The Jeffreys-Lindley Paradox and Discovery Criteria in High Energy Physics

The Jeffreys-Lindley paradox displays how the use of a p-value (or number of standard deviations z) in a frequentist hypothesis test can lead to an inference that is radically different from that of a Bayesian hypothesis test in the form advocated by Harold Jeffreys in the 1930s and common today. The setting is the test of a well-specified null hypothesis (such as the Standard Model of elementary particle physics, possibly with "nuisance parameters") versus a composite alternative (such as the Standard Model plus a new force of nature of unknown strength). The p-value, as well as the ratio of the likelihood under the null hypothesis to the maximized likelihood under the alternative, can strongly disfavor the null hypothesis, while the Bayesian posterior probability for the null hypothesis can be arbitrarily large. The academic statistics literature contains many impassioned comments on this paradox, yet there is no consensus either on its relevance to scientific communication or on its correct resolution. The paradox is quite relevant to frontier research in high energy physics. This paper is an attempt to explain the situation to both physicists and statisticians, in the hope that further progress can be made.Comment: v4: Continued editing for clarity. Figure added. v5: Minor fixes to biblio. Same as published version except for minor copy-edits, Synthese (2014). v6: fix typos, and restore garbled sentence at beginning of Sec 4 to v

Constraining Supersymmetry using the relic density and the Higgs boson

Recent measurements by Planck, LHC experiments, and Xenon100 have significant impact on supersymmetric models and their parameters. We first illustrate the constraints in the mSUGRA plane and then perform a detailed analysis of the general MSSM with 13 free parameters. Using SFitter, Bayesian and Profile Likelihood approaches are applied and their results compared. The allowed structures in the parameter spaces are largely defined by different mechanisms of dark matter annihilation in combination with the light Higgs mass prediction. In mSUGRA the pseudoscalar Higgs funnel and stau co-annihilation processes are still avoiding experimental pressure. In the MSSM stau co-annihilation, the light Higgs funnel, a mixed bino--higgsino region including the heavy Higgs funnel, and a large higgsino region predict the correct relic density. Volume effects and changes in the model parameters impact the extracted mSUGRA and MSSM parameter regions in the Bayesian analysis

Long lived charginos in Natural SUSY?

Supersymmetric models with a small neutralino-chargino mass difference, and as a result metastable charginos, have been a popular topic of investigation in collider phenomenology, e.g. in anomaly-mediated models of supersymmetry breaking. Recently, the absence of any supersymmetric signal at the 8 TeV LHC data has led to significant interest in the so-called Natural SUSY models with light higgsinos. These models also have a naturally small neutralino-chargino mass difference. However, we show here that when relevant indirect constraints from results at the LHC and elsewhere are applied, this possibility is heavily constrained within the Minimal Supersymmetric Standard Model (MSSM): massive metastable higgsinos are not a signature of Natural SUSY.Comment: Extended discussion, updated references, matches version to appear in JHE

On the detectability of the CMSSM light Higgs boson at the Tevatron

We examine the prospects of detecting the light Higgs h^0 of the Constrained MSSM at the Tevatron. To this end we explore the CMSSM parameter space with \mu>0, using a Markov Chain Monte Carlo technique, and apply all relevant collider and cosmological constraints including their uncertainties, as well as those of the Standard Model parameters. Taking 50 GeV < m_{1/2}, m_0 < 4 TeV, |A_0| < 7 TeV and 2 < tan(beta) < 62 as flat priors and using the formalism of Bayesian statistics we find that the 68% posterior probability region for the h^0 mass lies between 115.4 GeV and 120.4 GeV. Otherwise, h^0 is very similar to the Standard Model Higgs boson. Nevertheless, we point out some enhancements in its couplings to bottom and tau pairs, ranging from a few per cent in most of the CMSSM parameter space, up to several per cent in the favored region of tan(beta)\sim 50 and the pseudoscalar Higgs mass of m_A\lsim 1 TeV. We also find that the other Higgs bosons are typically heavier, although not necessarily much heavier. For values of the h^0 mass within the 95% probability range as determined by our analysis, a 95% CL exclusion limit can be set with about 2/fb of integrated luminosity per experiment, or else with 4/fb (12/fb) a 3 sigma evidence (5 sigma discovery) will be guaranteed. We also emphasize that the alternative statistical measure of the mean quality-of-fit favors a somewhat lower Higgs mass range; this implies even more optimistic prospects for the CMSSM light Higgs search than the more conservative Bayesian approach. In conclusion, for the above CMSSM parameter ranges, especially m_0, either some evidence will be found at the Tevatron for the light Higgs boson or, at a high confidence level, the CMSSM will be ruled out.Comment: JHEP versio

