Search

Nested sampling (NS) is a popular algorithm for Bayesian computation. We investigate statistical errors in NS both analytically and numerically. We show two analytic results. First, we show that the leading terms in Skilling's expression using information theory match the leading terms in Keeton's expression from an analysis of moments. This approximate agreement was previously only known numerically and was somewhat mysterious. Second, we show that the uncertainty in single NS runs approximately equals the standard deviation in repeated NS runs. Whilst intuitive, this was previously taken for granted. We close by investigating our results and their assumptions in several numerical examples, including cases in which NS uncertainties increase without bound., 12 pages + appendices, 3 figures

Prior to the execution of this project, there were limited options for repairing a failed production packer. Conventional oilfield practice would default to a well workover to replace the failed component. In an offshore environment, this approach not only carries significant capital cost, but also material risk and health, safety and environment exposure associated with the large operational footprint and time requirement of the operation. An innovative solution was developed to remediate the failed packer without a workover while simultaneously significantly reducing cost and risk. A new packer was formed by melting a bismuth alloy plug into the annulus using wireline equipment, eliminating the requirement for a workover rig. Bismuth alloy pellets were deposited onto the packer via precisely drilled holes in the tubing before being melted into an annular plug, forming a gas-tight metal-to-metal seal. As this was an industry first, prototype testing of the annular bismuth plug was undertaken to demonstrate concept feasibility. After a series of iterative testing a viable concept was achieved, and the prototype was taken forward to qualification. The annular plug was qualified to industry standard ISO 14310 V0 for the well’s operating conditions which included both pressure differential and axial loads. After the bismuth annular plug was qualified, the deployment method for the bismuth pellets was optimised to ensure they reached targeted location without compromising well integrity. After 2 years of design, the industry-first wireline intervention was successfully executed in 2021 and the well was returned to production.

There are now two single measurements of precision observables that have major anomalies in the Standard Model: the recent CDF measurement of the $W$ mass shows a $7\sigma$ deviation and the Muon $g-2$ experiment at FNAL confirmed a long-standing anomaly, implying a $4.2 \sigma$ deviation. Doubts regarding new physics interpretations of these anomalies could stem from uncertainties in the common hadronic contributions. We demonstrate that these two anomalies pull the hadronic contributions in opposite directions by performing electroweak fits in which the hadronic contribution was allowed to float. The fits show that including the $g - 2$ measurement worsens the tension with the CDF measurement and conversely that adjustments that alleviate the CDF tension worsen the $g-2$ tension beyond $5 \sigma$. This means that if we adopt the CDF $W$ mass measurement, the case for new physics in either the $W$ mass or muon $g-2$ is inescapable regardless of the size of the SM hadronic contributions. Lastly, we demonstrate that a mixed scalar leptoquark extension of the Standard Model could explain both anomalies simultaneously., Comment: 8 pages, 3 Figures. Comments are welcome; v2: tables and plots updated; v3: match the pulished version; v4: improve the supplemental Material

We point out that the Neyman-Pearson lemma applies to Bayes factors if we consider expected type-1 and type-2 error rates. That is, the Bayes factor is the test statistic that maximises the expected power for a fixed expected type-1 error rate. For Bayes factors involving a simple null hypothesis, the expected type-1 error rate is just the completely frequentist type-1 error rate. Lastly we remark on connections between the Karlin-Rubin theorem and uniformly most powerful tests, and Bayes factors. This provides frequentist motivations for computing the Bayes factor and could help reconcile Bayesians and frequentists., Comment: 8 pages

We investigate the extent to which perturbative calculations of the electroweak phase transition are arbitrary and uncertain, owing to their gauge, renormalisation scale and scheme dependence, as well as treatments of the Goldstone catastrophe and daisy diagrams. Using the complete parameter space of the Standard Model extended by a real scalar singlet with a $\mathbb{Z}_2$ symmetry as a test, we explore the properties of the electroweak phase transition in general $R_\xi$ and covariant gauges, OS and $\overline{\text{MS}}$ renormalisation schemes, and for common treatments of the Goldstone catastrophe and daisy diagrams. Reassuringly, we find that different renormalisation schemes and different treatments of the Goldstone catastrophe and daisy diagrams typically lead to only modest changes in predictions for the critical temperature and strength of the phase transition. On the other hand, the gauge and renormalisation scale dependence may be significant, and often impact the existence of the phase transition altogether., Comment: 45 pages, 16 figures and 2 tables; version accepted for publication in JHEP; Correct the signs of mu in Table 2

Helical Auxetic Yarns (HAYs) can be used in a variety of applications from healthcare to blast and impact resistance. This work focuses on the effect of the use of different core materials (e.g. rubber, polyurethane, polytetrafluoroethylene/teflon, polypropylene, polyetheretherketone, polycarbonate, acetal) with a nitinol wire wrap component on the maximum Negative Poisson Ratio (NPR) produced and thus the auxetic performance of Helical Auxetic Yarns (HAYs). From the analytical model, it was found that an acetal core produced the largest NPR when compared to the other six materials. The trend obtained from the experimental tensile tests (validation) correlated closely with the theoretical predictions of the NPR as axial strain was increased. The experimental method presented a maximum NPR at an average axial strain of 0.148 which was close to the strain of 0.155 predicted by theory. However, the maximum experimental NPR was significantly lower than that predicted by the analytical model.

