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We introduce our novel Bayesian parton density determination code, PartonDensity.jl. The motivation for this new code, the framework and its validation are described. As we show, PartonDensity.jl provides both a flexible environment for the determination of parton densities and a wealth of information concerning the knowledge update provided by the analyzed data set., Comment: Accepted version. Code available here: https://github.com/cescalara/PartonDensity.jl

A Higgs Factory is considered the highest priority next collider project by the high-energy physics community. Very advanced designs based on radio-frequency cavities exist, and variations on this approach are still being developed. Recently, an option based on electron-bunch driven plasma wakefield acceleration has also been proposed. In this article, we discuss a further option based on proton-driven plasma wakefield acceleration. This option has significant potential advantages due to the high energy of the plasma wakefield driver, simplifying the plasma acceleration stage. Its success will depend on further developments in producing compact high-energy proton bunches at a high rate, which would also make possible a broad range of synergistic particle-physics research., Comment: 11 pages, 3 figures

We describe a novel reconstruction algorithm for time-resolved images obtained using a streak camera. This algorithm operates by decomposing a recorded image into a set of individual photoelectron-induced signals, thereby providing a powerful method for streak camera image reconstruction. This deconstruction allows for a standard statistical analysis of the resulting image. We demonstrate the effectiveness of this technique by analyzing the temporal spacing between the emitted fs-long laser pulse and its succeeding first, second, and third reflections within a thick glass captured by a streak image., Comment: 18 pages, 12 Figures, 1 table, 1 algorithm block

Finding upper limits on the rate of events from a proposed process in the presence of unknown backgrounds is an often encountered problem in the search for rare processes. Methods based on unusually large "gaps", or spacings, in the event distribution allow to set limits on the rate of the proposed signal distribution. In this paper, we present two novel spacings-based methods: the "Sum of sorted spacings" and the "Product of complementary spacings" as tests and compare these to existing tests on synthetic data as well as on a published data set.

Goodness-of-fit tests are often used in data analysis to test the agreement of a distribution to a set of data. These tests can be used to detect an unknown signal against a known background or to set limits on a proposed signal distribution in experiments contaminated by poorly understood backgrounds. Out-of-the-box non-parametric tests that can target any proposed distribution are only available in the univariate case. In this paper, we discuss how to build goodness-of-fit tests for arbitrary multivariate distributions or multivariate data generation models.

The high-$x$ data from the ZEUS Collaboration are used to extract parton density distributions of the proton deep in the perturbative regime of QCD. The data primarily constrain the up-quark valence distribution and new results are presented on its $x$-dependence as well as on the momentum carried by the up-quark. The results were obtained using Bayesian analysis methods which can serve as a model for future parton density extractions., Comment: Minor changes in final published version

We evaluate the discovery probability of a combined analysis of proposed neutrinoless double-beta decay experiments in a scenario with normal ordered neutrino masses. The discovery probability strongly depends on the value of the lightest neutrino mass, ranging from zero in case of vanishing masses and up to 80-90\% for values just below the current constraints. We study the discovery probability in different scenarios, focusing on the exciting prospect in which cosmological surveys will measure the sum of neutrino masses. Uncertainties in nuclear matrix element calculations partially compensate each other when data from different isotopes are available. Although a discovery is not granted, the theoretical motivations for these searches and the presence of scenarios with high discovery probability strongly motivates the proposed international, multi-isotope experimental program.

Plasma wakefield acceleration is a promising technology to reduce the size of particle accelerators. Use of high energy protons to drive wakefields in plasma has been demonstrated during Run 1 of the AWAKE programme at CERN. Protons of energy 400 GeV drove wakefields that accelerated electrons to 2 GeV in under 10 m of plasma. The AWAKE collaboration is now embarking on Run 2 with the main aims to demonstrate stable accelerating gradients of 0.5-1 GV/m, preserve emittance of the electron bunches during acceleration and develop plasma sources scalable to 100s of metres and beyond. By the end of Run 2, the AWAKE scheme should be able to provide electron beams for particle physics experiments and several possible experiments have already been evaluated. This article summarises the programme of AWAKE Run 2 and how it will be achieved as well as the possible application of the AWAKE scheme to novel particle physics experiments., Comment: 21 pages, 8 figures. Submitted to Symmetry journal

