MFV Reductions of MSSM Parameter Space

The 100+ free parameters of the minimal supersymmetric standard model (MSSM) make it computationally difficult to compare systematically with data, motivating the study of specific parameter reductions such as the cMSSM and pMSSM. Here we instead study the reductions of parameter space implied by using minimal flavour violation (MFV) to organise the R-parity conserving MSSM, with a view towards systematically building in constraints on flavour-violating physics. Within this framework the space of parameters is reduced by expanding soft supersymmetry-breaking terms in powers of the Cabibbo angle, leading to a 24-, 30- or 42-parameter framework (which we call MSSM-24, MSSM-30, and MSSM-42 respectively), depending on the order kept in the expansion. We provide a Bayesian global fit to data of the MSSM-30 parameter set to show that this is manageable with current tools. We compare the MFV reductions to the 19-parameter pMSSM choice and show that the pMSSM is not contained as a subset. The MSSM-30 analysis favours a relatively lighter TeV-scale pseudoscalar Higgs boson and $\tan \beta \sim 10$ with multi-TeV sparticles.Comment: 2nd version, minor comments and references added, accepted for publication in JHE

The impact of the ATLAS zero-lepton, jets and missing momentum search on a CMSSM fit

Recent ATLAS data significantly extend the exclusion limits for supersymmetric particles. We examine the impact of such data on global fits of the constrained minimal supersymmetric standard model (CMSSM) to indirect and cosmological data. We calculate the likelihood map of the ATLAS search, taking into account systematic errors on the signal and on the background. We validate our calculation against the ATLAS determinaton of 95% confidence level exclusion contours. A previous CMSSM global fit is then re-weighted by the likelihood map, which takes a bite at the high probability density region of the global fit, pushing scalar and gaugino masses up.Comment: 16 pages, 7 figures. v2 has bigger figures and fixed typos. v3 has clarified explanation of our handling of signal systematic

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

Sphalerons and the Electroweak Phase Transition in Models with Higher Scalar Representations

In this work we investigate the sphaleron solution in a $SU(2)\times U(1)_X$ gauge theory, which also encompasses the Standard Model, with higher scalar representation(s) ($J^{(i)},X^{(i)}$). We show that the field profiles describing the sphaleron in higher scalar multiplet, have similar trends like the doublet case with respect to the radial distance. We compute the sphaleron energy and find that it scales linearly with the vacuum expectation value of the scalar field and its slope depends on the representation. We also investigate the effect of $U(1)$ gauge field and find that it is small for the physical value of the mixing angle, $\theta_{W}$ and resembles the case for the doublet. For higher representations, we show that the criterion for strong first order phase transition, $v_{c}/T_{c}>\eta$, is relaxed with respect to the doublet case, i.e. $\eta<1$.Comment: 20 pages, 5 figures & 1 table, published versio

Tuning supersymmetric models at the LHC: A comparative analysis at two-loop level

We provide a comparative study of the fine tuning amount (Delta) at the two-loop leading log level in supersymmetric models commonly used in SUSY searches at the LHC. These are the constrained MSSM (CMSSM), non-universal Higgs masses models (NUHM1, NUHM2), non-universal gaugino masses model (NUGM) and GUT related gaugino masses models (NUGMd). Two definitions of the fine tuning are used, the first (Delta_{max}) measures maximal fine-tuning wrt individual parameters while the second (Delta_q) adds their contribution in "quadrature". As a direct result of two theoretical constraints (the EW minimum conditions), fine tuning (Delta_q) emerges as a suppressing factor (effective prior) of the averaged likelihood (under the priors), under the integral of the global probability of measuring the data (Bayesian evidence p(D)). For each model, there is little difference between Delta_q, Delta_{max} in the region allowed by the data, with similar behaviour as functions of the Higgs, gluino, stop mass or SUSY scale (m_{susy}=(m_{\tilde t_1} m_{\tilde t_2})^{1/2}) or dark matter and g-2 constraints. The analysis has the advantage that by replacing any of these mass scales or constraints by their latest bounds one easily infers for each model the value of Delta_q, Delta_{max} or vice versa. For all models, minimal fine tuning is achieved for M_{higgs} near 115 GeV with a Delta_q\approx Delta_{max}\approx 10 to 100 depending on the model, and in the CMSSM this is actually a global minimum. Due to a strong ($\approx$ exponential) dependence of Delta on M_{higgs}, for a Higgs mass near 125 GeV, the above values of Delta_q\approx Delta_{max} increase to between 500 and 1000. Possible corrections to these values are briefly discussed.Comment: 23 pages, 46 figures; references added; some clarifications (section 2