In this work, we study the impact of electroweak and Higgs precision measurements at future electron-positron colliders on several typical supersymmetric models, including the Constrained Minimal Supersymmetric Standard Model (CMSSM), Non-Universal Higgs Mass generalisations (NUHM1, NUHM2), and the 7-dimensional Minimal Supersymmetric Standard Model (MSSM7). Using publicly-available data from the \textsf{GAMBIT} community, we post-process previous SUSY global fits with additional likelihoods to explore the discovery potential of Higgs factories, such as the Circular Electron Positron Collider (CEPC), the Future Circular Collider (FCC) and the International Linear Collider (ILC). We show that the currently allowed parameter space of these models will be further tested by future precision measurements. In particular, dark matter annihilation mechanisms may be distinguished by precise measurements of Higgs observables., Comment: 24 pages, 8 figures, 4 tables. Contribution to Snowmass 2021. Version accepted for publication in PRD

We consider the Jeffreys-Lindley paradox from an objective Bayesian perspective by attempting to find priors representing complete indifference to sample size in the problem. This means that we ensure that the prior for the unknown mean and the prior predictive for the $t$-statistic are independent of the sample size. If successful, this would lead to Bayesian model comparison that was independent of sample size and ameliorate the paradox. Unfortunately, it leads to an improper scale-invariant prior for the unknown mean. We show, however, that a truncated scale-invariant prior delays the dependence on sample size, which could be practically significant. Lastly, we shed light on the paradox by relating it to the fact that the scale-invariant prior is improper., Comment: 6 pages, 1 figure, added one comment and reference

We review Skilling's nested sampling (NS) algorithm for Bayesian inference and more broadly multi-dimensional integration. After recapitulating the principles of NS, we survey developments in implementing efficient NS algorithms in practice in high-dimensions, including methods for sampling from the so-called constrained prior. We outline the ways in which NS may be applied and describe the application of NS in three scientific fields in which the algorithm has proved to be useful: cosmology, gravitational-wave astronomy, and materials science. We close by making recommendations for best practice when using NS and by summarizing potential limitations and optimizations of NS., Comment: 20 pages + supplementary information, 5 figures. preprint version; published version at https://www.nature.com/articles/s43586-022-00121-x

The European physical journal / C 81(11), 992 (2021). doi:10.1140/epjc/s10052-021-09712-6, We assess the status of a wide class of WIMP dark matter (DM) models in light of the latest experimental results using the global fitting framework GAMBIT. We perform a global analysis of effective field theory (EFT) operators describing the interactions between a gauge-singlet Dirac fermion and the Standard Model quarks, the gluons and the photon. In this bottom-up approach, we simultaneously vary the coefficients of 14 such operators up to dimension 7, along with the DM mass, the scale of new physics and several nuisance parameters. Our likelihood functions include the latest data from Planck, direct and indirect detection experiments, and the LHC. For DM masses below 100 GeV, we find that it is impossible to satisfy all constraints simultaneously while maintaining EFT validity at LHC energies. For new physics scales around 1 TeV, our results are influenced by several small excesses in the LHC data and depend on the prescription that we adopt to ensure EFT validity. Furthermore, we find large regions of viable parameter space where the EFT is valid and the relic density can be reproduced, implying that WIMPs can still account for the DM of the universe while being consistent with the latest data., Published by Springer, Heidelberg

The statistical models used to derive the results of experimental analyses are of incredible scientific value and are essential information for analysis preservation and reuse. In this paper, we make the scientific case for systematically publishing the full statistical models and discuss the technical developments that make this practical. By means of a variety of physics cases -- including parton distribution functions, Higgs boson measurements, effective field theory interpretations, direct searches for new physics, heavy flavor physics, direct dark matter detection, world averages, and beyond the Standard Model global fits -- we illustrate how detailed information on the statistical modelling can enhance the short- and long-term impact of experimental results., Comment: 60 pages, 15 figures

We propose a novel method for computing $p$-values based on nested sampling (NS) applied to the sampling space rather than the parameter space of the problem, in contrast to its usage in Bayesian computation. The computational cost of NS scales as $\log^2{1/p}$, which compares favorably to the $1/p$ scaling for Monte Carlo (MC) simulations. For significances greater than about $4\sigma$ in both a toy problem and a simplified resonance search, we show that NS requires orders of magnitude fewer simulations than ordinary MC estimates. This is particularly relevant for high-energy physics, which adopts a $5\sigma$ gold standard for discovery. We conclude with remarks on new connections between Bayesian and frequentist computation and possibilities for tuning NS implementations for still better performance in this setting., Comment: 5 pages + refs, 3 figures. added refs + schematic of algorithm. closely matches published version

The excess of electron recoil events seen by the XENON1T experiment has been interpreted as a potential signal of axion-like particles (ALPs), either produced in the Sun, or constituting part of the dark matter halo of the Milky Way. It has also been explained as a consequence of trace amounts of tritium in the experiment. We consider the evidence for the solar and dark-matter ALP hypotheses from the combination of XENON1T data and multiple astrophysical probes, including horizontal branch stars, red giants, and white dwarfs. We briefly address the influence of ALP decays and supernova cooling. While the different datasets are in clear tension for the case of solar ALPs, all measurements can be simultaneously accommodated for the case of a sub-dominant fraction of dark-matter ALPs. Nevertheless, this solution requires the tuning of several a priori unknown parameters, such that for our choices of priors a Bayesian analysis shows no strong preference for the ALP interpretation of the XENON1T excess over the background hypothesis., 40 pages, 9 figures. V3 corresponds to the accepted manuscript; added appendices on the DIC and MC simulations; supplementary material now available on Zenodo at https://doi.org/10.5281/zenodo.4384061

