Extreme rays of the (N,k)(N, k)-Schur Cone

We discuss several partial results towards proving Dennis White's conjecture on the extreme rays of the $(N,2)$-Schur cone. We are interested in which vectors are extreme in the cone generated by all products of Schur functions of partitions with $k$ or fewer parts. For the case where $k =2$, White conjectured that the extreme rays are obtained by excluding a certain family of "bad pairs," and proved a special case of the conjecture using Farkas' Lemma. We present an alternate proof of the special case, in addition to showing more infinite families of extreme rays and reducing White's conjecture to two simpler conjectures.Comment: This paper has been withdrawn by the authors due to a misinterpretation of the generalized Littlewood-Richardson rule in several proof

Les droits disciplinaires des fonctions publiques : « unification », « harmonisation » ou « distanciation ». A propos de la loi du 26 avril 2016 relative à la déontologie et aux droits et obligations des fonctionnaires

The production of tt‾ , W+bb‾ and W+cc‾ is studied in the forward region of proton–proton collisions collected at a centre-of-mass energy of 8 TeV by the LHCb experiment, corresponding to an integrated luminosity of 1.98±0.02 fb−1 . The W bosons are reconstructed in the decays W→ℓν , where ℓ denotes muon or electron, while the b and c quarks are reconstructed as jets. All measured cross-sections are in agreement with next-to-leading-order Standard Model predictions.The production of $t\overline{t}$, $W+b\overline{b}$ and $W+c\overline{c}$ is studied in the forward region of proton-proton collisions collected at a centre-of-mass energy of 8 TeV by the LHCb experiment, corresponding to an integrated luminosity of 1.98 $\pm$ 0.02 \mbox{fb}^{-1}. The $W$ bosons are reconstructed in the decays $W\rightarrow\ell\nu$, where $\ell$ denotes muon or electron, while the $b$ and $c$ quarks are reconstructed as jets. All measured cross-sections are in agreement with next-to-leading-order Standard Model predictions

Measurement of ϒ production in pp collisions at √s = 2.76 TeV

The production of ϒ(1S), ϒ(2S) and ϒ(3S) mesons decaying into the dimuon final state is studied with the LHCb detector using a data sample corresponding to an integrated luminosity of 3.3 pb−1 collected in proton–proton collisions at a centre-of-mass energy of √s = 2.76 TeV. The differential production cross-sections times dimuon branching fractions are measured as functions of the ϒ transverse momentum and rapidity, over the ranges pT < 15 GeV/c and 2.0 < y < 4.5. The total cross-sections in this kinematic region, assuming unpolarised production, are measured to be σ (pp → ϒ(1S)X) × B ϒ(1S)→μ+μ− = 1.111 ± 0.043 ± 0.044 nb, σ (pp → ϒ(2S)X) × B ϒ(2S)→μ+μ− = 0.264 ± 0.023 ± 0.011 nb, σ (pp → ϒ(3S)X) × B ϒ(3S)→μ+μ− = 0.159 ± 0.020 ± 0.007 nb, where the first uncertainty is statistical and the second systematic

Study of the rare B-s(0) and B-0 decays into the pi(+) pi(-) mu(+) mu(-) final state

