Densities of short uniform random walks

We study the densities of uniform random walks in the plane. A special focus is on the case of short walks with three or four steps and less completely those with five steps. As one of the main results, we obtain a hypergeometric representation of the density for four steps, which complements the classical elliptic representation in the case of three steps. It appears unrealistic to expect similar results for more than five steps. New results are also presented concerning the moments of uniform random walks and, in particular, their derivatives. Relations with Mahler measures are discussed.Comment: 32 pages, 9 figure

A diffuse scattering model of ultracold neutrons on wavy surfaces

Metal tubes plated with nickel-phosphorus are used in many fundamental physics experiments using ultracold neutrons (UCN) because of their ease of fabrication. These tubes are usually polished to a average roughness of 25-150 nm. However, there is no scattering model that accurately describes UCN scattering on such a rough guide surface with a mean-square roughness larger than 5 nm. We therefore developed a scattering model for UCN in which scattering from random surface waviness with a size larger than the UCN wavelength is described by a microfacet Bidirectional Reflectance Distribution Function model (mf-BRDF model), and scattering from smaller structures by the Lambert's cosine law (Lambert model). For the surface waviness, we used the statistical distribution of surface slope measured by an atomic force microscope on a sample piece of guide tube as input of the model. This model was used to describe UCN transmission experiments conducted at the pulsed UCN source at J-PARC. In these experiments, a UCN beam collimated to a divergence angle smaller than $\pm 6^{\circ}$ was directed into a guide tube with a mean-square roughness of 6.4 nm to 17 nm at an oblique angle, and the UCN transport performance and its time-of-flight distribution were measured while changing the angle of incidence. The mf-BRDF model combined with the Lambert model with scattering probability $p_{L} = 0.039\pm0.003$ reproduced the experimental results well. We have thus established a procedure to evaluate the characteristics of UCN guide tubes with a surface roughness of approximately 10 nm.Comment: 15 pages, 11 figure

Measuring the frequency of a Sr optical lattice clock using a 120-km coherent optical transfer

We demonstrate a precision frequency measurement using a phase-stabilized 120-km optical fiber link over a physical distance of 50 km. The transition frequency of the 87Sr optical lattice clock at the University of Tokyo is measured to be 429228004229874.1(2.4) Hz referenced to international atomic time (TAI). The measured frequency agrees with results obtained in Boulder and Paris at a 6*10^-16 fractional level, which matches the current best evaluations of Cs primary frequency standards. The results demonstrate the excellent functions of the intercity optical fibre link, and the great potential of optical lattice clocks for use in the redefinition of the second.Comment: 14 pages, 3 figure

Z boson production in Pb+Pb collisions at √Snn = 5.02 TeV measured by the ATLAS experiment

The production yield of Z bosons is measured in the electron and muon decay channels in Pb+Pb collisions at √S = 5.02 TeV with the ATLAS detector. Data from the 2015 LHC run corresponding to an integrated luminosity of 0.49 nb are used for the analysis. The Z boson yield, normalised by the total number of minimum-bias events and the mean nuclear thickness function, is measured as a function of dilepton rapidity and event centrality. The measurements in Pb+Pb collisions are compared with similar measurements made in proton-proton collisions at the same centre-of-mass energy. The nuclear modification factor is found to be consistent with unity for all centrality intervals. The results are compared with theoretical predictions obtained at next-to-leading order using nucleon and nuclear parton distribution functions. The normalised Z boson yields in Pb+Pb collisions lie 1-3σ above the predictions. The nuclear modification factor measured as a function of rapidity agrees with unity and is consistent with a next-to-leading-order QCD calculation including the isospin effect. nn -

Measurement of J/ψ production in association with a W ± boson with pp data at 8 TeV

A measurement of the production of a prompt J/ψ meson in association with a W± boson with W± → μν and J/ψ → μ+μ− is presented for J/ψ transverse momenta in the range 8.5–150 GeV and rapidity |yJ/ψ| < 2.1 using ATLAS data recorded in 2012 at the LHC. The data were taken at a proton-proton centre-of-mass energy of s = 8 TeV and correspond to an integrated luminosity of 20.3 fb−1. The ratio of the prompt J/ψ plus W± cross-section to the inclusive W± cross-section is presented as a differential measurement as a function of J/ψ transverse momenta and compared with theoretical predictions using different double-parton-scattering cross-sections. [Figure not available: see fulltext.]

Measurement of Azimuthal Anisotropy of Muons from Charm and Bottom Hadrons in pp Collisions at sqrt[s]=13 TeV with the ATLAS Detector.

The elliptic flow of muons from the decay of charm and bottom hadrons is measured in pp collisions at sqrt[s]=13  TeV using a data sample with an integrated luminosity of 150  pb^{-1} recorded by the ATLAS detector at the LHC. The muons from heavy-flavor decay are separated from light-hadron decay muons using momentum imbalance between the tracking and muon spectrometers. The heavy-flavor decay muons are further separated into those from charm decay and those from bottom decay using the distance-of-closest-approach to the collision vertex. The measurement is performed for muons in the transverse momentum range 4-7 GeV and pseudorapidity range |η|<2.4. A significant nonzero elliptic anisotropy coefficient v_{2} is observed for muons from charm decays, while the v_{2} value for muons from bottom decays is consistent with zero within uncertainties

Search for flavour-changing neutral currents in processes with one top quark and a photon using 81 fb−1 of pp collisions at s=13TeV with the ATLAS experiment

A search for flavour-changing neutral current (FCNC) events via the coupling of a top quark, a photon, and an up or charm quark is presented using 81 fb−1 of proton–proton collision data taken at a centre-of-mass energy of 13 TeV with the ATLAS detector at the LHC. Events with a photon, an electron or muon, a b-tagged jet, and missing transverse momentum are selected. A neural network based on kinematic variables differentiates between events from signal and background processes. The data are consistent with the background-only hypothesis, and limits are set on the strength of the tqγ coupling in an effective field theory. These are also interpreted as 95% CL upper limits on the cross section for FCNC tγ production via a left-handed (right-handed) tuγ coupling of 36 fb (78 fb) and on the branching ratio for t→γu of 2.8×10−5 (6.1×10−5). In addition, they are interpreted as 95% CL upper limits on the cross section for FCNC tγ production via a left-handed (right-handed) tcγ coupling of 40 fb (33 fb) and on the branching ratio for t→γc of 22×10−5 (18×10−5)