In this paper we present a technique to reconstruct the scaling variables defining $ep$ deep inelastic scattering by performing a kinematic fit. This reconstruction technique makes use of the full potential of the data collected. It is based on Bayes Theorem and involves the use of informative priors. The kinematic fit method has been tested for the neutral current ep simulated sample at a center of mass energy of 318 GeV with $Q^2$ > 400 GeV$^2$. In addition to the scaling variables, this method is able to estimate the energy of possible initial state radiation (E$_\gamma$ ) which otherwise goes undetected. A better resolution than standard electron and double angle techniques in the reconstruction of scaling variables is achieved using a kinematic fit., Comment: 17 pages, 12 figures, revised version of paper

We describe the development of a multi-purpose software for Bayesian statistical inference, BAT.jl, written in the Julia language. The major design considerations and implemented algorithms are summarized here, together with a test suite that ensures the proper functioning of the algorithms. We also give an extended example from the realm of physics that demonstrates the functionalities of BAT.jl.

Efficient sampling of many-dimensional and multimodal density functions is a task of great interest in many research fields. We describe an algorithm that allows parallelizing inherently serial Markov chain Monte Carlo (MCMC) sampling by partitioning the space of the function parameters into multiple subspaces and sampling each of them independently. The samples of the different subspaces are then reweighted by their integral values and stitched back together. This approach allows reducing sampling wall-clock time by parallel operation. It also improves sampling of multimodal target densities and results in less correlated samples. Finally, the approach yields an estimate of the integral of the target density function.

We provide the analytic forms of the distributions for the sum of ordered spacings. We do this both for the case where the boundaries are included in the calculation of the spacings and the case where they are excluded. Both the probability densities as well as their cumulatives are provided. These results will have useful applications in the physical sciences and possibly elsewhere.

There are many hard-to-reconcile numbers circulating concerning Covid-19. Using reports from random testing, the fatality ratio per infection is evaluated and used to extract further information on the actual fraction of infections and the success of their identification for different countries.

The GERmanium Detector Array (GERDA) experiment at the Gran Sasso underground laboratory (LNGS) of INFN is searching for neutrinoless double-beta ($0\nu\beta\beta$) decay of $^{76}$Ge. The technological challenge of GERDA is to operate in a "background-free" regime in the region of interest (ROI) after analysis cuts for the full 100$\,$kg$\cdot$yr target exposure of the experiment. A careful modeling and decomposition of the full-range energy spectrum is essential to predict the shape and composition of events in the ROI around $Q_{\beta\beta}$ for the $0\nu\beta\beta$ search, to extract a precise measurement of the half-life of the double-beta decay mode with neutrinos ($2\nu\beta\beta$) and in order to identify the location of residual impurities. The latter will permit future experiments to build strategies in order to further lower the background and achieve even better sensitivities. In this article the background decomposition prior to analysis cuts is presented for GERDA Phase II. The background model fit yields a flat spectrum in the ROI with a background index (BI) of $16.04^{+0.78}_{-0.85} \cdot 10^{-3}\,$cts/(kg$\cdot$keV$\cdot$yr) for the enriched BEGe data set and $14.68^{+0.47}_{-0.52} \cdot 10^{-3}\,$cts/(kg$\cdot$keV$\cdot$yr) for the enriched coaxial data set. These values are similar to the one of Gerda Phase I despite a much larger number of detectors and hence radioactive hardware components.