I would like to thank Junk and Lyons (arXiv:2009.06864) for beginning a discussion about replication in high-energy physics (HEP). Junk and Lyons ultimately argue that HEP learned its lessons the hard way through past failures and that other fields could learn from our procedures. They emphasize that experimental collaborations would risk their legacies were they to make a type-1 error in a search for new physics and outline the vigilance taken to avoid one, such as data blinding and a strict $5\sigma$ threshold. The discussion, however, ignores an elephant in the room: there are regularly anomalies in searches for new physics that result in substantial scientific activity but don't replicate with more data., Comment: closely matches published comment & final words on rejoinder

A recent paper [2109.02650] accumulates evidence for a new fundamental particle by combining several CMS and ATLAS searches for the Standard Model Higgs boson. The putative particle is a neutral scalar, $S$, with a mass of about 151 GeV. The reported significances are $5.1\sigma$ local and $4.8\sigma$ global. This nearly reaches the $5\sigma$ threshold for a discovery in high-energy physics. In this brief note we cast doubt on the strength of the evidence for a new particle. After taking into account the fact that signals were fitted to six different channels, we find that the significances are only $4.1\sigma$ local and $3.5\sigma$ global. The code and instructions for reproducing our calculations are available at https://github.com/andrewfowlie/accumulating_evidence., Comment: 2 pages + refs, 1 figure. added further discussion of LEE. closely matches version accepted for publication in Phys.Lett.B

Physical theories that depend on many parameters or are tested against data from many different experiments pose unique challenges to statistical inference. Many models in particle physics, astrophysics and cosmology fall into one or both of these categories. These issues are often sidestepped with statistically unsound ad hoc methods, involving intersection of parameter intervals estimated by multiple experiments, and random or grid sampling of model parameters. Whilst these methods are easy to apply, they exhibit pathologies even in low-dimensional parameter spaces, and quickly become problematic to use and interpret in higher dimensions. In this article we give clear guidance for going beyond these procedures, suggesting where possible simple methods for performing statistically sound inference, and recommendations of readily-available software tools and standards that can assist in doing so. Our aim is to provide any physicists lacking comprehensive statistical training with recommendations for reaching correct scientific conclusions, with only a modest increase in analysis burden. Our examples can be reproduced with the code publicly available at https://doi.org/10.5281/zenodo.4322283., 15 pages, 4 figures. extended discussions. closely matches version accepted for publication

Nested sampling (NS) is an invaluable tool in data analysis in modern astrophysics, cosmology, gravitational wave astronomy and particle physics. We identify a previously unused property of NS related to order statistics: the insertion indexes of new live points into the existing live points should be uniformly distributed. This observation enabled us to create a novel cross-check of single NS runs. The tests can detect when an NS run failed to sample new live points from the constrained prior and plateaus in the likelihood function, which break an assumption of NS and thus leads to unreliable results. We applied our cross-check to NS runs on toy functions with known analytic results in 2 - 50 dimensions, showing that our approach can detect problematic runs on a variety of likelihoods, settings and dimensions. As an example of a realistic application, we cross-checked NS runs performed in the context of cosmological model selection. Since the cross-check is simple, we recommend that it become a mandatory test for every applicable NS run., minor changes & clarifications. closely matches published version

We present a C++ software package called PhaseTracer for mapping out cosmological phases, and potential transitions between them, for Standard Model extensions with any number of scalar fields. PhaseTracer traces the minima of effective potential as the temperature changes, and then calculates the critical temperatures, at which the minima are degenerate. PhaseTracer is constructed with modularity, flexibility and practicality in mind. It is fast and stable, and can receive potentials provided by other packages such as FlexibleSUSY. PhaseTracer can be useful analysing cosmological phase transitions which played an important role in the very early evolution of the Universe. If they were first order they could generate detectable gravitational waves and/or trigger electroweak baryogenesis to generate the observed matter anti-matter asymmetry of the Universe. The code can be obtained from https://github.com/PhaseTracer/PhaseTracer., Comment: 32 pages, 5 figures, matches published version

It was recently emphasised by Riley (2019); Schittenhelm & Wacker (2020) that that in the presence of plateaus in the likelihood function nested sampling (NS) produces faulty estimates of the evidence and posterior densities. After informally explaining the cause of the problem, we present a modified version of NS that handles plateaus and can be applied retrospectively to NS runs from popular NS software using anesthetic. In the modified NS, live points in a plateau are evicted one by one without replacement, with ordinary NS compression of the prior volume after each eviction but taking into account the dynamic number of live points. The live points are replenished once all points in the plateau are removed. We demonstrate it on a number of examples. Since the modification is simple, we propose that it becomes the canonical version of Skilling's NS algorithm., 7 pages, 6 figures. minor changes and clarifications. closely matches published version

We provide a small C++ library with Mathematica and Python interfaces for computing thermal functions, defined $$ J_\text{B/F}(y^2) \equiv \Re \int_0^\infty x^2 \log\left[1 \mp e^{-\sqrt{x^2 + y^2}} \right] \,\text{d}x, $$ which appear in finite-temperature quantum field theory and play a role in phase-transitions in the early Universe, including baryogenesis, electroweak symmetry breaking and the Higgs mechanism., Comment: 16 pages, 7 figures. To appear in Comput.Phys.Commun. The code is available from https://github.com/andrewfowlie/thermal_funcs

