Challenges of Profile Likelihood Evaluation in Multi-Dimensional SUSY Scans

Statistical inference of the fundamental parameters of supersymmetric theories is a challenging and active endeavor. Several sophisticated algorithms have been employed to this end. While Markov-Chain Monte Carlo (MCMC) and nested sampling techniques are geared towards Bayesian inference, they have also been used to estimate frequentist confidence intervals based on the profile likelihood ratio. We investigate the performance and appropriate configuration of MultiNest, a nested sampling based algorithm, when used for profile likelihood-based analyses both on toy models and on the parameter space of the Constrained MSSM. We find that while the standard configuration is appropriate for an accurate reconstruction of the Bayesian posterior, the profile likelihood is poorly approximated. We identify a more appropriate MultiNest configuration for profile likelihood analyses, which gives an excellent exploration of the profile likelihood (albeit at a larger computational cost), including the identification of the global maximum likelihood value. We conclude that with the appropriate configuration MultiNest is a suitable tool for profile likelihood studies, indicating previous claims to the contrary are not well founded.Comment: 21 pages, 9 figures, 1 table; minor changes following referee report. Matches version accepted by JHE

Neutrino Coherent Scattering Rates at Direct Dark Matter Detectors

Neutrino-induced recoil events may constitute a background to direct dark matter searches, particularly for those detectors that strive to reach the ton-scale and beyond. This paper discusses the expected neutrino-induced background spectrum due to several of the most important sources, including solar, atmospheric, and diffuse supernova neutrinos. The largest rate arises from $^8$B produced solar neutrinos, providing upwards of $\sim 10^3$ events per ton-year over all recoil energies for the heaviest nuclear targets. However the majority of these $^8$B events are expected to be below the recoil threshold of modern detectors. The remaining neutrino sources are found to constitute a background to the WIMP-induced recoil rate only if the WIMP-nucleon cross section is less than $10^{-12}$ pb. Finally the sensitivity to diffuse supernova neutrino flux for non-electron neutrino flavors is discussed, and projected flux limits are compared with existing flux limits

Predictions for Constrained Minimal Supersymmetry with Bottom-Tau Mass Unification

We examine the Constrained Minimal Supersymmetric Standard Model (CMSSM) with an additional requirement of strict b - tau unification in the region of small tan(beta). We find that the parameter space becomes completely limited below about 1 TeV by physical constraints alone, without a fine-tuning constraint. We study the resulting phenomenological consequences, and point out several ways of falsifying the adopted b - tau unification assumption. We also comment on the effect of a constraint from the non-observation of proton decay.Comment: Michigan preprint UM-TH-94-03, LaTeX, 18 pages with inline figures (figures included in uuencoded file). Complete PS file also available by anonymous FTP to williams.physics.lsa.umich.edu in /pub/preprints/UM-TH-94-03.ps.Z or by e-mailing reques

The Gravitino-Stau Scenario after Catalyzed BBN

We consider the impact of Catalyzed Big Bang Nucleosynthesis on theories with a gravitino LSP and a charged slepton NLSP. In models where the gravitino to gaugino mass ratio is bounded from below, such as gaugino-mediated SUSY breaking, we derive a lower bound on the gaugino mass parameter m_1/2. As a concrete example, we determine the parameter space of gaugino mediation that is compatible with all cosmological constraints.Comment: 1+14 pages, 6 figures; v2: minor clarifications, 1 reference added, matches version to appear in JCA

Hydrodynamics of galactic dark matter

We consider simple hydrodynamical models of galactic dark matter in which the galactic halo is a self-gravitating and self-interacting gas that dominates the dynamics of the galaxy. Modeling this halo as a sphericaly symmetric and static perfect fluid satisfying the field equations of General Relativity, visible barionic matter can be treated as ``test particles'' in the geometry of this field. We show that the assumption of an empirical ``universal rotation curve'' that fits a wide variety of galaxies is compatible, under suitable approximations, with state variables characteristic of a non-relativistic Maxwell-Boltzmann gas that becomes an isothermal sphere in the Newtonian limit. Consistency criteria lead to a minimal bound for particle masses in the range $30 \hbox{eV} \leq m \leq 60 \hbox{eV}$ and to a constraint between the central temperature and the particles mass. The allowed mass range includes popular supersymmetric particle candidates, such as the neutralino, axino and gravitino, as well as lighter particles ($m\approx$ keV) proposed by numerical N-body simulations associated with self-interactive CDM and WDM structure formation theories.Comment: LaTeX article style, 16 pages including three figures. Final version to appear in Classical and Quantum Gravit