Initial simulations investigating using the RHIC-EIC proton beam as the drive beam in a plasma wakefield acceleration experiment are presented. The proton beam enters the plasma and undergoes self-modulation, forming a series of microbunches. These microbunches resonantly drive electron density perturbations within the plasma, exciting a longitudinal electric field with accelerating gradients in excess of $\mathrm{GVm^{-1}}$. Injecting electrons into the resulting wakefield offers an efficient method for accelerating electron bunches for use in the proposed EIC collider., Comment: 6 pages, 3 figures, submitted as proceedings for the XXVII International Workshop on Deep-Inelastic Scattering and Related Subjects (DIS2019)

A number of experiments are currently underway on antimatter, particularly anti-hydrogen, to test whether the fundamental interactions behave the same way as for matter. Here we present a simple argument showing that a bound on a difference in gravitational forces exerted on matter and antimatter is already so severe that is goes well beyond the sensitivity of the above measurements.

Proton-driven plasma wakefield acceleration allows the transfer of energy from a proton bunch to a trailing bunch of particles, the `witness' particles, via plasma electrons. The AWAKE experiment at CERN is pursuing a demonstration of this scheme using bunches of protons from the CERN SPS. Assuming continued success of the AWAKE program, high energy electron or muon beams will become available, opening up an extensive array of future particle physics projects from beam dump searches for new weakly interacting particles such as Dark Photons, to fixed target physics programs, to energy frontier electron-proton, electron-ion, electron-positron and muon colliders. The time is right for the particle physics community to offer strong support to the pursuit of this new technology as it will open up new avenues for high energy particle physics.

The diverse community of scientists involved in Deep Inelastic Scattering includes about 2000 experimental and theoretical physicists worldwide and envisages projects such as the EIC, LHeC, FCC-eh and VHEeP as future lepton-hadron scattering facilities. The proposed facilities will address fundamental questions in strong interaction / QCD physics, including a first-ever tomographic mapping of the hadrons' internal structure, a solution to the proton mass and spin problems, understanding of the high-energy structure of hadronic matter and insight into connections between gravity and the strong interactions. They also extend and enhance the CERN programme of searches for new physics at the energy frontier, through a standalone precision Higgs and top programme, considerable sensitivity to the direct production of new particles and the most precise determinations of proton and nuclear structure in the kinematic range that is relevant to the LHC. In particular, we highlight the complementary aspects of the different lepton-hadron projects, and underscore how all are required to provide a complete characterization of the physics across the full kinematic reach. This review of the proposed facilities and their vast potential for particle physics was inspired by the discussions in the 2018 "DIS and Related Subjects" Workshop., Comment: 15 pages, 7 figures, EPPSU Strategy Document #103

Numerically estimating the integral of functions in high dimensional spaces is a non-trivial task. A oft-encountered example is the calculation of the marginal likelihood in Bayesian inference, in a context where a sampling algorithm such as a Markov Chain Monte Carlo provides samples of the function. We present an Adaptive Harmonic Mean Integration (AHMI) algorithm. Given samples drawn according to a probability distribution proportional to the function, the algorithm will estimate the integral of the function and the uncertainty of the estimate by applying a harmonic mean estimator to adaptively chosen regions of the parameter space. We describe the algorithm and its mathematical properties, and report the results using it on multiple test cases.

The AWAKE experiment requires an automated online rubidium (Rb) plasma density and gradient diagnostic for densities between 1 and 10$\cdot$10$^{14}$ cm$^{-3}$. A linear density gradient along the plasma source at the percent level may be useful to improve the electron acceleration process. Because of full laser ionization of Rb vapor to Rb$^{+}$ within a radius of 1 mm, the plasma density equals the vapor density. We measure the Rb vapor densities at both ends of the source, with high precision using, white light interferometry. At either source end, broadband laser light passes a remotely controlled Mach-Zehnder interferometer built out of single mode fibers. The resulting interference signal, influenced by dispersion in the vicinity of the Rb D1 and D2 transitions, is dispersed in wavelength by a spectrograph. Fully automated Fourier-based signal conditioning and a fit algorithm yield the density with an uncertainty between the measurements at both ends of 0.11 to 0.46 $\%$ over the entire density range. These densities used to operate the plasma source are displayed live in the control room., Comment: 5 pages, 8 figures, EAAC2017 conference proceeding