There has been a steady interest in flavor anomalies and their global fits as ideal probes of new physics. If the anomalies are real, one promising explanation is a new Z′ gauge boson with a flavor-changing coupling to bottom and strange quarks and a flavor-conserving coupling to muons and, possibly, electrons. We point out that direct production of such a Z′, emerging from the collision of b and s quarks, may offer a complementary window into these phenomena because collider searches already provide competitive constraints. On top of that, we analyze the same Z′ scenario in relation to another long-standing discrepancy between theory and experiment that concerns the anomalous magnetic moment of the muon. By scanning the allowed Z′ coupling strengths in the low-mass region, we assess the compatibility of the signals from LHCb with the Z′ searches in the high energy LHC data and the measurements of the anomalous magnetic moments of the involved leptons. We also argue that observations of the latter can break the degeneracy pattern in the Wilson coefficients C9 and C10 presented by LHCb data. The Z′ model we consider is compatible with the new measurement of RK⁎, therefore it can potentially account for the long-standing deviations observed in B-physics.

There has been a steady interest in flavor anomalies and their global fits as ideal probes of new physics. If the anomalies are real, one promising explanation is a new Z′ gauge boson with a flavor-changing coupling to bottom and strange quarks and a flavor-conserving coupling to muons and, possibly, electrons. We point out that direct production of such a Z′, emerging from the collision of b and s quarks, may offer a complementary window into these phenomena because collider searches already provide competitive constraints. On top of that, we analyze the same Z′ scenario in relation to another long-standing discrepancy between theory and experiment that concerns the anomalous magnetic moment of the muon. By scanning the allowed Z′ coupling strengths in the low-mass region, we assess the compatibility of the signals from LHCb with the Z′ searches in the high energy LHC data and the measurements of the anomalous magnetic moments of the involved leptons. We also argue that observations of the latter can break the degeneracy pattern in the Wilson coefficients C9 and C10 presented by LHCb data. The Z′ model we consider is compatible with the new measurement of RK⁎, therefore it can potentially account for the long-standing deviations observed in B-physics.

We present an algorithm for the reconstruction of the Higgs mass in events with Higgs bosons decaying into a pair of leptons. The algorithm is based on matrix element (ME) techniques and achieves a relative resolution on the Higgs boson mass of typically 15–20%. A previous version of the algorithm has been used in analyses of Higgs boson production performed by the CMS collaboration during LHC Run 1. The algorithm is described in detail and its performance on simulated events is assessed. The development of techniques to handle decays in the ME formalism represents an important result of this paper., Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 862, ISSN:0168-9002, ISSN:1872-9576

We present BubbleProfiler, a C++ software package for finding field profiles in bubble walls and calculating the bounce action during phase transitions involving multiple scalar fields. Our code uses a recently proposed perturbative method for potentials with multiple fields and a shooting method for single field cases. BubbleProfiler is constructed with modularity, flexibility and practicality in mind. These principles extend from the input of an arbitrary potential with multiple scalar fields in various forms, through the code structure, to the testing suite. After reviewing the physics context, we describe how the methods are implemented in BubbleProfiler, provide an overview of the code structure and detail usage scenarios. We present a number of examples that serve as test cases of BubbleProfiler and comparisons to existing public codes with similar functionality. We also show a physics application of BubbleProfiler in the scalar singlet extension of the Standard Model of particle physics by calculating the action as a function of model parameters during the electroweak phase transition. BubbleProfiler completes an important link in the toolchain for studying the properties of the thermal phase transition driving baryogenesis and properties of gravitational waves in models with multiple scalar fields. The code can be obtained from: https://github.com/bubbleprofiler/bubbleprofiler, 43 pages, 12 figures, 1 table

Motivated by the fact that the Next-to-Minimal Supersymmetric Standard Model is one of the most plausible models that can accommodate electroweak baryogenesis, we analyze its phase structure by tracing the temperature dependence of the minima of the effective potential. Our results reveal rich patterns of phase structure that end in the observed electroweak symmetry breaking vacuum. We classify these patterns according to the first transition in their history and show the strong first-order phase transitions that may be possible in each type of pattern. These could allow for the generation of the matter-antimatter asymmetry or potentially observable gravitational waves. For a selection of benchmark points, we checked that the phase transitions completed and calculated the nucleation temperatures. We furthermore present samples that feature strong first-order phase transitions from an extensive scan of the whole parameter space. We highlight common features of our samples, including the fact that the Standard Model like Higgs is often not the lightest Higgs in the model., Comment: 41 pages, 13 figures. V3: corrected typos and extended discussion about Higgs masses. Accepted in JHEP

We present a Bayesian and frequentist analysis of the DAMPE charged cosmic ray spectrum. The spectrum, by eye, contained a spectral break at about 1 TeV and a monochromatic excess at about 1.4 TeV. The break was supported by a Bayes factor of about $10^{10}$ and we argue that the statistical significance was resounding. We investigated whether we should attribute the excess to dark matter annihilation into electrons in a nearby subhalo. We found a local significance of about $3.6\sigma$ and a global significance of about $2.3\sigma$, including a two-dimensional look-elsewhere effect by simulating 1000 pseudo-experiments. The Bayes factor was sensitive to our choices of priors, but favoured the excess by about 2 for our choices. Thus, whilst intriguing, the evidence for a signal is not currently compelling., Comment: 4 pages, 2 figures

