No abstract

First passage under restart has recently emerged as a conceptual framework suitable for the description of a wide range of phenomena, but the endless variety of ways in which restart mechanisms and first passage processes mix and match hindered the identification of unifying principles and general truths. Hope that these exist came from a recently discovered universality displayed by processes under optimal, constant rate, restart-but extensions and generalizations proved challenging as they marry arbitrarily complex processes and restart mechanisms. To address this challenge, we develop a generic approach to first passage under restart. Key features of diffusion under restart-the ultimate poster boy for this wide and diverse class of problems-are then shown to be completely universal.

We study a Brownian particle diffusing under a time-modulated stochastic resetting mechanism to a fixed position. The rate of resetting r(t) is a function of the time t since the last reset event. We derive a sufficient condition on r(t) for a steady-state probability distribution of the position of the particle to exist. We derive the form of the steady-state distributions under some particular choices of r(t) and also consider the late time relaxation behavior of the probability distribution. We consider first passage time properties for the Brownian particle to reach the origin and derive a formula for the mean first passage time. Finally, we study optimal properties of the mean first passage time and show that a threshold function is at least locally optimal for the problem of minimizing the mean first passage time.

We give a detailed description of the measurement of the W boson mass, MW , performed on an integrated luminosity of 4.3 fb −1 , which is based on similar techniques as used for our previous measurement done on an independent data set of 1 fb −1 of data. The data were collected using the D0 detector at the Fermilab Tevatron Collider. This data set yields 1.68 × 10 6 W → eν candidate events. We measure the mass using the transverse mass, electron transverse momentum, and missing transverse energy distributions. The MW measurements using the transverse mass and the electron transverse momentum distributions are the most precise of these three and are combined to give MW = 80.367 ± 0.013 (stat) ± 0.022 (syst) GeV = 80.367 ± 0.026 GeV. When combined with our earlier measurement on 1 fb −1 of data, we obtain MW = 80.375 ± 0.023 GeV.

We present the FP420 R&D project, which has been studying the key aspects of the development and installation of a silicon tracker and fast-timing detectors in the LHC tunnel at 420 m from the interaction points of the ATLAS and CMS experiments. These detectors would measure precisely very forward protons in conjunction with the corresponding central detectors as a means to study Standard Model (SM) physics, and to search for and characterise new physics signals. This report includes a detailed description of the physics case for the detector and, in particular, for the measurement of Central Exclusive Production, pp→p+ϕ+p, in which the outgoing protons remain intact and the central system ϕ may be a single particle such as a SM or MSSM Higgs boson. Other physics topics discussed are γγ and γp interactions, and diffractive processes. The report includes a detailed study of the trigger strategy, acceptance, reconstruction efficiencies, and expected yields for a particular pp→pHp measurement with Higgs boson decay in the bb̄ mode. The document also describes the detector acceptance as given by the LHC beam optics between the interaction points and the FP420 location, the machine backgrounds, the new proposed connection cryostat and the moving (``Hamburg'') beam-pipe at 420 m, and the radio-frequency impact of the design on the LHC. The last part of the document is devoted to a description of the 3D silicon sensors and associated tracking performances, the design of two fast-timing detectors capable of accurate vertex reconstruction for background rejection at high-luminosities, and the detector alignment and calibration strategy.