A search for the rare decays $B_s^0 \to \pi^+\pi^-\mu^+\mu^-$ and $B^0 \to \pi^+\pi^-\mu^+\mu^-$ is performed in a data set corresponding to an integrated luminosity of 3.0 fb$^{-1}$ collected by the LHCb detector in proton-proton collisions at centre-of-mass energies of 7 and 8 TeV. Decay candidates with pion pairs that have invariant mass in the range 0.5-1.3 GeV/$c^2$ and with muon pairs that do not originate from a resonance are considered. The first observation of the decay $B_s^0 \to \pi^+\pi^-\mu^+\mu^-$ and the first evidence of the decay $B^0 \to \pi^+\pi^-\mu^+\mu^-$ are obtained and the branching fractions are measured to be $\mathcal{B}(B_s^0 \to \pi^+\pi^-\mu^+\mu^-)=(8.6\pm 1.5\,({\rm stat}) \pm 0.7\,({\rm syst})\pm 0.7\,({\rm norm}))\times 10^{-8}$ and $\mathcal{B}(B^0 \to \pi^+\pi^-\mu^+\mu^-)=(2.11\pm 0.51\,({\rm stat}) \pm 0.15\,({\rm syst})\pm 0.16\,({\rm norm}) )\times 10^{-8}$, where the third uncertainty is due to the branching fraction of the decay $B^0\to J/\psi(\to \mu^+\mu^-)K^*(890)^0(\to K^+\pi^-)$, used as a normalisation.A search for the rare decays Bs0→π+π−μ+μ− and B0→π+π−μ+μ− is performed in a data set corresponding to an integrated luminosity of 3.0 fb−1 collected by the LHCb detector in proton–proton collisions at centre-of-mass energies of 7 and 8 TeV . Decay candidates with pion pairs that have invariant mass in the range 0.5–1.3 GeV/c2 and with muon pairs that do not originate from a resonance are considered. The first observation of the decay Bs0→π+π−μ+μ− and the first evidence of the decay B0→π+π−μ+μ− are obtained and the branching fractions, restricted to the dipion-mass range considered, are measured to be B(Bs0→π+π−μ+μ−)=(8.6±1.5 (stat)±0.7 (syst)±0.7(norm))×10−8 and B(B0→π+π−μ+μ−)=(2.11±0.51(stat)±0.15(syst)±0.16(norm))×10−8 , where the third uncertainty is due to the branching fraction of the decay B0→J/ψ(→μ+μ−)K⁎(892)0(→K+π−) , used as a normalisation.A search for the rare decays Bs0→π+π−μ+μ− and B0→π+π−μ+μ− is performed in a data set corresponding to an integrated luminosity of 3.0 fb−1 collected by the LHCb detector in proton–proton collisions at centre-of-mass energies of 7 and 8 TeV . Decay candidates with pion pairs that have invariant mass in the range 0.5–1.3 GeV/c2 and with muon pairs that do not originate from a resonance are considered. The first observation of the decay Bs0→π+π−μ+μ− and the first evidence of the decay B0→π+π−μ+μ− are obtained and the branching fractions, restricted to the dipion-mass range considered, are measured to be B(Bs0→π+π−μ+μ−)=(8.6±1.5 (stat)±0.7 (syst)±0.7(norm))×10−8 and B(B0→π+π−μ+μ−)=(2.11±0.51(stat)±0.15(syst)±0.16(norm))×10−8 , where the third uncertainty is due to the branching fraction of the decay B0→J/ψ(→μ+μ−)K⁎(892)0(→K+π−) , used as a normalisation.A search for the rare decays $B_s^0 \to \pi^+\pi^-\mu^+\mu^-$ and $B^0 \to \pi^+\pi^-\mu^+\mu^-$ is performed in a data set corresponding to an integrated luminosity of 3.0 fb$^{-1}$ collected by the LHCb detector in proton-proton collisions at centre-of-mass energies of 7 and 8 TeV. Decay candidates with pion pairs that have invariant mass in the range 0.5-1.3 GeV/$c^2$ and with muon pairs that do not originate from a resonance are considered. The first observation of the decay $B_s^0 \to \pi^+\pi^-\mu^+\mu^-$ and the first evidence of the decay $B^0 \to \pi^+\pi^-\mu^+\mu^-$ are obtained and the branching fractions, restricted to the dipion-mass range considered, are measured to be $\mathcal{B}(B_s^0 \to \pi^+\pi^-\mu^+\mu^-)=(8.6\pm 1.5\,({\rm stat}) \pm 0.7\,({\rm syst})\pm 0.7\,({\rm norm}))\times 10^{-8}$ and $\mathcal{B}(B^0 \to \pi^+\pi^-\mu^+\mu^-)=(2.11\pm 0.51\,({\rm stat}) \pm 0.15\,({\rm syst})\pm 0.16\,({\rm norm}) )\times 10^{-8}$, where the third uncertainty is due to the branching fraction of the decay $B^0\to J/\psi(\to \mu^+\mu^-)K^*(890)^0(\to K^+\pi^-)$, used as a normalisation