We perform frequentist and Bayesian statistical analyses of Higgs- and Z-portal models of dark matter particles with spin 0, 1/2 and 1. Our analyses incorporate data from direct detection and indirect detection experiments, as well as LHC searches for monojet and monophoton events, and we also analyze the potential impacts of future direct detection experiments. We find acceptable regions of the parameter spaces for Higgs-portal models with real scalar, neutral vector, Majorana or Dirac fermion dark matter particles, and Z-portal models with Majorana or Dirac fermion dark matter particles. In many of these cases, there are interesting prospects for discovering dark matter particles in Higgs or Z decays, as well as dark matter particles weighing $\gtrsim 100$ GeV. Negative results from planned direct detection experiments would still allow acceptable regions for Higgs- and Z-portal models with Majorana or Dirac fermion dark matter particles., Comment: 9 figures, 8 tables, 34 pages. v3: closely matches published version

A new gauge singlet scalar field can undergo a strongly first-order phase transition (PT) leading to gravitational waves (GW) potentially observable at aLIGO and simultaneously stabilize the electroweak vacuum. aLIGO (O5) is potentially sensitive to cosmological PTs at $10^7$-$10^8$ GeV, which coincides with the requirement that the singlet scale is less than the Standard Model (SM) vacuum instability scale, which is between $10^8$ GeV and $10^{14}$ GeV. After sampling its parameter space, we identify three benchmark points with a PT at about $T\approx 10^7$ GeV in a gauge singlet extension of the SM. We calculate the nucleation temperature, order parameter, characteristic timescale, and peak amplitude and frequency of GW from bubble collisions during the PT for the benchmarks and find that, in an optimistic scenario, GW from such a PT may be in reach of aLIGO (O5). We confirm that the singlet stabilizes the electroweak vacuum whilst remaining consistent with zero-temperature phenomenology as well. Thus, this scenario presents an intriguing possibility that aLIGO may detect traces of fundamental physics motivated by vacuum stability at an energy scale that is well above the reach of any other experiment., Comment: 10 pages, 7 figures. Improved calculation of beta parameter. Conclusions unchanged. Closely matches published version

As an example of using Bayesian statistics in searches for new physics at the LHC, we present a calculation of Bayes factors for the erstwhile digamma resonance (\(\digamma\)) versus the SM in light of ATLAS 8 TeV 20.3/fb, 13 TeV 3.2/fb and 13 TeV 15.4/fb data. We matched, wherever possible, parameterisations in the ATLAS analysis. We calculated that the plausibility of the \(\digamma\)versus the Standard Model increased by about eight in light of the 8 TeV 20.3/fb and 13 TeV 3.2/fb ATLAS data, somewhat justifying interest in \(\digamma\) models. All told, however, in light of 15.4/fb data, the \(\digamma\) was disfavoured by about 0.7. We argue that Bayes factors could play an important role in future anomalies by clarifying the plausibility of new physics and sidestepping look-elsewhere effects.

The Higgs boson discovery stirred interest in next-to-minimal supersymmetric models, due to the apparent fine-tuning required to accommodate it in minimal theories. To assess their naturalness, we compare fine-tuning in a $\mathbb{Z}_3$ conserving semi-constrained Next-to-Minimal Supersymmetric Standard Model (NMSSM) to the constrained MSSM (CMSSM). We contrast popular fine-tuning measures with naturalness priors, which automatically appear in statistical measures of the plausibility that a given model reproduces the weak scale. Our comparison shows that naturalness priors provide valuable insight into the hierarchy problem and rigorously ground naturalness in Bayesian statistics. For the CMSSM and semi-constrained NMSSM we demonstrate qualitative agreement between naturalness priors and popular fine tuning measures. Thus, we give a clear plausibility argument that favours relatively light superpartners., Comment: 52 pages, 11 figures and 3 tables, Published in JHEP

The Dark Matter Particle Explorer (DAMPE) recently released measurements of the electron spectrum with a hint of a narrow peak at about 1.4 TeV. We investigate dark matter (DM) models that could produce such a signal by annihilation in a nearby subhalo whilst simultaneously satisfying constraints from DM searches. In our model-independent approach, we consider all renormalizable interactions via a spin 0 or 1 mediator between spin 0 or 1/2 DM particles and the Standard Model leptons. We find that of the 20 combinations, 10 are ruled out by velocity or helicity suppression of the annihilation cross section to fermions. The remaining 10 models, though, evade constraints from the relic density, collider and direct detection searches, and include models of spin 0 and 1/2 DM coupling to a spin 0 or 1 mediator. We delineate the regions of mediator mass and couplings that could explain the DAMPE excess. In all cases the mediator is required to be heaver than about 2 TeV by LEP limits., Comment: 28 pages, 5 figures and 2 tables. v2: references added. v3: minor changes, matches published version

Motivated by a hint in a CMS search for right-handed $W$-bosons in $eejj$ final states, we propose an experimental test of quark-mixing matrices in a general left-right symmetric model, based on counting the numbers of $b$-tags from right-handed $W$-boson hadronic decays. We find that, with our test, differences between left- and right-handed quark-mixing matrices could be detected at the LHC with $\sqrt{s}=14$ TeV. With an integrated luminosity of about $20/\textrm{fb}$, our test is sensitive to right-handed quark-mixing angles as small as about $30^\circ$ and with $3000/\textrm{fb}$, our test's sensitivity improves to right-handed mixing angles as small as about $7.5^\circ$. Our test's sensitivity might be further enhanced by tuning $b$-tagging efficiency against purity., 14 pages, 4 figures. Matches version published in Nucl.Phys. B. Expanded descriptions of figures but conclusions unchanged

