Any l-state analytical solutions of the Klein-Gordon equation for the Woods-Saxon potential

The radial part of the Klein-Gordon equation for the Woods-Saxon potential is solved. In our calculations, we have applied the Nikiforov-Uvarov method by using the Pekeris approximation to the centrifugal potential for any $l$ states. The exact bound state energy eigenvalues and the corresponding eigenfunctions are obtained on the various values of the quantum numbers $n$ and $l$. The non-relativistic limit of the bound state energy spectrum was also found.Comment: 15 pages, 1 tabl

Analytical solutions of the Schr\"{o}dinger equation with the Woods-Saxon potential for arbitrary ll state

In this work, the analytical solution of the radial Schr\"{o}dinger equation for the Woods-Saxon potential is presented. In our calculations, we have applied the Nikiforov-Uvarov method by using the Pekeris approximation to the centrifugal potential for arbitrary $l$ states. The bound state energy eigenvalues and corresponding eigenfunctions are obtained for various values of $n$ and $l$ quantum numbers.Comment: 14 page

Structural, electronic and phononic properties of PtSe2: From monolayer to bulk

The layer dependent structural, electronic and vibrational properties of the 1T phase of two dimensional (2D) platinum diselenide are investigated by means of state-of-the-art first-principles calculations. The main findings of the study are: (i) monolayer platinum diselenide has a dynamically stable 2D octahedral structure with 1.66 eV indirect band gap, (ii) the semiconducting nature of 1T-PtSe2 monolayers remains unaffected even at high biaxial strains, (iii) top-to-top (AA) arrangement is found to be energetically the most favorable stacking of 1T-PtSe2 layers, (iv) the lattice constant (layer-layer distance) increases (decreases) with increasing number of layers, (v) while monolayer and bilayer 1T-PtSe2 are indirect semiconductors, bulk and few-layered 1T-PtSe2 are metals, (vi) Raman intensity and peak positions of the A1g and Eg modes are found to be highly dependent on the layer thickness of the material, hence; the number of layers of the material can be determined via Raman measurements.TUBITAK under the project number 117F09

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

Observation of associated production of a ZZ boson with a DD meson in the~forward region

A search for associated production of a $Z$ boson with an open charm meson is presented using a data sample, corresponding to an integrated luminosity of $1.0\,\mathrm{fb}^{-`}$ of proton--proton collisions at a centre-of-mass energy of 7\,TeV, collected by the LHCb experiment. %% Seven candidate events for associated production of a $Z$ boson with a $D^0$ meson and four candidate events for a $Z$ boson with a $D^+$ meson are observed with a combined significance of 5.1standard deviations. The production cross-sections in the forward region are measured to be $$\sigma_{Z\rightarrow\mu^+\mu^-\!,D^0} = 2.50\pm1.12\pm0.22pb$$ $$\sigma_{Z\rightarrow\mu^+\mu^-\!,D^+} = 0.44\pm0.23\pm0.03pb,$$ where the first uncertainty is statistical and the second systematic.Comment: 18 pages, 2 figure

Measurement of the Bs0→J/ψηB_{s}^{0} \rightarrow J/\psi \eta 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 $B^0_s \rightarrow J/\psi \eta$ decay mode, $\tau_{\textrm{eff}}$, is measured to be $\tau_{\textrm{eff}} = 1.479 \pm 0.034~\textrm{(stat)} \pm 0.011 ~\textrm{(syst)}$ ps. Assuming $CP$ conservation, $\tau_{\textrm{eff}}$ corresponds to the lifetime of the light $B_s^0$ mass eigenstate. This is the first measurement of the effective lifetime in this decay mode.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-2016-017.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

Measurements of the B+B^+, B0B^0, Bs0B_s^0 meson and Λb0\Lambda_b^0 baryon lifetimes

Measurements of $b$-hadron lifetimes are reported using $pp$ collision data, corresponding to an integrated luminosity of 1.0fb$^{-1}$, collected by the LHCb detector at a centre-of-mass energy of $7$Tev. Using the exclusive decays $B^+\to J/\psi K^+$, $B^0\to J/\psi K^*(892)^0$, $B^0\to J/\psi K^0_{\rm S}$, $\Lambda_b^0\to J/\psi \Lambda$ and $B^0_s\to J/\psi \phi$ the average decay times in these modes are measured to be $\tau_{B^+\to J/\psi K^+}$ = $1.637 \pm$ 0.004 $\pm$ 0.003 ps, $\tau_{B^0\to J/\psi K^*(892)^0}$ = $1.524 \pm$ 0.006 $\pm$ 0.004 ps, $\tau_{B^0\to J/\psi K^0_{\rm S}}$ = $1.499 \pm$ 0.013 $\pm$ 0.005 ps, $\tau_{\Lambda_b^0\to J/\psi \Lambda}$ = $1.415 \pm$ 0.027 $\pm$ 0.006 ps and $\tau_{B^0_s\to J/\psi \phi}$ = $1.480 \pm$ 0.011 $\pm$ 0.005 ps, where the first uncertainty is statistical and the second is systematic. These represent the most precise lifetime measurements in these decay modes. In addition, ratios of these lifetimes, and the ratio of the decay-width difference, $\Delta\Gamma_d$, to the average width, $\Gamma_d$, in the $B^0$ system, $\Delta \Gamma_d/\Gamma_d = -0.044 \pm 0.025 \pm 0.011$, are reported. All quantities are found to be consistent with Standard Model expectations.Comment: 28 pages, 4 figures. Updated reference

Bose-Einstein correlations of same-sign charged pions in the forward region in pp collisions at √s=7 TeV

Bose-Einstein correlations of same-sign charged pions, produced in protonproton collisions at a 7 TeV centre-of-mass energy, are studied using a data sample collected by the LHCb experiment. The signature for Bose-Einstein correlations is observed in the form of an enhancement of pairs of like-sign charged pions with small four-momentum difference squared. The charged-particle multiplicity dependence of the Bose-Einstein correlation parameters describing the correlation strength and the size of the emitting source is investigated, determining both the correlation radius and the chaoticity parameter. The measured correlation radius is found to increase as a function of increasing charged-particle multiplicity, while the chaoticity parameter is seen to decreas