Reheating Temperature and Gauge Mediation Models of Supersymmetry Breaking

For supersymmetric theories with gravitino dark matter, the maximal reheating temperature consistent with big bang nucleosynthesis bounds arises when the physical gaugino masses are degenerate. We consider the cases of a stau or sneutrino next-to-lightest superpartner, which have relatively less constraint from big bang nucleosynthesis. The resulting parameter space is consistent with leptogenesis requirements, and can be reached in generalized gauge mediation models. Such models illustrate a class of theories that overcome the well-known tension between big bang nucleosynthesis and leptogenesis.Comment: 30 pages, 4 figures; v2: refs adde

Supersymmetry Without Prejudice

We begin an exploration of the physics associated with the general CP-conserving MSSM with Minimal Flavor Violation, the pMSSM. The 19 soft SUSY breaking parameters in this scenario are chosen so as to satisfy all existing experimental and theoretical constraints assuming that the WIMP is a conventional thermal relic, ie, the lightest neutralino. We scan this parameter space twice using both flat and log priors for the soft SUSY breaking mass parameters and compare the results which yield similar conclusions. Detailed constraints from both LEP and the Tevatron searches play a particularly important role in obtaining our final model samples. We find that the pMSSM leads to a much broader set of predictions for the properties of the SUSY partners as well as for a number of experimental observables than those found in any of the conventional SUSY breaking scenarios such as mSUGRA. This set of models can easily lead to atypical expectations for SUSY signals at the LHC.Comment: 61 pages, 24 figs. Refs., figs, and text added, typos fixed; This version has reduced/bitmapped figs. For a version with better figs please go to http://www.slac.stanford.edu/~rizz

Axions and the Strong CP Problem

Current upper bounds of the neutron electric dipole moment constrain the physically observable quantum chromodynamic (QCD) vacuum angle $|\bar\theta| \lesssim 10^{-11}$. Since QCD explains vast experimental data from the 100 MeV scale to the TeV scale, it is better to explain this smallness of $|\bar\theta|$ in the QCD framework, which is the strong \Ca\Pa problem. Now, there exist two plausible solutions to this problem, one of which leads to the existence of the very light axion. The axion decay constant window, $10^9\ {\gev}\lesssim F_a\lesssim 10^{12} \gev$for a${\cal O}(1)$initial misalignment angle$\theta_1$, has been obtained by astrophysical and cosmological data. For$F_a\gtrsim 10^{12}$GeV with$\theta_1<{\cal O}(1)$, axions may constitute a significant fraction of dark matter of the universe. The supersymmetrized axion solution of the strong \Ca\Pa problem introduces its superpartner the axino which might have affected the universe evolution significantly. Here, we review the very light axion (theory, supersymmetrization, and models) with the most recent particle, astrophysical and cosmological data, and present prospects for its discovery.Comment: 47 pages with 32 figure

Dark Matter in the MSSM

We have recently examined a large number of points in the parameter space of the phenomenological MSSM, the 19-dimensional parameter space of the CP-conserving MSSM with Minimal Flavor Violation. We determined whether each of these points satisfied existing experimental and theoretical constraints. This analysis provides insight into general features of the MSSM without reference to a particular SUSY breaking scenario or any other assumptions at the GUT scale. This study opens up new possibilities for SUSY phenomenology both in colliders and in astrophysical experiments. Here we shall discuss the implications of this analysis relevant to the study of dark matter.Comment: 27 pages, 19 figs; Journal version in NJP issue "Focus on Dark Matter and Particle Physics". Previous version had 26 pages, 19 figures. Text and some figures have been update

Study of Constrained Minimal Supersymmetry

Taking seriously phenomenological indications for supersymmetry, we have made a detailed study of unified minimal SUSY, including effects at the few percent level in a consistent fashion. We report here a general analysis without choosing a particular unification gauge group. We find that the encouraging SUSY unification results of recent years do survive the challenge of a more complete and accurate analysis. Taking into account effects at the 5-10% level leads to several improvements of previous results, and allows us to sharpen our predictions for SUSY in the light of unification. We perform a thorough study of the parameter space. The results form a well-defined basis for comparing the physics potential of different facilities. Very little of the acceptable parameter space has been excluded by LEP or FNAL so far, but a significant fraction can be covered when these accelerators are upgraded. A number of initial applications to the understanding of the SUSY spectrum, detectability of SUSY at LEP II or FNAL, BR($b\to s\gamma$), Width($Z\to b\bar b$), dark matter, etc, are included in a separate section. We formulate an approach to extracting SUSY parameters from data when superpartners are detected. For small tan(beta) or large $m_top$ both $M_half$ and $M_0$ are entirely bounded from above at O(1 tev) without having to use a fine-tuning constraint.Comment: Michigan preprint UM-TH-93-24, LaTeX, 60 pages without figures. Complete paper with inline figures available by anonymous ftp to williams.physics.lsa.umich.edu in /pub/preprints/UM-TH-93-24.ps.Z (uncompresses to 10MB / 77 pages), or by e-mailing reques