We investigate Bayesian and frequentist approaches to resonance searches using a toy model based on an ATLAS search for the Higgs boson in the diphoton channel. We draw pseudo-data from the background only model and background plus signal model at multiple luminosities, from $10^{-3}$/fb to $10^7$/fb. We chart the change in the Bayesian posterior of the background only model and the global p-value. We find that, as anticipated, the posterior converges to certainty about the model as luminosity increases. The p-value, on the other hand, randomly walks between 0 and 1 if the background only model is true, and otherwise converges to 0. After briefly commenting on the frequentist properties of the posterior, we make a direct comparison of the significances obtained in Bayesian and frequentist frameworks. We find that the well-known look-elsewhere effect reduces local significances by about 1$\sigma$. We furthermore find that significances from our Bayesian framework are typically about 1 to 2$\sigma$ smaller than the global significances, though the reduction depends on the prior, global significance and integrated luminosity. This suggests that even global significances could significantly overstate the evidence against the background only model. We checked that this effect --- the Bayes effect --- was robust with respect to fourteen choices of prior and investigated the Jeffreys-Lindley paradox for three of them., Comment: 12 pages, 11 figures, edited & expanded, includes discussion of Jeffreys-Lindley paradox, but conclusions unchanged

We investigate the impact of uncertainty in the velocity distribution of dark matter on direct detection experiments. We construct an multinomial prior with a hyperparameter $\beta$ that describes the strength of our belief in an isotropic Maxwell-Boltzmann velocity distribution. By varying $\beta$, we interpolate between a halo-independent and halo-dependent analysis. We present a novel approximation for the marginalisation of this prior that is applicable to any counting experiment. With this formula, we investigate the impact of the uncertainty in limits from XENON1T. For dark matter masses greater than about 60 GeV, we find extremely mild sensitivity to the distribution. Below about 60 GeV, the limit weakens by less than an order of magnitude if we assume an isotropic distribution in the galactic frame. If we permit anisotropic distributions, the limit further weakens, but at most by about two orders of magnitude. Lastly, we check the impact of parametric uncertainties and discuss the possible inclusion and impact of our technique in global fits., Comment: to appear in JCAP. Numerical results unchanged, but moderate changes to presentation and interpretation of formalism

The relaxion mechanism is a novel solution to the hierarchy problem. In this first statistical analysis of the relaxion mechanism, we quantify the relative plausibility of a QCD and a non-QCD relaxion model versus the Standard Model with Bayesian statistics, which includes an automatic penalty for fine-tuning. We find that in light of the hierarchy between the weak and Planck scales, relaxion models are favoured by colossal Bayes-factors. Constraints upon \eg the vacuum energy during relaxation, however, shrink the Bayes-factors such that relaxion models are only slightly favoured. Including the bounds on $\left|\theta_\text{QCD}\right|$ shatters the plausibility of the QCD relaxion model as it typically yields $\left|\theta_\text{QCD}\right| \gg 0$. Finally, we augment our models with scalar-field inflation and consider measurements of inflationary observables from BICEP/Planck. We find that, all told, the Standard Model is favoured by huge Bayes-factors as the relaxion models require fine-tuning such that the Hubble parameter is less than the height of the periodic barriers. Thus, whilst we confirm that relaxion models could solve the hierarchy problem, we find that their unconventional cosmology demolishes their plausibility.

We present an application, Superplot, for calculating and plotting statistical quantities relevant to parameter inference from a "chain" of samples drawn from a parameter space, produced by e.g. MultiNest. A simple graphical interface allows one to browse a chain of many variables quickly, and make publication quality plots of, inter alia, one- and two-dimensional profile likelihood, posterior pdf (with kernel density estimation), confidence intervals and credible regions. In this short manual, we document installation and basic usage, and define all statistical quantities and conventions. The code is fully compatible with Linux, Windows and Mac OSX. Furthermore, if preferred, all functionality is available through the command line rather than a graphical interface., 19 pages, 4 colour figures, added information about Mac and combining plots into a single figure

We present a new Python module - LHCO_reader - for reading detector-level events in LHCO format generated from detector-simulators such as PGS and Delphes. Emphasis is placed upon ease of use. The module is installed via pip. Once installed, one can read and scrutinize events, with helpful functions and classes for cutting, plotting and inspecting events, and manipulating four-momenta by e.g. boosting. Implementing complicated analyses should be straight-forward by coding any cuts into Python. Furthermore, common kinematic variables, including $\alpha_T$ and razor are included out of the box, and $m_{T2}$ and $m_{T2}^W$ are provided by interfaces with external libraries., Comment: 28 pages, new features of code described, including alpha_T, razor and mT2

