Name: setting limits on supersymmetry using simplified models
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Description: Watch this Scientific Journal Video about Setting Limits on Supersymmetry Using Simplified Models at JoVE.com

The authors would like to thank Jay Wacker for significant discussion of simplified models and potential pitfalls. Many thanks also to Max Baak and Till Eifert for constructive criticism and encouragement whenever it was necessary. Thanks to the CERN Summer Student Program for making this collaboration possible.

1. Model Deconstruction
<ol>
	<li>Generate proton-proton collision events covering a plane in the parameter space of the NPM. Any event generator configuration that includes a parton shower and hadronization model can be used. In the case of MSUGRA for example, the mass spectra are generated using Isasugra33, and the branching fractions and decay widths are calculated using MSSMCalc34. For the event generation itself, MadGraph 5 1.3.934 with CTEQ 6L1 parton density functions35</sup...

<ol>
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The application of simplified model limits to produce an exclusion contour in a complete new physics model has been demonstrated. Despite the apparent complexity of MSUGRA parameter space points, the kinematics can be well-reproduced by a combination of only a small number of simplified models. The kinematic agreement is further improved when looking within a particular signal region, since the searches thus far conducted at the LHC tend to favor simplified model-like event topologies with a (relatively) small number of ...

One of the most promising extensions of the Standard Model, supersymmetry (SUSY)1-14, is the central focus of many searches by the LHC experiments at CERN. The data collected in 2011 are already sufficient to push the limits of new physics beyond those of any previous collider15-22. As new data arrive and the exclusions are pushed still farther, it will be increasingly important to clearly communicate to the physics community what regions of the extensive supersymmetric parameter space have been excluded. Current limits are typically set on constrained two-dimensional planes, which frequently do not represent the diverse available SUSY parameter space and are difficult to understand as limits on physical masses or branching fractions. A large set of simplified models23, 24 have been proposed for aiding in the understanding of these limits, and both ATLAS and CMS have provided exclusion results for several of these models15-20.
This paper demonstrates the application of these simplified model exclusions to a full new physics model using the example of the minimal supergravity (MSUGRA, also known as the CMSSM)25-30. This model is chosen in order to compare the limits set using simplified models to those published independently by the experiments. The procedure is sufficiently general to be extendable to any new physics model (NPM). As this represents the first attempt to &#34;close the loop&#34; and set limits on SUSY using simplified models, a number of assumptions about the applicability of limits on particular simplified models are explored, resulting in recipes for setting conservative and aggressive limits on theories that have not been examined by the LHC experiments.
For setting a limit in a NPM, three separate operations are required. First, the NPM must be deconstructed into its constituent pieces, separating the various production modes and decay modes for all new particles in the model. Second, a set of simplified models must be chosen to recreate the kinematics and relevant event topologies in the NPM. Third, the available limits on these simplified models must be combined in order to produce limits on the NPM. These three procedures are described in the protocol. Some additional approximations are also provided that may expand the applicability of the already-available simplified models to a broader range of event topologies.
A complete NPM typically involves many production modes and many possible subsequent decays. The deconstruction of new physics models into their components and the application of simplified model limits to those components allows the construction of an exclusion limit directly. For any signal region, the most conservative limit can be set using the production fraction P(a,b)&#160;(where a,b represents the simplified model sparticle production mode) of events identical to a simplified model i and the branching fraction for the produced sparticles to decay in the manner described by the simplified model&#8224;, BRa&#8594; i x BRb &#8594; i. The expected number of events in a given signal region from these simple topologies can then be written as
<img alt="Equation 1" fo:src="/files/ftp_upload/50419/50419eq1highres.jpg" src="/files/ftp_upload/50419/50419eq1.jpg" /> 
where the sum is over simplified models, &#963;tot is the total cross section for the NPM point, Lint is the integrated luminosity used in the search, and AEa,b &#8594; i is the acceptance times efficiency for the simplified model events in the signal region being considered. This number can be compared to the expected 95% confidence level upper limit on the number of new physics events to select the optimal search region. The model can then be excluded if N is larger than the observed number of new physics events excluded at the 95% confidence level. Exclusions in nonoverlapping regions may be combined if information about the correlations of their uncertainties is available. If this information is not available, the best signal region or analysis that provides the best expected limit can be used to attempt to exclude the model.
In order to construct concrete limits with this method, the A&#949; for various simplified models must be made available by the LHC experiments. Both CMS and ATLAS have published figures with the A&#949; for several models, and a few of the figures are available in the HepData database31. In order to demonstrate the value of publishing all such tables, we feel it is important to provide concrete limits that are comparable to those already published. Therefore we use (and describe in the protocol as an optional step) a fast detector simulation to emulate the effect of the ATLAS or CMS detector. The A&#949; derived from the Pretty Good Simulation (PGS)32 is compared to that published by ATLAS in a simplified model grid in Figure 1. These results are sufficiently close to one another (within roughly 25%) that, rather than wait for all results to be public, A&#949; results for the remaining grids are derived using PGS and used directly in the remainder of this paper. As the number of publicly available simplified model A&#949; results grows, the need for such approximations should be significantly reduced.
Two conservative assumptions allow the inclusion of a larger number of production and decay modes in the limit. The first is that for associated production the experimental A&#949; is at least as high as the A&#949; for the worse of the two production modes. For inclusive searches, this is generally a good assumption. The minimum expected number of events would then be
<img alt="Equation 2" fo:src="/files/ftp_upload/50419/50419eq2highres.jpg" src="/files/ftp_upload/50419/50419eq2.jpg" /> 
where the first sum runs over all production modes, and only those where a and b are exactly those particles from the simplified model are included in Equation 1. Similarly, the A&#949; for decays with different legs can be assumed to be at least as high as the A&#949; for the worse of the two legs. That is,
<img alt="Equation 3" fo:src="/files/ftp_upload/50419/50419eq3highres.jpg" src="/files/ftp_upload/50419/50419eq3.jpg" /> 
where diagrams with different decays on either side have now been included.
Two further assumptions would allow the setting of stricter limits. One can assume that the experimental A&#949; for all production modes in the theory is similar to the average A&#949; for the production modes covered by simplified models. In that case, the expected number of events can instead be written as
<img alt="Equation 4" fo:src="/files/ftp_upload/50419/50419eq4highres.jpg" src="/files/ftp_upload/50419/50419eq4.jpg" /> 
where the sums are both over only those production modes covered by simplified models. One might further assume that the A&#949; for all decay modes in the theory is similar to the average A&#949; for those events covered by the simplified model topologies. Then the expected number of events may be written as:
<img alt="Equation 5" fo:src="/files/ftp_upload/50419/50419eq5highres.jpg" src="/files/ftp_upload/50419/50419eq5.jpg" /> 
where again the sums run only over the simplified models. Clearly, the most aggressive MSUGRA limit is provided under this assumption, and a limit set in this manner risks claiming exclusion for regions that would not, in fact, be excluded at the 95% confidence level by a dedicated search. Although the accuracy of these two approximations might be suspect, if the inclusive event kinematics of the simplified models compare favorably to a complete SUSY parameter space point, they may not be unreasonable.
&#8224; Some simplified models now used at the LHC include associated production. While not explicitly discussed here, the equations can be trivially extended to allow for this case.

