Pseudospectral Calculation of the Wavefunction of Helium and the Negative Hydrogen Ion

We study the numerical solution of the non-relativistic Schr\"{o}dinger equation for two-electron atoms in ground and excited S-states using pseudospectral (PS) methods of calculation. The calculation achieves convergence rates for the energy, Cauchy error in the wavefunction, and variance in local energy that are exponentially fast for all practical purposes. The method requires three separate subdomains to handle the wavefunction's cusp-like behavior near the two-particle coalescences. The use of three subdomains is essential to maintaining exponential convergence. A comparison of several different treatments of the cusps and the semi-infinite domain suggest that the simplest prescription is sufficient. For many purposes it proves unnecessary to handle the logarithmic behavior near the three-particle coalescence in a special way. The PS method has many virtues: no explicit assumptions need be made about the asymptotic behavior of the wavefunction near cusps or at large distances, the local energy is exactly equal to the calculated global energy at all collocation points, local errors go down everywhere with increasing resolution, the effective basis using Chebyshev polynomials is complete and simple, and the method is easily extensible to other bound states. This study serves as a proof-of-principle of the method for more general two- and possibly three-electron applications.Comment: 23 pages, 20 figures, 2 tables, Final refereed version - Some references added, some stylistic changes, added paragraph to matrix methods section, added last sentence to abstract

Lie families: theory and applications

We analyze families of non-autonomous systems of first-order ordinary differential equations admitting a common time-dependent superposition rule, i.e., a time-dependent map expressing any solution of each of these systems in terms of a generic set of particular solutions of the system and some constants. We next study relations of these families, called Lie families, with the theory of Lie and quasi-Lie systems and apply our theory to provide common time-dependent superposition rules for certain Lie families.Comment: 23 pages, revised version to appear in J. Phys. A: Math. Theo

Observation of an Excited Bc+ State

Using pp collision data corresponding to an integrated luminosity of 8.5 fb-1 recorded by the LHCb experiment at center-of-mass energies of s=7, 8, and 13 TeV, the observation of an excited Bc+ state in the Bc+π+π- invariant-mass spectrum is reported. The observed peak has a mass of 6841.2±0.6(stat)±0.1(syst)±0.8(Bc+) MeV/c2, where the last uncertainty is due to the limited knowledge of the Bc+ mass. It is consistent with expectations of the Bc∗(2S31)+ state reconstructed without the low-energy photon from the Bc∗(1S31)+→Bc+γ decay following Bc∗(2S31)+→Bc∗(1S31)+π+π-. A second state is seen with a global (local) statistical significance of 2.2σ (3.2σ) and a mass of 6872.1±1.3(stat)±0.1(syst)±0.8(Bc+) MeV/c2, and is consistent with the Bc(2S10)+ state. These mass measurements are the most precise to date

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

Measurement of the inelastic pp cross-section at a centre-of-mass energy of 13TeV

The cross-section for inelastic proton-proton collisions at a centre-of-mass energy of 13TeV is measured with the LHCb detector. The fiducial cross-section for inelastic interactions producing at least one prompt long-lived charged particle with momentum p > 2 GeV/c in the pseudorapidity range 2 < η < 5 is determined to be ϭ acc = 62:2 ± 0:2 ± 2:5mb. The first uncertainty is the intrinsic systematic uncertainty of the measurement, the second is due to the uncertainty on the integrated luminosity. The statistical uncertainty is negligible. Extrapolation to full phase space yields the total inelastic proton-proton cross-section ϭ inel = 75:4 ± 3:0 ± 4:5mb, where the first uncertainty is experimental and the second due to the extrapolation. An updated value of the inelastic cross-section at a centre-of-mass energy of 7TeV is also reported

