Database Definitions

The SModelS database collects experimental results from both ATLAS and CMS. The results from each publication or conference note can be included in the database either as an Upper Limit Analysis or Efficiency Map Analysis.

Upper Limit Analyses

Upper Limit (UL) analyses refer to the experimental constraints on the cross-section times branching ratio ( \(\sigma \times BR\) ) from a specific experimental publication or conference note. Each UL analysis corresponds to the 95% upper limit constraints on \(\sigma \times BR\) for a given element or sum of elements. For illustration, consider this CMS example:

_images/ULexample.png

In this case the UL analysis constrains the element \([[[jet]],[[jet]]]\), where we are using the notation defined in Bracket Notation.

Each individual UL analysis holds the upper limit values on \(\sigma \times BR\) as a function of the respective parameter space (usually BSM masses or slices over mass planes). Furthermore, the corresponding constraints and conditions must also be specified. UL analyses may also contain information about the analysis luminosity, center-of-mass, publication reference and others. We also point out that the exclusion curve is never used by SModelS.

Note that a given experimental publication (or conference note) may contain several UL analyses, since a single publication may contain upper limits for several different elements (or constraints).

Analysis Constraints

Constraints are defined as the element or sum over elements which is constrained by the experimental upper limits. The analysis constraints can also be simply expressed in the bracket notation as a sum of individual elements.

As an example, consider the ATLAS analysis shown below:

_images/constraintExample.png

As we can see, the upper limits apply to the sum of the cross-sections:

\[\sigma = \sigma([[[e^+]],[[e^-]]]) + \sigma([[[\mu^+]],[[\mu^-]]])\]

In this case the analysis constraint is simply:

\[[[[e^+]],[[e^-]]] + [[[\mu^+]],[[\mu^-]]]\]

where it is understood that the sum is over the weights of the respective elements and not over the elements themselves.

Note that the sum can be over particle charges, flavors or more complex combinations of elements. However, almost all analyses sum only over elements sharing a common topology.

Analysis Conditions

When the analysis constraints are non-trivial (refer to a sum of elements), it is often the case that there are implicit (or explicit) assumptions about the contribution of each element. For instance, in the figure above, it is implicitly assumed that each lepton flavor contributes equally to the summed cross-section:

\[\sigma([[[e^+]],[[e^-]]]) = \sigma([[[\mu^+]],[[\mu^-]]]) \;\;\; \mbox{(condition)}\]

Therefore, when applying these constraints to general models, one must also verify if these conditions are satisfied. Once again we can express these conditions in bracket notation:

\[[[[e^+]],[[e^-]]] = [[[\mu^+]],[[\mu^-]]] \;\;\; \mbox{(condition)}\]

where it is understood that the condition refers to the weights of the respective elements and not to the elements themselves.

In several cases it is desirable to relax the analysis conditions, so the analysis upper limits can be applied to a broader spectrum of models. Once again, for the example mentioned above, it might be reasonable to impose instead:

\[[[[e^+]],[[e^-]]] \simeq [[[\mu^+]],[[\mu^-]]] \;\;\; \mbox{(fuzzy condition)}\]

The departure from the exact condition can then be properly quantified and one can decide whether the analysis upper limits are applicable or not to the model being considered. Concretely, for each condition a number between 0 and 1 is returned, where 0 means the condition is exactly satisfied and 1 means it is maximally violated. Allowing for a \(20\%\) violation of a condition corresponds approximately to a ‘’condition violation value’’ (or simply condition value) of 0.2. The condition values are given as an output of SModelS, so the user can decide what are the maximum acceptable values.

Efficiency Map Analyses

Efficiency Map (EM) analyses are more fundamental than UL analyses. Instead of holding cross-section upper limits, they correspond to one or more efficiency maps together with the information about the expected and observed data for the relevant signal region(s).:

Note: Efficiency Map analyses are not yet functional in the public release!!!

Efficiency Maps

Efficiency maps correspond to a grid of simulated acceptance times efficiency ( \(A \times \epsilon\) ) values for specific signal region(s). In the following we will refer to \(A \times \epsilon\) simply as efficiency.

The signal is assumed to correspond to a single element, which characterizes the basic signal kinematics and hence its efficiency. The efficiency grid is usually a function of the BSM masses appearing in the element, as shown by the example below:

_images/EMexample.png

Although efficiency maps are most useful for EM analyses, they can also be constructed for UL analyses. For the latter, the efficiencies for a given element are either 1, if the element belongs to the UL analysis constraint, or 0, if the element does not belong to the UL analysis constraint.

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