Constrained invariant mass distributions in cascade decays. The shape of the "mqllm_{qll}-threshold" and similar distributions

Considering the cascade decay $D\to c C \to c b B \to c b a A$ in which $D,C,B,A$ are massive particles and $c,b,a$ are massless particles, we determine for the first time the shape of the distribution of the invariant mass of the three massless particles $m_{abc}$ for the sub-set of decays in which the invariant mass $m_{ab}$ of the last two particles in the chain is (optionally) constrained to lie inside an arbitrary interval, $m_{ab} \in [ m_{ab}^\text{cut min}, m_{ab}^\text{cut max}]$. An example of an experimentally important distribution of this kind is the ``$m_{qll}$ threshold'' -- which is the distribution of the combined invariant mass of the visible standard model particles radiated from the hypothesised decay of a squark to the lightest neutralino via successive two body decay,: \squark \to q \ntlinoTwo \to q l \slepton \to q l l \ntlinoOne , in which the experimenter requires additionally that $m_{ll}$ be greater than ${m_{ll}^{max}}/\sqrt{2}$. The location of the ``foot'' of this distribution is often used to constrain sparticle mass scales. The new results presented here permit the location of this foot to be better understood as the shape of the distribution is derived. The effects of varying the position of the $m_{ll}$ cut(s) may now be seen more easily.Comment: 12 pages, 3 figure

Statistical coverage for supersymmetric parameter estimation: a case study with direct detection of dark matter

Models of weak-scale supersymmetry offer viable dark matter (DM) candidates. Their parameter spaces are however rather large and complex, such that pinning down the actual parameter values from experimental data can depend strongly on the employed statistical framework and scanning algorithm. In frequentist parameter estimation, a central requirement for properly constructed confidence intervals is that they cover true parameter values, preferably at exactly the stated confidence level when experiments are repeated infinitely many times. Since most widely-used scanning techniques are optimised for Bayesian statistics, one needs to assess their abilities in providing correct confidence intervals in terms of the statistical coverage. Here we investigate this for the Constrained Minimal Supersymmetric Standard Model (CMSSM) when only constrained by data from direct searches for dark matter. We construct confidence intervals from one-dimensional profile likelihoods and study the coverage by generating several pseudo-experiments for a few benchmark sets of pseudo-true parameters. We use nested sampling to scan the parameter space and evaluate the coverage for the benchmarks when either flat or logarithmic priors are imposed on gaugino and scalar mass parameters. The sampling algorithm has been used in the configuration usually adopted for exploration of the Bayesian posterior. We observe both under- and over-coverage, which in some cases vary quite dramatically when benchmarks or priors are modified. We show how most of the variation can be explained as the impact of explicit priors as well as sampling effects, where the latter are indirectly imposed by physicality conditions. For comparison, we also evaluate the coverage for Bayesian credible intervals, and observe significant under-coverage in those cases.Comment: 30 pages, 5 figures; v2 includes major updates in response to referee's comments; extra scans and tables added, discussion expanded, typos corrected; matches published versio

SUSY Stops at a Bump

We discuss collider signatures of the "natural supersymmetry" scenario with baryon-number violating R-parity violation. We argue that this is one of the few remaining viable incarnations of weak scale supersymmetry consistent with full electroweak naturalness. We show that this intriguing and challenging scenario contains distinctive LHC signals, resonances of hard jets in conjunction with relatively soft leptons and missing energy, which are easily overlooked by existing LHC searches. We propose novel strategies for distinguishing these signals above background, and estimate their potential reach at the 8 TeV LHC. We show that other multi-lepton signals of this scenario can be seen by currently existing searches with increased statistics, but these opportunities are more spectrum-dependent.Comment: 23 pages, 7 figures, 3 tables. V2: spectrum discussion corrected, most of the changes are in Sec. 2. Benchmarks, analysis and conclusions unchanged. References adde

The stransverse mass, MT2, in special cases

This document describes some special cases in which the stransverse mass, MT2, may be calculated by non-iterative algorithms. The most notable special case is that in which the visible particles and the hypothesised invisible particles are massless -- a situation relevant to its current usage in the Large Hadron Collider as a discovery variable, and a situation for which no analytic answer was previously known. We also derive an expression for MT2 in another set of new (though arguably less interesting) special cases in which the missing transverse momentum must point parallel or anti parallel to the visible momentum sum. In addition, we find new derivations for already known MT2 solutions in a manner that maintains manifest contralinear boost invariance throughout, providing new insights into old results. Along the way, we stumble across some unexpected results and make conjectures relating to geometric forms of M_eff and H_T and their relationship to MT2.Comment: 11 pages, no figures. v2 corrects minor typos. v3 corrects an incorrect statement in footnote 8 and inserts a missing term in eq (3.9). v4 and v5 correct minor typos spotted by reader

Supersymmetric models with minimal flavour violation and their running

We revisit the formulation of the principle of minimal flavor violation (MFV) in the minimal supersymmetric extension of the standard model, both at moderate and large tan(beta), and with or without new CP-violating phases. We introduce a counting rule which keeps track of the highly hierarchical structure of the Yukawa matrices. In this manner, we are able to control systematically which terms can be discarded in the soft SUSY breaking part of the Lagrangian. We argue that for the implementation of this counting rule, it is convenient to introduce a new basis of matrices in which both the squark (and slepton) mass terms as well as the trilinear couplings can be expanded. We derive the RGE for the MFV parameters and show that the beta functions also respect the counting rule. For moderate tan(beta), we provide explicit analytic solutions of these RGE and illustrate their behaviour by analyzing the neighbourhood (also switching on new phases) of the SPS-1a benchmark point. We then show that even in the case of large tan(beta), the RGE remain valid and that the analytic solutions obtained for moderate tan(beta) still allow us to understand the most important features of the running of the parameters, as illustrated with the help of the SPS-4 benchmark point.Comment: plain latex, 38 pages and 5 figures Eq. (12) corrected and one reference added, conclusions unchanged. Published versio

Report from Working Group 3: Beyond the standard model physics at the HL-LHC and HE-LHC

This is the third out of five chapters of the final report [1] of the Workshop on Physics at HL-LHC, and perspectives on HE-LHC [2]. It is devoted to the study of the potential, in the search for Beyond the Standard Model (BSM) physics, of the High Luminosity (HL) phase of the LHC, defined as $3$ ab$^{-1}$ of data taken at a centre-of-mass energy of 14 TeV, and of a possible future upgrade, the High Energy (HE) LHC, defined as $15$ ab$^{-1}$ of data at a centre-of-mass energy of 27 TeV. We consider a large variety of new physics models, both in a simplified model fashion and in a more model-dependent one. A long list of contributions from the theory and experimental (ATLAS, CMS, LHCb) communities have been collected and merged together to give a complete, wide, and consistent view of future prospects for BSM physics at the considered colliders. On top of the usual standard candles, such as supersymmetric simplified models and resonances, considered for the evaluation of future collider potentials, this report contains results on dark matter and dark sectors, long lived particles, leptoquarks, sterile neutrinos, axion-like particles, heavy scalars, vector-like quarks, and more. Particular attention is placed, especially in the study of the HL-LHC prospects, to the detector upgrades, the assessment of the future systematic uncertainties, and new experimental techniques. The general conclusion is that the HL-LHC, on top of allowing to extend the present LHC mass and coupling reach by $20-50\%$ on most new physics scenarios, will also be able to constrain, and potentially discover, new physics that is presently unconstrained. Moreover, compared to the HL-LHC, the reach in most observables will, generally more than double at the HE-LHC, which may represent a good candidate future facility for a final test of TeV-scale new physics