Many experiments in physics involve searching for a localized excess over background expectations in an observed spectrum. If the background is known and there is Gaussian noise, the amount of excess of successive observations can be quantified by the runs statistic taking care of the look-elsewhere effect. The distribution of the runs statistic under the background model is known analytically but the computation becomes too expensive for more than about a hundred observations. This work demonstrates a principled high-precision extrapolation from a few dozen up to millions of data points. It is most precise in the interesting regime when an excess is present. The method is verified for benchmark cases and successfully applied to real data from an axion search. The code that implements our method is available at https://github.com/fredRos/runs ., Comment: 18 pages, 8 figures. v2 fixes arxiv's parsing of the URL in the abstract

We perform a global Bayesian analysis of currently available neutrino data, putting data from oscillation experiments, neutrinoless double beta decay ($0\nu\beta\beta$), and precision cosmology on an equal footing. We evaluate the discovery potential of future $0\nu\beta\beta$ experiments and the Bayes factor of the two possible neutrino mass ordering schemes for different prior choices. We show that the indication for normal ordering is still very mild and does not strongly depend on realistic prior assumptions or different combinations of cosmological data sets. We find a wide range for $0\nu\beta\beta$ discovery potential, depending on the absolute neutrino mass scale, mass ordering and achievable background level., Comment: 17 pages, 10 figures

We propose a new strategy to search for dark matter axions in the mass range of 40--400 $\mu$eV by introducing dielectric haloscopes, which consist of dielectric disks placed in a magnetic field. The changing dielectric media cause discontinuities in the axion-induced electric field, leading to the generation of propagating electromagnetic waves to satisfy the continuity requirements at the interfaces. Large-area disks with adjustable distances boost the microwave signal (10--100 GHz) to an observable level and allow one to scan over a broad axion mass range. A sensitivity to QCD axion models is conceivable with 80 disks of 1 m$^2$ area contained in a $10$ Tesla field., Comment: 6 pages, 3 figures. v2: minor changes to align with published version

Assuming the form $\sigma^{\gamma P} \propto l^{\lambda_{\rm eff}}$ at fixed $Q^2$ for the behavior of the virtual-photon proton scattering cross section, where $l$ is the coherence length of the photon fluctuations, it is seen that the extrapolated values of $\sigma^{\gamma P}$ for different $Q^2$ cross for $l\approx 10^8$~fm. It is argued that this behavior is not physical, and that the behavior of the cross sections must change before this coherence length $l$ is reached. This could set the scale for the onset of saturation of parton densities.

Based on current CERN infrastructure, an electron-proton collider is proposed at a centre-of-mass energy of about 9 TeV. A 7 TeV LHC bunch is used as the proton driver to create a plasma wakefield which then accelerates electrons to 3 TeV, these then colliding with the other 7 TeV LHC proton beam. The basic parameters of the collider are presented, which although of very high energy, has integrated luminosities of the order of 1 pb$^{-1}$/year. For such a collider, with a centre-of-mass energy 30 times greater than HERA, parton momentum fractions, $x$, down to about $10^{-8}$ are accessible for $Q^2$ of 1 GeV$^2$ and could lead to effects of saturation or some other breakdown of DGLAP being observed. The total photon-proton cross section can be measured up to very high energies and also at different energies as the possibility of varying the electron beam energy is assumed; this could have synergy with cosmic-ray physics. Other physics which can be pursued at such a collider are contact interaction searches, such as quark and electron substructure, and measurements of the proton structure as well as other more conventional measurements of QCD at high energies and in a new kinematic regime. The events at very low $x$ will lead to electrons and the hadronic final state produced at very low angles and so a novel spectrometer device will be needed to measure these. First ideas of the physics programme of such a collider are given., Comment: 7 pages, 4 figures, presented at the DIS 2015 Workshop, Dallas

Techniques for evaluating the normalization integral of the target density for Markov Chain Monte Carlo algorithms are described and tested numerically. It is assumed that the Markov Chain algorithm has converged to the target distribution and produced a set of samples from the density. These are used to evaluate sample mean, harmonic mean and Laplace algorithms for the calculation of the integral of the target density. A clear preference for the sample mean algorithm applied to a reduced support region is found, and guidelines are given for implementation.