Observation of the Decay Λ0b→Λ+cτ−¯ν

The first observation of the semileptonic b-baryon decay Λb0→Λc+τ-ν¯τ, with a significance of 6.1σ, is reported using a data sample corresponding to 3 fb-1 of integrated luminosity, collected by the LHCb experiment at center-of-mass energies of 7 and 8 TeV at the LHC. The τ- lepton is reconstructed in the hadronic decay to three charged pions. The ratio K=B(Λb0→Λc+τ-ν¯τ)/B(Λb0→Λc+π-π+π-) is measured to be 2.46±0.27±0.40, where the first uncertainty is statistical and the second systematic. The branching fraction B(Λb0→Λc+τ-ν¯τ)=(1.50±0.16±0.25±0.23)% is obtained, where the third uncertainty is from the external branching fraction of the normalization channel Λb0→Λc+π-π+π-. The ratio of semileptonic branching fractions R(Λc+)B(Λb0→Λc+τ-ν¯τ)/B(Λb0→Λc+μ-ν¯μ) is derived to be 0.242±0.026±0.040±0.059, where the external branching fraction uncertainty from the channel Λb0→Λc+μ-ν¯μ contributes to the last term. This result is in agreement with the standard model prediction

Updated Determination of D⁰–D¯⁰Mixing and CP Violation Parameters with D⁰→K⁺π⁻ Decays

We report measurements of charm-mixing parameters based on the decay-time-dependent ratio of D⁰→K⁺π⁻ to D⁰→K⁻π⁺ rates. The analysis uses a data sample of proton-proton collisions corresponding to an integrated luminosity of 5.0  fb⁻¹ recorded by the LHCb experiment from 2011 through 2016. Assuming charge-parity (CP) symmetry, the mixing parameters are determined to be x′²=(3.9±2.7)×10⁻⁵, y′=(5.28±0.52)×10⁻³, and R[subscript D]=(3.454±0.031)×10⁻³. Without this assumption, the measurement is performed separately for D⁰ and D[over ¯]⁰ mesons, yielding a direct CP-violating asymmetry A[subscript D]=(-0.1±9.1)×10⁻³, and magnitude of the ratio of mixing parameters 1.00<|q/p|<1.35 at the 68.3% confidence level. All results include statistical and systematic uncertainties and improve significantly upon previous single-measurement determinations. No evidence for CP violation in charm mixing is observed

Observation of D⁰ Meson Decays to Π⁺π⁻μ⁺μ⁻ and K⁺K⁻μ⁺μ⁻ Final States

The first observation of the D⁰→π⁺π⁻μ⁺μ⁻ and D⁰→K⁺K⁻μ⁺μ⁻ decays is reported using a sample of proton-proton collisions collected by LHCb at a center-of-mass energy of 8 TeV, and corresponding to 2  fb⁻¹ of integrated luminosity. The corresponding branching fractions are measured using as normalization the decay D⁰→K⁻π⁺[μ⁺μ⁻][subscript ρ⁰/ω], where the two muons are consistent with coming from the decay of a ρ⁰ or ω meson. The results are B(D⁰→π⁺π⁻μ⁺μ⁻)=(9.64±0.48±0.51±0.97)×10⁻⁷ and B(D⁰→K⁺K⁻μ⁺μ⁻)=(1.54±0.27±0.09±0.16)×10⁻⁷, where the uncertainties are statistical, systematic, and due to the limited knowledge of the normalization branching fraction. The dependence of the branching fraction on the dimuon mass is also investigated

Precision measurement of the Ξcc++Ξcc++ {\varXi}_{cc}^{++} mass

A measurement of the Ξ++cc mass is performed using data collected by the LHCb experiment between 2016 and 2018 in pp collisions at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 5.6 fb−1. The Ξ++cc candidates are reconstructed via the decay modes Ξ++cc→Λ+cK−π+π+ and Ξ++cc→Ξ+cπ+. The result, 3621.55 ± 0.23 (stat) ± 0.30 (syst) MeV/c2, is the most precise measurement of the Ξ++cc mass to date

Searches for rare Bs0 and B 0 decays into four muons

Searches for rare Bs0 and B0 decays into four muons are performed using proton-proton collision data recorded by the LHCb experiment, corresponding to an integrated luminosity of 9 fb−1. Direct decays and decays via light scalar and J/ψ resonances are considered. No evidence for the six decays searched for is found and upper limits at the 95% confidence level on their branching fractions ranging between 1.8 × 10−10 and 2.6 × 10−9 are set. [Figure not available: see fulltext.