A review of naturalness and dark matter prediction for the Higgs mass in MSSM and beyond

Within a two-loop leading-log approximation, we review the prediction for the lightest Higgs mass (m_h) in the framework of constrained MSSM (CMSSM), derived from the naturalness requirement of minimal fine-tuning (Delta) of the electroweak scale and dark matter consistency. As a result, the Higgs mass is predicted to be just above the LEP2 bound, m_h=115.9\pm 2 GeV, corresponding to a minimal Delta=17.8, value obtained from consistency with electroweak and WMAP (3\sigma) constraints, but without the LEP2 bound. Due to quantum corrections (largely QCD ones for m_h above LEP2 bound), Delta grows \approx exponentially on either side of the above value of m_h, which stresses the relevance of this prediction. A value m_h>121 (126) GeV cannot be accommodated within the CMSSM unless one accepts a fine-tuning cost worse than Delta>100 (1000), respectively. We review how the above prediction for m_h and Delta changes under the addition of new physics beyond the MSSM Higgs sector, parametrized by effective operators of dimensions d=5 and d=6. For d=5 operators, one can obtain values m_h\leq 130 GeV for Delta<10. The size of the supersymmetric correction that each individual operator of d=6 brings to the value of m_h for points with Delta<100, is found to be small, of few (<4) GeV for M=8 TeV, where M is the scale of new physics. This value decreases (increases) by approximately 1 GeV for a 1 TeV increase (decrease) of the scale M. The relation of these results to the Atlas/CMS supersymmetry exclusion limits is presented together with their impact for the CMSSM regions of lowest fine-tuning.Comment: 27 pages, 19 figures; (new figures and references added; improved presentation

Objective estimation of visual Acuity with preferential looking

Purpose: A novel Preferential Looking (PL) procedure that uses quantitative analysis of visual scanning parameters is presented. Methods: Nine adult subjects were presented with a set of 14 visual stimuli (stimuli included 3 uniform grey fields and 1 field with black and white square wave gratings) spanning the range of spatial frequencies from 1.5 cycles/degree to 35.1 cycles/degree (1.3 logMAR to -0.07 logMAR). A remote gaze-tracking system was used to monitor the subject's eye movements and the relative fixation time (RFT) on the grating target. Subsequently, a four alternative forced-choice psychophysical test (4AFC) was performed with the same visual stimuli. Results: For visual stimuli for which the gratings' positions in the 4AFC test were identified correctly in 100% of the trials ("reliably discriminated"), the mean RFT was 72.5% ± 9.0%. For stimuli for which the spatial frequencies were higher than the subject's psychophysically determined VA threshold ("non-discriminated"), the mean RFT was 25.3% ± 8.5%. Using three repeated trials at each spatial frequency and a VA detector that is based on the conditional probability density functions of the RFT, the average VA was underestimated by 0.06 logMAR (range: 0.00 logMAR to 0.20 logMAR). Conclusions: In adults, automated quantitative analysis of visual scanning patterns can be used to estimate objectively and rapidly (210 seconds) VA with a mean error of 0.06 logMAR. The novel approach may form the basis for PL procedures that are more objective and accurate than the traditional clinical PL procedures

Fine-tuning implications for complementary dark matter and LHC SUSY searches

The requirement that SUSY should solve the hierarchy problem without undue fine-tuning imposes severe constraints on the new supersymmetric states. With the MSSM spectrum and soft SUSY breaking originating from universal scalar and gaugino masses at the Grand Unification scale, we show that the low-fine-tuned regions fall into two classes that will require complementary collider and dark matter searches to explore in the near future. The first class has relatively light gluinos or squarks which should be found by the LHC in its first run. We identify the multijet plus E_T^miss signal as the optimal channel and determine the discovery potential in the first run. The second class has heavier gluinos and squarks but the LSP has a significant Higgsino component and should be seen by the next generation of direct dark matter detection experiments. The combined information from the 7 TeV LHC run and the next generation of direct detection experiments can test almost all of the CMSSM parameter space consistent with dark matter and EW constraints, corresponding to a fine-tuning not worse than 1:100. To cover the complete low-fine-tuned region by SUSY searches at the LHC will require running at the full 14 TeV CM energy; in addition it may be tested indirectly by Higgs searches covering the mass range below 120 GeV.Comment: References added. Version accepted for publication in JHE

Lifting representations of finite reductive groups: a character relation

Given a connected reductive group $\tilde{G}$ over a finite field $k$, and a semisimple $k$-automorphism $\varepsilon$ of $\tilde{G}$ of finite order, let $G$ denote the connected part of the group of $\varepsilon$-fixed points. Then there exists a lifting from packets of representations of $G(k)$ to packets for $\tilde{G}(k)$. In the case of Deligne-Lusztig representations, we show that this lifting satisfies a character relation analogous to that of Shintani.Comment: Minor errors corrected, proofs streamlined. Main result slightly generalized, restated to emphasize analogy with stabilit

If you find a dead bird— and wonder if it has the bird flu virus

South Dakotans have been vigilant, sending dead blue jays, magpies, crows, hawks, owls, and eagles into the South Dakota Department of Health, seeking to know if the birds died fromWest Nile virus (WNV). We can stop looking. WNV is in South Dakota to stay. There is nothing further we can learn from testing birds forWNV. Therefore, if you find an individual dead blue jay, magpie, or crow, dispose of the bird, taking the safety precautions listed on the next page. But we cannot let down our guard. Birds are considered to be reservoirs for almost all influenza virsues, and occasionally a lethal new virus comes along. We must be on the lookout for a new avian influenza virus known as Asian High Path H5N1 in wild birds, particularly if we come across groups of dead ducks, geese, pheasants, chickens, or turkeys

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