Encouraged by a hint in a search for right-handed $W$ bosons at the LHC, we investigate whether the unitarity of a right-handed quark mixing matrix and the equality of the left- and right-handed quark mixing matrices could be tested at the LHC. We propose a particular test, involving counting the numbers of $b$-tags in the final state, and simulate the test at the event level with Monte-Carlo tools for the forthcoming $\sqrt{s}=13$ TeV LHC run. We find that testing unitarity with 20/fb will be challenging; our test successfully rejects unitarity if the right-handed quark mixing matrix is non-unitary, but only in particular cases. On the other hand, our test may provide the first opportunity to test the unitarity of a right-handed quark mixing matrix and with 3000/fb severely constrains possible departures from unitarity in the latter. We refine our previous work, testing the equality of quark mixing matrices, with full collider simulation. With 20/fb, we are sensitive to mixing angles as small as $30^\circ$, and with 3000/fb, angles as small as $7.5^\circ$, confirming our preliminary analysis. We briefly investigate testing the unitarity of the SM CKM matrix with a similar method by studying semileptonic $t\bar t$ production, concluding that systematics make it particularly difficult., 20 pages, 5 figures, matches version to appear in Nuclear Physics B

Using the DAMA/LIBRA anomaly as an example, we formalise the notion of halo-independence in the context of Bayesian statistics and quantified maximum entropy. We consider an infinite set of possible profiles, weighted by an entropic prior and constrained by a likelihood describing noisy measurements of modulated moments by DAMA/LIBRA. Assuming an isotropic dark matter (DM) profile in the galactic rest frame, we find the most plausible DM profiles and predictions for unmodulated signal rates at DAMA/LIBRA. The entropic prior contains an a priori unknown regularisation factor, $\beta$, that describes the strength of our conviction that the profile is approximately Maxwellian. By varying $\beta$, we smoothly interpolate between a halo-independent and a halo-dependent analysis, thus exploring the impact of prior information about the DM profile., Comment: 16 pages, 6 figures. Matches published version. Comments about isotropy added

The absence of supersymmetry or other new physics at the Large Hadron Collider (LHC) has lead many to question naturalness arguments. With Bayesian statistics, we argue that natural models are most probable and that naturalness is not merely an aesthetic principle. We calculate a probabilistic measure of naturalness, the Bayesian evidence, for the Standard Model (SM) with and without quadratic divergences, confirming that the SM with quadratic divergences is improbable. We calculate the Bayesian evidence for the Constrained Minimal Supersymmetric Standard Model (CMSSM) with naturalness priors in three cases: with only the $M_Z$ measurement; with the $M_Z$ measurement and LHC measurements; and with the $M_Z$ measurement, $m_h$ measurement and a hypothetical null result from a $\sqrt{s}=100\,\text{TeV}$ Very Large Hadron Collider (VLHC) with $3000/\text{fb}$. The "fine-tuning price" of the VLHC given LHC results would be $\sim400$, which is slightly less than that of the LHC results given the electroweak scale ($\sim500$)., 19 pages, 3 figures. Closely matches published version, Phys. Rev. D 90, 015010. Added discussion re effective versus UV-complete theories. Minor change to title

We explore the MSSM with 9 free parameters (p9MSSM) that have been selected as a minimum set that allows an investigation of neutralino dark matter and collider signatures while maintaining consistency with several constraints. These include measurement of the dark matter relic density from PLANCK, main properties of the discovered Higgs boson, LHC direct SUSY searches, recent evidence for a Standard Model-like BR(Bs -> \mu+ \mu-), and the measurement of \delta(g-2), plus a number of other electroweak and flavor physics constraints. We perform a simulation of two LHC direct SUSY searches at sqrt(s)=8 TeV: the CMS inclusive \alpha_T search for squarks and gluinos and the CMS electroweak production search with 3l+E_T^miss in the final state. We use the latter to identify the regions of the parameter space, consistent at 2\sigma\ with \delta(g-2), that are not excluded by the direct limits from the electroweak production. We find that they correspond to a neutralino mass in the window 200 GeV, Comment: 43 pages, 16 figures. Discussion of the Higgs sector extended, Fig. 9a (m_stop vs m_h) added. Version published in PRD

We present an updated and extended global analysis of the Constrained MSSM (CMSSM) taking into account new limits on supersymmetry from ~5/fb data sets at the LHC. In particular, in the case of the razor limit obtained by the CMS Collaboration we simulate detector efficiency for the experimental analysis and derive an approximate but accurate likelihood function. We discuss the impact on the global fit of a possible Higgs boson with mass near 125 GeV, as implied by recent data, and of a new improved limit on BR(B_s->\mu\mu). We identify high posterior probability regions of the CMSSM parameters as the stau-coannihilation and the A-funnel region, with the importance of the latter now being much larger due to the combined effect of the above three LHC results and of dark matter relic density. We also find that the focus point region is now disfavored. Ensuing implications for superpartner masses favor even larger values than before, and even lower ranges for dark matter spin-independent cross section, \sigma^{SI}_ps\gamma) and BR(B_s->\mu\mu)., Comment: 24 pages, 17 figures. PRD-approved version; Higgs bounds case removed as obsolete in light of the Higgs discovery