Angular analysis of the B-0 -> K*(0) e(+) e(-) decay in the low-q(2) region

An angular analysis of the $B^0 \rightarrow K^{*0} e^+ e^-$ decay is performed using a data sample, corresponding to an integrated luminosity of 3.0 {\mbox{fb}^{-1}}, collected by the LHCb experiment in $pp$ collisions at centre-of-mass energies of 7 and 8 TeV during 2011 and 2012. For the first time several observables are measured in the dielectron mass squared ($q^2$) interval between 0.002 and 1.120${\mathrm{\,Ge\kern -0.1em V^2\!/}c^4}$. The angular observables $F_{\mathrm{L}}$ and $A_{\mathrm{T}}^{\mathrm{Re}}$ which are related to the $K^{*0}$ polarisation and to the lepton forward-backward asymmetry, are measured to be $F_{\mathrm{L}}= 0.16 \pm 0.06 \pm0.03$ and $A_{\mathrm{T}}^{\mathrm{Re}} = 0.10 \pm 0.18 \pm 0.05$, where the first uncertainty is statistical and the second systematic. The angular observables $A_{\mathrm{T}}^{(2)}$ and $A_{\mathrm{T}}^{\mathrm{Im}}$ which are sensitive to the photon polarisation in this $q^2$ range, are found to be $A_{\mathrm{T}}^{(2)} = -0.23 \pm 0.23 \pm 0.05$ and $A_{\mathrm{T}}^{\mathrm{Im}} =0.14 \pm 0.22 \pm 0.05$. The results are consistent with Standard Model predictions.An angular analysis of the B$^{0}$ → K^{*}^{0} e$^{+}$ e$^{−}$ decay is performed using a data sample, corresponding to an integrated luminosity of 3.0 fb$^{−1}$, collected by the LHCb experiment in pp collisions at centre-of-mass energies of 7 and 8 TeV during 2011 and 2012. For the first time several observables are measured in the dielectron mass squared (q$^{2}$) interval between 0.002 and 1.120 GeV$^{2}$ /c$^{4}$. The angular observables F$_{L}$ and A$_{T}^{Re}$ which are related to the K^{*}^{0} polarisation and to the lepton forward-backward asymmetry, are measured to be F$_{L}$ = 0.16 ± 0.06 ± 0.03 and A$_{T}^{Re}$  = 0.10 ± 0.18 ± 0.05, where the first uncertainty is statistical and the second systematic. The angular observables A$_{T}^{(2)}$ and A$_{T}^{Im}$ which are sensitive to the photon polarisation in this q$^{2}$ range, are found to be A$_{T}^{(2)}$  = − 0.23 ± 0.23 ± 0.05 and A$_{T}^{Im}$  = 0.14 ± 0.22 ± 0.05. The results are consistent with Standard Model predictions.An angular analysis of the $B^0 \rightarrow K^{*0} e^+ e^-$ decay is performed using a data sample, corresponding to an integrated luminosity of 3.0 {\mbox{fb}^{-1}}, collected by the LHCb experiment in $pp$ collisions at centre-of-mass energies of 7 and 8 TeV during 2011 and 2012. For the first time several observables are measured in the dielectron mass squared ($q^2$) interval between 0.002 and 1.120${\mathrm{\,Ge\kern -0.1em V^2\!/}c^4}$. The angular observables $F_{\mathrm{L}}$ and $A_{\mathrm{T}}^{\mathrm{Re}}$ which are related to the $K^{*0}$ polarisation and to the lepton forward-backward asymmetry, are measured to be $F_{\mathrm{L}}= 0.16 \pm 0.06 \pm0.03$ and $A_{\mathrm{T}}^{\mathrm{Re}} = 0.10 \pm 0.18 \pm 0.05$, where the first uncertainty is statistical and the second systematic. The angular observables $A_{\mathrm{T}}^{(2)}$ and $A_{\mathrm{T}}^{\mathrm{Im}}$ which are sensitive to the photon polarisation in this $q^2$ range, are found to be $A_{\mathrm{T}}^{(2)} = -0.23 \pm 0.23 \pm 0.05$ and $A_{\mathrm{T}}^{\mathrm{Im}} =0.14 \pm 0.22 \pm 0.05$. The results are consistent with Standard Model predictions

Observation of the B0 → ρ0ρ0 decay from an amplitude analysis of B0 → (π+π−)(π+π−) decays

Proton–proton collision data recorded in 2011 and 2012 by the LHCb experiment, corresponding to an integrated luminosity of 3.0 fb−1 , are analysed to search for the charmless B0→ρ0ρ0 decay. More than 600 B0→(π+π−)(π+π−) signal decays are selected and used to perform an amplitude analysis, under the assumption of no CP violation in the decay, from which the B0→ρ0ρ0 decay is observed for the first time with 7.1 standard deviations significance. The fraction of B0→ρ0ρ0 decays yielding a longitudinally polarised final state is measured to be fL=0.745−0.058+0.048(stat)±0.034(syst) . The B0→ρ0ρ0 branching fraction, using the B0→ϕK⁎(892)0 decay as reference, is also reported as B(B0→ρ0ρ0)=(0.94±0.17(stat)±0.09(syst)±0.06(BF))×10−6