Direct Constraints on Minimal Supersymmetry from Fermi-LAT Observations of the Dwarf Galaxy Segue 1

The dwarf galaxy Segue 1 is one of the most promising targets for the indirect detection of dark matter. Here we examine what constraints 9 months of Fermi-LAT gamma-ray observations of Segue 1 place upon the Constrained Minimal Supersymmetric Standard Model (CMSSM), with the lightest neutralino as the dark matter particle. We use nested sampling to explore the CMSSM parameter space, simultaneously fitting other relevant constraints from accelerator bounds, the relic density, electroweak precision observables, the anomalous magnetic moment of the muon and B-physics. We include spectral and spatial fits to the Fermi observations, a full treatment of the instrumental response and its related uncertainty, and detailed background models. We also perform an extrapolation to 5 years of observations, assuming no signal is observed from Segue 1 in that time. Results marginally disfavour models with low neutralino masses and high annihilation cross-sections. Virtually all of these models are however already disfavoured by existing experimental or relic density constraints.Comment: 22 pages, 5 figures; added extra scans with extreme halo parameters, expanded introduction and discussion in response to referee's comment

Constraints on Extended Neutral Gauge Structures

Indirect precision data are used to constrain the masses of possible extra Z^prime bosons and their mixings with the ordinary Z. We study a variety of Z^prime bosons as they appear in E_6 and left-right unification models, the sequential Z boson, and the example of an additional U(1) in a concrete model from heterotic string theory. In all cases the mixings are severely constrained (sin theta < 0.01). The lower mass limits are generally of the order of several hundred GeV and competitive with collider bounds. The exception is the Z_psi boson, whose vector couplings vanish and whose limits are weaker. The results change little when the rho parameter is allowed, which corresponds to a completely arbitrary Higgs sector. On the other hand, in specific models with minimal Higgs structures the limits are generally pushed into the TeV region.Comment: 13 pages of LaTeX2e, 6 figure

Dark matter protohalos in MSSM-9 and implications for direct and indirect detection

We study how the kinetic decoupling of dark matter (DM) within a minimal supersymmetric extension of the standard model, by adopting nine independent parameters (MSSM-9), could improve our knowledge of the properties of the DM protohalos. We show that the most probable neutralino mass regions, which satisfy the relic density and the Higgs mass contraints, are those with the lightest supersymmetric neutralino mass around 1 TeV and 3 TeV, corresponding to Higgsino-like and Wino-like neutralino, respectively. The kinetic decoupling temperature in the MSSM-9 scenario leads to a most probable protohalo mass in a range of $M_{\mathrm{ph}}\sim 10^{-12}-10^{-7}\,M_\odot$. The part of the region closer to 2 TeV gives also important contributions from the neutralino-stau co-annihilation, reducing the effective annihilation rate in the early Universe. We also study how the size of the smallest DM substructures correlates to experimental signatures, such as the spin-dependent and spin-independent scattering cross sections, relevant for direct detection of DM. Improvements on the spin-independent sensitivity might reduce the most probable range of the protohalo mass between $\sim$10$^{-9}\,M_\odot$ and $\sim$10$^{-7}\,M_\odot$, while the expected spin-dependent sensitivity provides weaker constraints. We show how the boost of the luminosity due to DM annihilation increases, depending on the protohalo mass. In the Higgsino case, the protohalo mass is lower than the canonical value often used in the literature ($\sim$10$^{-6}\,M_\odot$), while $\langle\sigma v\rangle$ does not deviate from $\langle\sigma v\rangle\sim 10^{-26}$ cm$^3$ s$^{-1}$; there is no significant enhancement of the luminosity. On the contrary, in the Wino case, the protohalo mass is even lighter, and $\langle\sigma v\rangle$ is two orders of magnitude larger; as its consequence, we see a substantial enhancement of the luminosity.Comment: 26 pages, 8 figure