Approximate N3^{3}LO Parton Distribution Functions with Theoretical Uncertainties: MSHT20aN3^3LO PDFs

We present the first global analysis of parton distribution functions (PDFs) at approximate N$^{3}$LO in the strong coupling constant $\alpha_{s}$, extending beyond the current highest NNLO achieved in PDF fits. To achieve this, we present a general formalism for the inclusion of theoretical uncertainties from missing higher orders (MHOs) into a PDF fit. We demonstrate how using the currently available knowledge surrounding the next highest order (N$^{3}$LO) in $\alpha_{s}$ can provide consistent, justifiable and explainable approximate N$^{3}$LO (aN$^{3}$LO) PDFs, including estimates for missing higher order uncertainties (MHOUs). Specifically, we approximate the splitting functions, transition matrix elements, coefficient functions and $K$-factors for multiple processes to N$^{3}$LO. Crucially, these are constrained to be consistent with the wide range of already available information about N$^{3}$LO to match the complete result at this order as accurately as possible. Using this approach we perform a fully consistent approximate N$^{3}$LO global fit within the MSHT framework. This relies on an expansion of the Hessian procedure used in previous MSHT fits to allow for sources of theoretical uncertainties. These are included as nuisance parameters in a global fit, controlled by knowledge and intuition based prior distributions. We analyse the differences between our aN$^{3}$LO PDFs and the standard NNLO PDF set, and study the impact of using aN$^{3}$LO PDFs on the LHC production of a Higgs boson at this order. Finally, we provide guidelines on how these PDFs should be be used in phenomenological investigations.Comment: 150 pages, 48 figures, 20 tables. Updated LHAPDF Grids available which include a correction of a minor bug in the non-singlet splitting function leading to very small changes in fit quality and PDFs, but with no significant changes to any results or conclusion

Signal specific electric potential sensors for operation in noisy environments

Limitations on the performance of electric potential sensors are due to saturation caused by environmental electromagnetic noise. The work described involves tailoring the response of the sensors to reject the main components of the noise, thereby enhancing both the effective dynamic range and signal to noise. We show that by using real-time analogue signal processing it is possible to detect a human heartbeat at a distance of 40 cm from the front of a subject in an unshielded laboratory. This result has significant implications both for security sensing and biometric measurements in addition to the more obvious safety related applications

Updates of PDFs using the MMHT framework

We summarise recent developments in the path towards the "MMHT19" parton distribution functions. We concentrate on the extraction of the strange quark upon the improvement of theoretical calculations for NNLO charged current cross sections; the effect of an extension of our parameterisation; and the role of correlated uncertainties in some data sets which prove difficult to fit

Signatures of chaotic and non-chaotic-like behaviour in a non-linear quantum oscillator through photon detection

The driven non-linear duffing osillator is a very good, and standard, example of a quantum mechanical system from which classical-like orbits can be recovered from unravellings of the master equation. In order to generated such trajectories in the phase space of this oscillator in this paper we use a the quantum jumps unravelling together with a suitable application of the correspondence principle. We analyse the measured readout by considering the power spectra of photon counts produced by the quantum jumps. Here we show that localisation of the wave packet from the measurement of the oscillator by the photon detector produces a concomitant structure in the power spectra of the measured output. Furthermore, we demonstrate that this spectral analysis can be used to distinguish between different modes of the underlying dynamics of the oscillator.Comment: 7 pages, 6 figure

Caesium on Si(100) Studied by Biassed Secondary Electron Microscopy

An ultra-high vacuum scanning electron microscope (UHV-SEM) has been used to study sub-monolayers of Cs on Si(100) surface. Cs adsorption on the surface causes a considerable change in the work function. Coverages below 1/2 monolayer (ML) have been estimated by correlating the work function changes with the secondary electron (SE) signal. It has been found that this signal is sensitive down to ~ 0.005 ML when the sample is biassed to a few hundred volts. Electron trajectories from a biassed sample have been simulated for electrons originating from different areas with different work functions across the sample. This indicates that variations in coverage can be determined by secondary electron imaging provided these coverages are less than 1/2 ML. The diffusion of Cs (\u3c 1/2 ML) above room temperature has been studied using the biassed-SE imaging technique. Observed diffusion profiles have unusual features including two linear regions. These can be explained by a model which contains two competing adsorption sites, and includes blocking of the diffusion paths by other Cs atoms

Energy Down Conversion between Classical Electromagnetic Fields via a Quantum Mechanical SQUID Ring

We consider the interaction of a quantum mechanical SQUID ring with a classical resonator (a parallel $LC$ tank circuit). In our model we assume that the evolution of the ring maintains its quantum mechanical nature, even though the circuit to which it is coupled is treated classically. We show that when the SQUID ring is driven by a classical monochromatic microwave source, energy can be transferred between this input and the tank circuit, even when the frequency ratio between them is very large. Essentially, these calculations deal with the coupling between a single macroscopic quantum object (the SQUID ring) and a classical circuit measurement device where due account is taken of the non-perturbative behaviour of the ring and the concomitant non-linear interaction of the ring with this device.Comment: 7 pages, 6 figure

Instantons and Killing spinors

We investigate instantons on manifolds with Killing spinors and their cones. Examples of manifolds with Killing spinors include nearly Kaehler 6-manifolds, nearly parallel G_2-manifolds in dimension 7, Sasaki-Einstein manifolds, and 3-Sasakian manifolds. We construct a connection on the tangent bundle over these manifolds which solves the instanton equation, and also show that the instanton equation implies the Yang-Mills equation, despite the presence of torsion. We then construct instantons on the cones over these manifolds, and lift them to solutions of heterotic supergravity. Amongst our solutions are new instantons on even-dimensional Euclidean spaces, as well as the well-known BPST, quaternionic and octonionic instantons.Comment: 40 pages, 2 figures v2: author email addresses and affiliations adde