The CMS Collaboration has released the results of its search for supersymmetry, by applying an ${\ensuremath{\alpha}}_{T}$ method to $1.1/\mathrm{fb}$ of data at 7 TeV. The null result excludes (at 95% C.L.) a low-mass region of the Constrained MSSM's parameter space that was previously favored by other experiments. Additionally, the negative result of the XENON100 dark matter search has excluded (at 90% C.L.) values of the spin-independent scattering cross sections ${\ensuremath{\sigma}}_{p}^{\mathrm{SI}}$ as low as ${10}^{\ensuremath{-}8}\text{ }\text{ }\mathrm{pb}$. We incorporate these improved experimental constraints into a global Bayesian fit of the Constrained MSSM by constructing approximate likelihood functions. In the case of the ${\ensuremath{\alpha}}_{T}$ limit, we simulate detector efficiency for the CMS ${\ensuremath{\alpha}}_{T}1.1/\mathrm{fb}$ analysis and validate our method against the official 95% C.L. contour. We identify the 68% and 95% credible posterior regions of the CMSSM parameters, and also find the best-fit point. We find that the credible regions change considerably once a likelihood from ${\ensuremath{\alpha}}_{T}$ is included, in particular, the narrow light Higgs resonance region becomes excluded, but the focus point/horizontal branch region remains allowed at the $1\ensuremath{\sigma}$ level. Adding the limit from XENON100 has a weaker additional effect, in part due to large uncertainties in evaluating ${\ensuremath{\sigma}}_{p}^{\mathrm{SI}}$, which we include in a conservative way, although we find that it reduces the posterior probability of the focus point region to the $2\ensuremath{\sigma}$ level. The new regions of high posterior favor squarks lighter than the gluino and all but one Higgs bosons heavy. The dark matter neutralino mass is found in the range $250\text{ }\text{ }\mathrm{GeV}\ensuremath{\lesssim}{m}_{\ensuremath{\chi}}\ensuremath{\lesssim}343\text{ }\text{ }\mathrm{GeV}$ (at $1\ensuremath{\sigma}$) while, as the result of improved limits from the LHC, the favored range of ${\ensuremath{\sigma}}_{p}^{\mathrm{SI}}$ is pushed down to values below ${10}^{\ensuremath{-}9}\text{ }\text{ }\mathrm{pb}$. We highlight tension between $\ensuremath{\delta}(g\ensuremath{-}2{)}_{\ensuremath{\mu}}^{\mathrm{SUSY}}$ and $\mathcal{B}\mathcal{R}(\overline{B}\ensuremath{\rightarrow}{X}_{s}\ensuremath{\gamma})$, which is exacerbated by including the ${\ensuremath{\alpha}}_{T}$ limit; each constraint favors a different region of the CMSSM's mass parameters.

Experiments are once again under way at the LHC. This time around, however, the mood in the high-energy physics community is pessimistic. There is a growing suspicion that naturalness arguments that predict new physics near the weak scale are faulty and that prospects for a new discovery are limited. We argue that such doubts originate from a misunderstanding of the foundations of naturalness arguments. In spite of the first run at the LHC, which aggravated the little-hierarchy problem, there is no cause for doubting naturalness or natural theories. Naturalness is grounded in Bayesian probability logic - it is not a scientific theory and it makes no sense to claim that it could be falsified or that it is under pressure from experimental data. We should remain optimistic about discovery prospects; natural theories, such as supersymmetry, generally predict new physics close to the weak scale. Furthermore, from a Bayesian perspective, we briefly discuss 't Hooft's technical naturalness and a contentious claim that the little-hierarchy problem hints that the Standard Model is a fundamental theory., 17 pages, 1 figure. Fixed typos, missing references, expanded a few points and added brief discussion of fine-tuning in frequentist statistics

With Bayesian statistics, we investigate the full parameter space of the constrained "next-to-minimal" supersymmetric Standard Model (CNMSSM) with naturalness priors, which were derived in a previous work. In the past, most Bayesian analyses of the CNMSSM ignored naturalness of the electroweak (EW) scale by making prejudicial assumptions for parameters defined at the EW scale. We test the CNMSSM against the CMSSM with Bayesian evidence, which, with naturalness priors, incorporates a penalty for fine-tuning of the EW scale. With the evidence, we measure credibility with respect to all measurements, including the EW scale and LHC direct searches. We find that the evidence in favor of the CNMSSM versus the CMSSM is "positive" to "strong" but that if one ignores the $\mu$-problem, the evidence is "barely worth mentioning" to "positive." The $\mu$-problem significantly influences our findings. Unless one considers the $\mu$-problem, the evidence in favor of the CNMSSM versus the CMSSM is at best "positive," which is two grades below "very strong." We, furthermore, identify the most probable regions of the CMSSM and CNMSSM parameter spaces and examine prospects for future discovery at hadron colliders., Comment: 28 pages, 11 color figures. Closely matches version published in Eur.Phys.J. C. Minor changes to title and abstract, and additional information about scanning settings. Conclusions unchanged

Discussions are underway for a high-energy proton-proton collider. Two preliminary ideas are the $\sqrt{s}=33$ TeV HE-LHC and the $\sqrt{s}=100$ TeV VLHC. With Bayesian statistics, we calculate the probabilities that the LHC, HE-LHC and VLHC discover SUSY in the future, assuming that nature is described by the CMSSM and given the experimental data from the LHC, LUX and Planck. We find that the LHC with $300$/fb at $\sqrt{s}=14$ TeV has a $15$-$75%$ probability of discovering SUSY. Should that run fail to discover SUSY, the probability of discovering SUSY with $3000$/fb is merely $1$-$10%$. Were SUSY to remain undetected at the LHC, the HE-LHC would have a $35$-$85%$ probability of discovering SUSY with $3000$/fb. The VLHC, on the other hand, ought to be definitive; the probability of it discovering SUSY, assuming that the CMSSM is the correct model, is $100%$.