Measurement of the (eta c)(1S) production cross-section in proton-proton collisions via the decay (eta c)(1S) -> p(p)over-bar

The production of the $\eta_c (1S)$ state in proton-proton collisions is probed via its decay to the $p \bar{p}$ final state with the LHCb detector, in the rapidity range $2.0 6.5$ GeV/c. The cross-section for prompt production of $\eta_c (1S)$ mesons relative to the prompt $J/\psi$ cross-section is measured, for the first time, to be $\sigma_{\eta_c (1S)}/\sigma_{J/\psi} = 1.74 \pm 0.29 \pm 0.28 \pm 0.18 _{B}$ at a centre-of-mass energy $\sqrt{s} = 7$ TeV using data corresponding to an integrated luminosity of 0.7 fb$^{-1}$, and $\sigma_{\eta_c (1S)}/\sigma_{J/\psi} = 1.60 \pm 0.29 \pm 0.25 \pm 0.17 _{B}$ at $\sqrt{s} = 8$ TeV using 2.0 fb$^{-1}$. The uncertainties quoted are, in order, statistical, systematic, and that on the ratio of branching fractions of the $\eta_c (1S)$ and $J/\psi$ decays to the $p \bar{p}$ final state. In addition, the inclusive branching fraction of $b$-hadron decays into $\eta_c (1S)$ mesons is measured, for the first time, to be $B ( b \rightarrow \eta_c X ) = (4.88 \pm 0.64 \pm 0.25 \pm 0.67 _{B}) \times 10^{-3}$, where the third uncertainty includes also the uncertainty on the $J/\psi$ inclusive branching fraction from $b$-hadron decays. The difference between the $J/\psi$ and $\eta_c (1S)$ meson masses is determined to be $114.7 \pm 1.5 \pm 0.1$ MeV/c$^2$.The production of the $\eta _c (1S)$ state in proton-proton collisions is probed via its decay to the $p\overline{p}$ final state with the LHCb detector, in the rapidity range $2.0 6.5 \mathrm{{\,GeV/}{ c}}$ . The cross-section for prompt production of $\eta _c (1S)$ mesons relative to the prompt ${{ J}}/{\psi }$ cross-section is measured, for the first time, to be $\sigma _{\eta _c (1S)}/\sigma _{{{{ J}}/{\psi }}} = 1.74\, \pm \,0.29\, \pm \, 0.28\, \pm \,0.18 _{{\mathcal{B}}}$ at a centre-of-mass energy ${\sqrt{s}} = 7 {~\mathrm{TeV}}$ using data corresponding to an integrated luminosity of 0.7 fb$^{-1}$ , and $\sigma _{\eta _c (1S)}/\sigma _{{{{ J}}/{\psi }}} = 1.60 \pm 0.29 \pm 0.25 \pm 0.17 _{{\mathcal{B}}}$ at ${\sqrt{s}} = 8 {~\mathrm{TeV}}$ using 2.0 fb$^{-1}$ . The uncertainties quoted are, in order, statistical, systematic, and that on the ratio of branching fractions of the $\eta _c (1S)$ and ${{ J}}/{\psi }$ decays to the $p\overline{p}$ final state. In addition, the inclusive branching fraction of ${b}$ -hadron decays into $\eta _c (1S)$ mesons is measured, for the first time, to be ${\mathcal{B}}( b {\rightarrow } \eta _c X ) = (4.88\, \pm \,0.64\, \pm \,0.29\, \pm \, 0.67 _{{\mathcal{B}}}) \times 10^{-3}$ , where the third uncertainty includes also the uncertainty on the ${{ J}}/{\psi }$ inclusive branching fraction from ${b}$ -hadron decays. The difference between the ${{ J}}/{\psi }$ and $\eta _c (1S)$ meson masses is determined to be $114.7 \pm 1.5 \pm 0.1 {\mathrm {\,MeV\!/}c^2}$ .The production of the $\eta_c (1S)$ state in proton-proton collisions is probed via its decay to the $p \bar{p}$ final state with the LHCb detector, in the rapidity range $2.0 6.5$ GeV/c. The cross-section for prompt production of $\eta_c (1S)$ mesons relative to the prompt $J/\psi$ cross-section is measured, for the first time, to be $\sigma_{\eta_c (1S)}/\sigma_{J/\psi} = 1.74 \pm 0.29 \pm 0.28 \pm 0.18 _{B}$ at a centre-of-mass energy $\sqrt{s} = 7$ TeV using data corresponding to an integrated luminosity of 0.7 fb$^{-1}$, and $\sigma_{\eta_c (1S)}/\sigma_{J/\psi} = 1.60 \pm 0.29 \pm 0.25 \pm 0.17 _{B}$ at $\sqrt{s} = 8$ TeV using 2.0 fb$^{-1}$. The uncertainties quoted are, in order, statistical, systematic, and that on the ratio of branching fractions of the $\eta_c (1S)$ and $J/\psi$ decays to the $p \bar{p}$ final state. In addition, the inclusive branching fraction of $b$-hadron decays into $\eta_c (1S)$ mesons is measured, for the first time, to be $B ( b \rightarrow \eta_c X ) = (4.88 \pm 0.64 \pm 0.29 \pm 0.67 _{B}) \times 10^{-3}$, where the third uncertainty includes also the uncertainty on the $J/\psi$ inclusive branching fraction from $b$-hadron decays. The difference between the $J/\psi$ and $\eta_c (1S)$ meson masses is determined to be $114.7 \pm 1.5 \pm 0.1$ MeV/c$^2$