setting limits on supersymmetry using simplified models

Experimental limits on supersymmetry and similar theories are difficult to set because of the enormous available parameter space and difficult to generalize because of the complexity of single points. Therefore, more phenomenological, simplified models are becoming popular for setting experimental limits, as they have clearer physical interpretations. The use of these simplified model limits to set a real limit on a concrete theory has not, however, been demonstrated. This paper recasts simplified model limits into limits on a specific and complete supersymmetry model, minimal supergravity. Limits obtained under various physical assumptions are comparable to those produced by directed searches. A prescription is provided for calculating conservative and aggressive limits on additional theories. Using acceptance and efficiency tables along with the expected and observed numbers of events in various signal regions, LHC experimental results can be recast in this manner into almost any theoretical framework, including nonsupersymmetric theories with supersymmetry-like signatures.

Having applied the model deconstruction step to a point in the parameter space of MSUGRA, a breakdown of the output can be best visualized by counting up the various production and decay modes for every generated event and plotting the corresponding production rates and branching fractions according to the relative frequencies. The branching fractions for the various production and decay modes for representative MSUGRA points are illustrated in Figures 2 and 3. A large number of similar ...

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Setting Limits on Supersymmetry Using Simplified Models

This paper demonstrates a protocol for recasting experimental simplified model limits into conservative and aggressive limits on an arbitrary new physics model. Publicly available LHC experimental results can be recast in this manner into limits on almost any new physics model with a supersymmetry-like signature.

Experimental limits on supersymmetry and similar theories are difficult to set because of the enormous available parameter space and difficult to ...

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Friction and wear are detrimental to engineered systems. Ultrasonic lubrication is achieved when the interface between two sliding surfaces is vibrated at ...

Fabrication of 1-D Photonic Crystal Cavity on a Nanofiber Using Femtosecond Laser-induced Ablation

We present a protocol for fabricating 1-D Photonic Crystal (PhC) cavities on subwavelength-diameter tapered optical fibers, optical nanofibers, using ...

3D Printing of Biomolecular Models for Research and Pedagogy

The construction of physical three-dimensional (3D) models of biomolecules can uniquely contribute to the study of the structure-function relationship. 3D ...

Surgical Techniques for Catheter Placement and 5/6 Nephrectomy in Murine Models of Peritoneal Dialysis

Peritoneal dialysis (PD) is a renal replacement therapy consistent on the administration and posterior recovery of a hyperosmotic fluid in the peritoneal ...

Fabrication of Magnetic Nanostructures on Silicon Nitride Membranes for Magnetic Vortex Studies Using Transmission Microscopy Techniques

Electron and x-ray magnetic microscopies allow for high-resolution magnetic imaging down to tens of nanometers. However, the samples need to be prepared ...

Automated Deployment of an Internet Protocol Telephony Service on Unmanned Aerial Vehicles Using Network Functions Virtualization

The Network Function Virtualization (NFV) paradigm is one of the key enabling technologies in the development of the 5th generation of mobile networks. ...

Study of a Dot-patterning Process on Flexible Materials using Impact Print-Type Hot Embossing Technology

Here we present our study on an impact print-type hot embossing process which can create dot patterns with various designs, widths, and depths in real ...

Fabrication of Surface Acoustic Wave Devices on Lithium Niobate

Manipulation of fluids and particles by acoustic actuation at small scale is aiding the rapid growth of lab-on-a-chip applications. Megahertz-order ...

Manufacturing, Control, and Performance Evaluation of a Gecko-Inspired Soft Robot

This protocol presents a method for manufacturing, control, and evaluation of the performance of a soft robot that can climb inclined flat surfaces with ...