Interpreting LHC SUSY searches in the phenomenological MSSM

We interpret within the phenomenological MSSM (pMSSM) the results of SUSY searches published by the CMS collaboration based on the first ~1 fb^-1 of data taken during the 2011 LHC run at 7 TeV. The pMSSM is a 19-dimensional parametrization of the MSSM that captures most of its phenomenological features. It encompasses, and goes beyond, a broad range of more constrained SUSY models. Performing a global Bayesian analysis, we obtain posterior probability densities of parameters, masses and derived observables. In contrast to constraints derived for particular SUSY breaking schemes, such as the CMSSM, our results provide more generic conclusions on how the current data constrain the MSSM.Comment: 15 pages, 7 figures; minor revision, some references and a comment on prior dependence added; version accepted by JHE

Using rates to measure mixed modulus-anomaly mediated supersymmetry breaking at the LHC

If SUSY is discovered at the LHC, the task will immediately turn to determining the model of SUSY breaking. Here, we employ a Mixed Modulus-Anomaly Mediated SUSY Breaking (MMAMSB) model with very similar LHC phenomenology to the more conventionally studied Constrained Minimal SUSY Model (CMSSM) and minimal Anomaly Mediated SUSY Breaking (mAMSB) models. We then study whether the models can be distinguished and measured. If we only fit to the various mass edges and mass end-points from cascade decay chains that are normally studied, a unique determination and measurement of the model is problematic without substantial amounts of LHC data. However, if event rate information is included, we can quickly distinguish and measure the correct SUSY model and exclude alternatives.Comment: 28 pages, 11 figure

Neutralino versus axion/axino cold dark matter in the 19 parameter SUGRA model

We calculate the relic abundance of thermally produced neutralino cold dark matter in the general 19 parameter supergravity (SUGRA-19) model. A scan over GUT scale parameters reveals that models with a bino-like neutralino typically give rise to a dark matter density \Omega_{\tz_1}h^2\sim 1-1000, i.e. between 1 and 4 orders of magnitude higher than the measured value. Models with higgsino or wino cold dark matter can yield the correct relic density, but mainly for neutralino masses around 700-1300 GeV. Models with mixed bino-wino or bino-higgsino CDM, or models with dominant co-annihilation or A-resonance annihilation can yield the correct abundance, but such cases are extremely hard to generate using a general scan over GUT scale parameters; this is indicative of high fine-tuning of the relic abundance in these cases. Requiring that m_{\tz_1}\alt 500 GeV (as a rough naturalness requirement) gives rise to a minimal probably dip in parameter space at the measured CDM abundance. For comparison, we also scan over mSUGRA space with four free parameters. Finally, we investigate the Peccei-Quinn augmented MSSM with mixed axion/axino cold dark matter. In this case, the relic abundance agrees more naturally with the measured value. In light of our cumulative results, we conclude that future axion searches should probe much more broadly in axion mass, and deeper into the axion coupling.Comment: 23 pages including 17 .eps figure

A Profile Likelihood Analysis of the Constrained MSSM with Genetic Algorithms

The Constrained Minimal Supersymmetric Standard Model (CMSSM) is one of the simplest and most widely-studied supersymmetric extensions to the standard model of particle physics. Nevertheless, current data do not sufficiently constrain the model parameters in a way completely independent of priors, statistical measures and scanning techniques. We present a new technique for scanning supersymmetric parameter spaces, optimised for frequentist profile likelihood analyses and based on Genetic Algorithms. We apply this technique to the CMSSM, taking into account existing collider and cosmological data in our global fit. We compare our method to the MultiNest algorithm, an efficient Bayesian technique, paying particular attention to the best-fit points and implications for particle masses at the LHC and dark matter searches. Our global best-fit point lies in the focus point region. We find many high-likelihood points in both the stau co-annihilation and focus point regions, including a previously neglected section of the co-annihilation region at large m_0. We show that there are many high-likelihood points in the CMSSM parameter space commonly missed by existing scanning techniques, especially at high masses. This has a significant influence on the derived confidence regions for parameters and observables, and can dramatically change the entire statistical inference of such scans.Comment: 47 pages, 8 figures; Fig. 8, Table 7 and more discussions added to Sec. 3.4.2 in response to referee's comments; accepted for publication in JHE