Geometric and spectral properties of causal maps

We study the random planar map obtained from a critical, finite variance, Galton-Watson plane tree by adding the horizontal connections between successive vertices at each level. This random graph is closely related to the well-known causal dynamical triangulation that was introduced by Ambj{\o}rn and Loll and has been studied extensively by physicists. We prove that the horizontal distances in the graph are smaller than the vertical distances, but only by a subpolynomial factor: The diameter of the set of vertices at level $n$ is both $o(n)$ and $n^{1-o(1)}$. This enables us to prove that the spectral dimension of the infinite version of the graph is almost surely equal to 2, and consequently that the random walk is diffusive almost surely. We also initiate an investigation of the case in which the offspring distribution is critical and belongs to the domain of attraction of an $\alpha$-stable law for $\alpha \in (1,2)$, for which our understanding is much less complete.Institut Universitaire de France, ANR Graal (ANR-14-CE25-0014), ANR Liouville (ANR-15-CE40-0013), ERC GeoBrown, ISF grant 1207/15 and ERC grant 676970 RandGeom

Prospects for K+→π+ννˉK^+ \to \pi^+ \nu \bar{ \nu } at CERN in NA62

The NA62 experiment will begin taking data in 2015. Its primary purpose is a 10% measurement of the branching ratio of the ultrarare kaon decay $K^+ \to \pi^+ \nu \bar{ \nu }$, using the decay in flight of kaons in an unseparated beam with momentum 75 GeV/c.The detector and analysis technique are described here.Comment: 8 pages for proceedings of 50 Years of CP

Performance of the LHCb vertex locator

The Vertex Locator (VELO) is a silicon microstrip detector that surrounds the proton-proton interaction region in the LHCb experiment. The performance of the detector during the first years of its physics operation is reviewed. The system is operated in vacuum, uses a bi-phase CO2 cooling system, and the sensors are moved to 7 mm from the LHC beam for physics data taking. The performance and stability of these characteristic features of the detector are described, and details of the material budget are given. The calibration of the timing and the data processing algorithms that are implemented in FPGAs are described. The system performance is fully characterised. The sensors have a signal to noise ratio of approximately 20 and a best hit resolution of 4 μm is achieved at the optimal track angle. The typical detector occupancy for minimum bias events in standard operating conditions in 2011 is around 0.5%, and the detector has less than 1% of faulty strips. The proximity of the detector to the beam means that the inner regions of the n+-on-n sensors have undergone space-charge sign inversion due to radiation damage. The VELO performance parameters that drive the experiment's physics sensitivity are also given. The track finding efficiency of the VELO is typically above 98% and the modules have been aligned to a precision of 1 μm for translations in the plane transverse to the beam. A primary vertex resolution of 13 μm in the transverse plane and 71 μm along the beam axis is achieved for vertices with 25 tracks. An impact parameter resolution of less than 35 μm is achieved for particles with transverse momentum greater than 1 GeV/c

Precision luminosity measurements at LHCb

Measuring cross-sections at the LHC requires the luminosity to be determined accurately at each centre-of-mass energy √s. In this paper results are reported from the luminosity calibrations carried out at the LHC interaction point 8 with the LHCb detector for √s = 2.76, 7 and 8 TeV (proton-proton collisions) and for √sNN = 5 TeV (proton-lead collisions). Both the "van der Meer scan" and "beam-gas imaging" luminosity calibration methods were employed. It is observed that the beam density profile cannot always be described by a function that is factorizable in the two transverse coordinates. The introduction of a two-dimensional description of the beams improves significantly the consistency of the results. For proton-proton interactions at √s = 8 TeV a relative precision of the luminosity calibration of 1.47% is obtained using van der Meer scans and 1.43% using beam-gas imaging, resulting in a combined precision of 1.12%. Applying the calibration to the full data set determines the luminosity with a precision of 1.16%. This represents the most precise luminosity measurement achieved so far at a bunched-beam hadron collider

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

Differential branching fraction and angular analysis of the decay B0→K∗0μ+μ−

The angular distribution and differential branching fraction of the decay B 0→ K ∗0 μ + μ − are studied using a data sample, collected by the LHCb experiment in pp collisions at s√=7 TeV, corresponding to an integrated luminosity of 1.0 fb−1. Several angular observables are measured in bins of the dimuon invariant mass squared, q 2. A first measurement of the zero-crossing point of the forward-backward asymmetry of the dimuon system is also presented. The zero-crossing point is measured to be q20=4.9±0.9GeV2/c4 , where the uncertainty is the sum of statistical and systematic uncertainties. The results are consistent with the Standard Model predictions

Opposite-side flavour tagging of B mesons at the LHCb experiment

The calibration and performance of the oppositeside flavour tagging algorithms used for the measurements of time-dependent asymmetries at the LHCb experiment are described. The algorithms have been developed using simulated events and optimized and calibrated with B + →J/ψK +, B0 →J/ψK ∗0 and B0 →D ∗− μ + νμ decay modes with 0.37 fb−1 of data collected in pp collisions at √ s = 7 TeV during the 2011 physics run. The oppositeside tagging power is determined in the B + → J/ψK + channel to be (2.10 ± 0.08 ± 0.24) %, where the first uncertainty is statistical and the second is systematic

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