Adaptive importance sampling is a powerful tool to sample from complicated target densities, but its success depends sensitively on the initial proposal density. An algorithm is presented to automatically perform the initialization using Markov chains and hierarchical clustering. The performance is checked on challenging multimodal examples in up to 20 dimensions and compared to results from nested sampling. Our approach yields a proposal that leads to rapid convergence and accurate estimation of overall normalization and marginal distributions., Comment: 17 pages, 4 figures

Recent simulation shows that a self-modulated high energy proton bunch can excite a large amplitude plasma wakefield and accelerate an externally injected electron bunch to the energy frontier in a single stage acceleration through a long plasma channel. Based on this scheme, future colliders, either an electron-positron linear collider (e+-e- collider) or an electron-hadron collider (e-p collider) can be conceived. In this paper, we discuss some key design issues for an e+-e- collider and a high energy e-p collider, based on the existing infrastructure of the CERN accelerator complex., Comment: Proceedings of IPAC12

The common practice for displaying error bars on distributions of numbers of events is confusing and can lead to incorrect conclusions. A proposal is made for a different style of presentation that more directly indicates the level of agreement between expectations and observations., Comment: New data presentation scheme in Fig 2 (bands offset by 1/2 a unit). Different prior for the case of limited MC events. A few typos corrected

One of the focuses of research and development towards the construction of a muon collider is muon beam preparation. Simulation of frictional cooling shows that it can achieve the desired emittance reduction to produce high-luminosity muon beams. We show that for positively charged particles, charge exchange interactions necessitate significant changes to schemes previously developed for negatively charged particles. We also demonstrate that foil-based schemes are not viable for positive particles., Comment: 15 pages, 6 figures

The plasma wakefield amplitudes which could be achieved via the modulation of a long proton bunch are investigated. We find that in the limit of long bunches compared to the plasma wavelength, the strength of the accelerating fields is directly proportional to the number of particles in the drive bunch and inversely proportional to the square of the transverse bunch size. The scaling laws were tested and verified in detailed simulations using parameters of existing proton accelerators, and large electric fields were achieved, reaching 1 GV/m for LHC bunches. Energy gains for test electrons beyond 6 TeV were found in this case., Comment: 9 pages, 7 figures

A muon collider would open new frontiers of investigation in high energy particle physics, allowing precision measurements to be made at the TeV energy frontier. One of the greatest challenges to constructing a muon collider is the preparation of a beam of muons on a timescale comparable to the lifetime of the muon. Frictional cooling is a potential solution to this problem. In this paper, we briefly describe frictional cooling and detail the Frictional Cooling Demonstration (FCD) experiment at the Max Planck Institute for Physics, Munich. The FCD experiment, which aims to verify the working principles behind frictional cooling, is at the end of the commissioning phase and will soon begin data taking., Comment: 27 pages, 25 figures

A proof of concept detector is presented for scintillation light detection in liquid argon using Silicon Photo-Multipliers. The aim of the work is to build an anti-Compton veto for germanium detectors operated directly in liquid argon like in the GERDA experiment. Properties of the Multi-Pixel Photon Counter (MPPC) are studied at cryogenic temperatures. To increase the light collection efficiency of the MPPCs wavelength shifting fibers were used. A veto efficiency comparable to a similar setup with a Photo-Multiplier Tube was achieved., Comment: 18 pages, 13 figures

Deciding whether a model provides a good description of data is often based on a goodness-of-fit criterion summarized by a p-value. Although there is considerable confusion concerning the meaning of p-values, leading to their misuse, they are nevertheless of practical importance in common data analysis tasks. We motivate their application using a Bayesian argumentation. We then describe commonly and less commonly known discrepancy variables and how they are used to define p-values. The distribution of these are then extracted for examples modeled on typical data analysis tasks, and comments on their usefulness for determining goodness-of-fit are given., Comment: 33 pages, 13 figures; added figure for runs test, changed to coherent notation, updated bibliography; fixed formula in the appendix

