c^+$ mass to date