The Eccentric-distance Sum of Some Graphs

Let $G = (V,E)$ be a simple connected graph. Theeccentric-distance sum of $G$ is defined as\xi^{ds}(G) =\ds\sum_{\{u,v\}\subseteq V(G)} [e(u)+e(v)] d(u,v), where $e(u)$ %\dsis the eccentricity of the vertex $u$ in $G$ and $d(u,v)$ is thedistance between $u$ and $v$. In this paper, we establish formulaeto calculate the eccentric-distance sum for some graphs, namelywheel, star, broom, lollipop, double star, friendship, multi-stargraph and the join of $P_{n-2}$ and $P_2$

Measurement of the CP violation parameter A_{Γ} in D^{0}→K^{+}K^{-} and D^{0}→π^{+}π^{-} decays

Asymmetries in the time-dependent rates of D^{0}→K^{+}K^{-} and D^{0}→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 D^{0} and D[over ¯]^{0} decays, sensitive to indirect CP violation, are measured to be A_{Γ}(K^{+}K^{-})=(-0.30±0.32±0.10)×10^{-3} and A_{Γ}(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

Study of prompt D0 meson production in pPb collisions at sNN=5 TeV

Production of prompt D0 mesons is studied in proton-lead and lead-proton collisions recorded at the LHCb detector at the LHC. The data sample corresponds to an integrated luminosity of 1.58±0.02 nb−1 recorded at a nucleon-nucleon centre-of-mass energy of sNN=5 TeV. Measurements of the differential cross-section, the forward-backward production ratio and the nuclear modification factor are reported using D0 candidates with transverse momenta less than 10 GeV/c and rapidities in the ranges 1.5 < y∗< 4.0 and −5.0 < y∗< −2.5 in the nucleon-nucleon centre-of-mass system

Measurements of prompt charm production cross-sections in pp collisions at s=5 TeV

Production cross-sections of prompt charm mesons are measured using data from pp collisions at the LHC at a centre-of-mass energy of 5 TeV. The data sample corresponds to an integrated luminosity of 8.60 ± 0.33 pb−1 collected by the LHCb experiment. The production cross-sections of D0, D+, Ds+, and D∗+ mesons are measured in bins of charm meson transverse momentum, pT, and rapidity, y. They cover the rapidity range 2.0 < y < 4.5 and transverse momentum ranges 0 < pT< 10 GeV/c for D0 and D+ and 1 < pT< 10 GeV/c for Ds+ and D∗+ mesons. The inclusive cross-sections for the four mesons, including charge-conjugate states, within the range of 1 < pT< 8 GeV/c are determined to be σpp→D0X=1004±3±54μb,σpp→D+X=402±2±30μb,σpp→Ds+X=170±4±16μb,σpp→D∗+X=421±5±36μb, where the uncertainties are statistical and systematic, respectively

Measurement of the properties of the Ξb∗ 0 baryon

We perform a search for near-threshold Ξb0 resonances decaying to Ξb−π+ in a sample of proton-proton collision data corresponding to an integrated luminosity of 3 fb−1 collected by the LHCb experiment. We observe one resonant state, with the following properties: mΞb∗0−mΞb−−mπ+=15.727±0.068stat±0.023systMeV/c2ΓΞb∗0=0.90±0.16stat±0.08systMeV.This confirms the previous observation by the CMS collaboration. The state is consistent with the JP = 3/2+ Ξb∗ 0 resonance expected in the quark model. This is the most precise determination of the mass and the first measurement of the natural width of this state. We have also measured the ratio σpp→Ξb∗0XℬΞb∗0→Ξb−π+σpp→Ξb−X=0.28±0.03stat.±0.01syst.

Differential branching fraction and angular analysis of Λb0→Λμ+μ−\Lambda^{0}_{b} \rightarrow \Lambda \mu^+\mu^- decays

The differential branching fraction of the rare decay $\Lambda^{0}_{b} \rightarrow \Lambda \mu^+\mu^-$ is measured as a function of $q^{2}$, the square of the dimuon invariant mass. The analysis is performed using proton-proton collision data, corresponding to an integrated luminosity of 3.0 \mbox{ fb}^{-1}, collected by the LHCb experiment. Evidence of signal is observed in the $q^2$ region below the square of the $J/\psi$ mass. Integrating over 15 < q^{2} < 20 \mbox{ GeV}^2/c^4 the branching fraction is measured as d\mathcal{B}(\Lambda^{0}_{b} \rightarrow \Lambda \mu^+\mu^-)/dq^2 = (1.18 ^{+ 0.09} _{-0.08} \pm 0.03 \pm 0.27) \times 10^{-7} ( \mbox{GeV}^{2}/c^{4})^{-1}, where the uncertainties are statistical, systematic and due to the normalisation mode, $\Lambda^{0}_{b} \rightarrow J/\psi \Lambda$, respectively. In the $q^2$ intervals where the signal is observed, angular distributions are studied and the forward-backward asymmetries in the dimuon ($A^{l}_{\rm FB}$) and hadron ($A^{h}_{\rm FB}$) systems are measured for the first time. In the range 15 < q^2 < 20 \mbox{ GeV}^2/c^4 they are found to be A^{l}_{\rm FB} = -0.05 \pm 0.09 \mbox{ (stat)} \pm 0.03 \mbox{ (syst)} and A^{h}_{\rm FB} = -0.29 \pm 0.07 \mbox{ (stat)} \pm 0.03 \mbox{ (syst)}.Comment: 27 pages, 10 figures, Erratum adde

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

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