Simulations have shown that a high energy, short and intense proton beam can drive a large amplitude plasma wave and accelerate an electron beam to the energy frontier in a single plasma channel. To verify this novel idea, a proof-of-principle demonstration experiment is now being planned. The idea is to use the available high energy proton beams either from the Proton Synchrotron (PS) or the Super Proton Synchrotron (SPS) at CERN, to shoot the beam into a plasma cell and to excite the plasma wakefield. A strong density modulation due to the excited plasma wakefield is produced for a long drive beam and this modulated beam in turn produces a high electric field. The proposed experimental setup is introduced in this paper. The interactions between the plasma and the proton beam are simulated and the results are presented. The compression of an SPS bunch is also discussed., Comment: This paper is submitted to the proceedings of the first International Particle Accelerator Conference (IPAC10)in Kyoto, Japan

A new test statistic based on success runs of weighted deviations is introduced. Its use for observations sampled from independent normal distributions is worked out in detail. It supplements the classic $\chi^{2}$ test which ignores the ordering of observations and provides additional sensitivity to local deviations from expectations. The exact distribution of the statistic in the non-parametric case is derived and an algorithm to compute $p$-values is presented. The computational complexity of the algorithm is derived employing a novel identity for integer partitions., Comment: 20 pages, 4 figures. Match published paper as close as possible

Low-energy muon beams are useful for a range of physics experiments. We consider the production of low-energy muon beams with small energy spreads using frictional cooling. As the input beam, we take a surface muon source such as that at the Paul Scherrer Institute. Simulations show that the efficiency of low energy muon production can potentially be raised to 1%, which is significantly higher than that of current schemes.

We describe the development of a new toolkit for data analysis. The analysis package is based on Bayes' Theorem, and is realized with the use of Markov Chain Monte Carlo. This gives access to the full posterior probability distribution. Parameter estimation, limit setting and uncertainty propagation are implemented in a straightforward manner. A goodness-of-fit criterion is presented which is intuitive and of great practical use., Comment: 31 pages, 10 figures

Plasma wakefield acceleration, either laser driven or electron-bunch driven, has been demonstrated to hold great potential. However, it is not obvious how to scale these approaches to bring particles up to the TeV regime. In this paper, we discuss the possibility of proton-bunch driven plasma wakefield acceleration, and show that high energy electron beams could potentially be produced in a single accelerating stage., Comment: 13 pages, 4 figures

Various parametrizations of sigma(gamma p) are tried out on the small-x fixed target and HERA data. A two-Pomeron type parametrization is found to give the best reproduction of the data. The data indicate that the value of lambda(eff) for parametrizations of the form sigma(gamma p)~l^lambda(eff) approaches a constant value at high Q^2. The extrapolated values of sigma(gamma p) to very long coherence lengths are found to cross in some parametrizations for l>10^7 fm, indicating the possibility that sigma(gamma p) becomes Q^2 independent at large values of the coherence length l., Comment: 34 pages, 20 figures

A Bayesian analysis of the probability of a signal in the presence of background is developed, and criteria are proposed for claiming evidence for, or the discovery of a signal. The method is general and in particular applicable to sparsely populated spectra. Monte Carlo techniques to evaluate the sensitivity of an experiment are described. As an example, the method is used to calculate the sensitivity of the GERDA experiment to neutrinoless double beta decay., Comment: 15 pages, 5 figures

We apply the Golec-Biernat Wuesthoff model in the calculation of vector meson photo- and electroproduction. Starting from very simple non-relativistic wave functions we show that the model provides a good description of $J/\Psi$ cross sections in wide $Q^2$ and $W$ ranges. For the light mesons one obtains the approximately correct $W$ dependence and ratio of longitudinal to transverse cross sections, although in this case the normalization, affected mainly by the wave function employed, is not in good agreement with data.