Search for the lepton flavour violating decay tau(-) -> mu(-)mu(+)mu(-)

A search for the lepton flavour violating decay $\tau^-\rightarrow\mu^-\mu^+\mu^-$ is performed with the LHCb experiment. The data sample corresponds to an integrated luminosity of 1.0 fb$^{−1}$ of proton-proton collisions at a centre-of-mass energy of 7 TeV and 2.0 fb$^{−1}$ at 8 TeV. No evidence is found for a signal, and a limit is set at 90% confidence level on the branching fraction, $\mathcal{B}(\tau^-\rightarrow\mu^-\mu^+\mu^-)<4.6\times10^{−8}$.A search for the lepton flavour violating decay τ$^{−}$ → μ$^{−}$ μ$^{+}$ μ$^{−}$ is performed with the LHCb experiment. The data sample corresponds to an integrated luminosity of 1.0 fb$^{−1}$ of proton-proton collisions at a centre-of-mass energy of 7 TeV and 2.0 fb$^{−1}$ at 8 TeV. No evidence is found for a signal, and a limit is set at 90% confidence level on the branching fraction, $\mathrm{\mathcal{B}}\left({\tau}^{-}\to {\mu}^{-}{\mu}^{+}{\mu}^{-}\right)<4.6\times {10}^{-8}$ .A search for the lepton flavour violating decay $\tau^-\to \mu^-\mu^+\mu^-$ is performed with the LHCb experiment. The data sample corresponds to an integrated luminosity of $1.0\mathrm{\,fb}^{-1}$ of proton-proton collisions at a centre-of-mass energy of $7\mathrm{\,Te\kern -0.1em V}$ and $2.0\mathrm{\,fb}^{-1}$ at $8\mathrm{\,Te\kern -0.1em V}$. No evidence is found for a signal, and a limit is set at $90\%$ confidence level on the branching fraction, $\mathcal{B}(\tau^-\to \mu^-\mu^+\mu^-) < 4.6 \times 10^{-8}$

Measurement of CPCP asymmetries and polarisation fractions in Bs0→K∗0Kˉ∗0B_s^0 \rightarrow K^{*0}\bar{K}{}^{*0} decays

An angular analysis of the decay $B_s^0 \rightarrow K^{*0}\overline{K}{}^{*0}$ is performed using $pp$ collisions corresponding to an integrated luminosity of $1.0$ ${fb}^{-1}$ collected by the LHCb experiment at a centre-of-mass energy $\sqrt{s} = 7$ TeV. A combined angular and mass analysis separates six helicity amplitudes and allows the measurement of the longitudinal polarisation fraction $f_L = 0.201 \pm 0.057 {(stat.)} \pm 0.040{(syst.)}$ for the $B_s^0 \rightarrow K^*(892)^0 \overline{K}{}^*(892)^0$ decay. A large scalar contribution from the $K^{*}_{0}(1430)$ and $K^{*}_{0}(800)$ resonances is found, allowing the determination of additional $CP$ asymmetries. Triple product and direct $CP$ asymmetries are determined to be compatible with the Standard Model expectations. The branching fraction $\mathcal{B}(B_s^0 \rightarrow K^*(892)^0 \overline{K}^*(892)^0)$ is measured to be $(10.8 \pm 2.1 {(stat.)} \pm 1.4 {(syst.)} \pm 0.6 (f_d/f_s) ) \times 10^{-6}$