Theory Definitions
The so-called theory module contains the basic tools necessary for decomposing the input model (either in LHE or SLHA format) into simplified model topologies <topology>
and using the output of the decomposition to compute the theoretical prediction <theoryPredictions>
for a given experimental result <ExpResult>
.
The applicability of SModelS is currently restricted to models which contain a Z2 symmetry (R-parity in SUSY, K-parity in UED, ...) and result in a missing transverse energy (MET) final state at experiments. This is required in order to provide a clear structure for the simplified model topologies appearing during the decomposition <decomposition>
of the input model. Below we describe the basic concepts and language used in SModelS to describe the simplified model topologies.
A simplified model topology representing a specific cascade decay of a pair of BSM states produced in the hard scattering is called an element in the SModelS language. Elements contain the final states (Z2-even) particles appearing in the cascade decay as well as the masses of the BSM (Z2-odd) states which have decayed or appear in the last step of the decay. A representation of an element is shown below:
An element may also hold information about its corresponding weight (cross section times branching ratio times efficiency).1 The overall properties of an element are illustrated in the scheme below:
SModelS works under the inherent assumption that, for collider purposes, all the essential properties of a BSM model can be encapsulated by its elements. Such an assumption is extremely helpful to cast the theoretical predictions of a specific BSM model in a model-independent framework, which can then be compared against the corresponding experimental limits. For instance, as shown in the scheme above <elementscheme>
, only the masses of the BSM states are used and other properties, such as their spins or other quantum numbers are ignored (the PID's are, however, stored for book-keeping).
Below we describe in more detail the element properties and their implementation in SModelS.
- Elements are described by the Element Class
Each Z2-odd decay is represented by a vertex containing its final states (one Z2-odd state and the Z2-even particles), as shown in the scheme above <topscheme>
.
Final states indicate all Z2-even states coming out of a vertex (see scheme above <topscheme>
). In most cases, these correspond to Standard Model particles (electrons, gauge bosons, Higgs,...). Note that, if the input model contains BSM states which are Z2-even (such as additional Higgs bosons), these also appear as final states. In contrast, stable or long-lived Z2-odd particles which might appear in the detector (either as MET or charged tracks) are not classified as final states.
- Z2-even states are defined (and can be easily modified) in
particles.py <images/particles.py>
The Z2-odd states are always assumed to consist of BSM particles with Z2 conserving decays of the form: (Z2-odd state) → (Z2-odd state') + final states <final states>
. The only information kept from the intermediate states are their masses (see scheme above <topscheme>
). If an intermediate state is stable and neutral, it is considered as a MET signal.
- Z2-odd states are defined (and can be easily modified) in
particles.py <images/particles.py>
A branch is the basic substructure of an element <element>
. It represents a series of cascade decays of a single initial Z2-odd state. The diagram below illustrates an example of a branch.
The structure of each branch is fully defined by its number of vertices and the number of final states <final states>
coming out of each vertex. Furthermore, the branch also holds the information about the particle labels for the final states <final states>
coming out of each vertex and the masses of the intermediate states <odd states>
, as shown below.
- Branches are described by the Branch Class
The structure and final states of elements <element>
are represented in textual form using a nested brackets notation. The scheme below shows how to convert between the graphical and bracket representations of an element:
The brackets are ordered and nested in the following way. The outermost brackets correspond to the branches <branch>
of the element <element>
. The branches are sorted according to their size (see element sorting <elementsorting>
) and each branch contains an ordered list of vertices <vertex>
. Each vertex contains a list of the final states <final states>
(sorted alphabetically) coming out of the vertex. Schematically, for the example in the figure above <bracketnotation>
, we have:
element = [branch1, branch2]
branch1 = [vertex1]
vertex1 = [l+,l-]
branch2 = [vertex1,vertex2]
vertex1 = [l+]
vertex2 = [nu]
Using the above scheme it is possible to unambiguously describe each element <element>
with a simple list of nested brackets. However, in order to fully specify all the information relative to a single element <element>
, we must also include the list of intermediate state <odd states>
masses and the element weight. The intermediate state <odd states>
masses can also be represented by a mass array for each branch, as shown below:
It is often useful to classify elements <element>
according to their overall structure or topology. Each topology corresponds to an undressed element <element>
, removed of its final states <final states>
and Z2-odd masses. Therefore the topology is fully determined by its number of branches, number of vertices in each branch <branch>
and number of final states <final states>
coming out of each vertex <vertex>
. An example of a topology is shown below:
Within SModelS, elements are grouped according to their topology. Hence topologies represent a list of elements sharing a common basic structure (same number of branches, vertices and final states in each vertex).
- Topologies are described by the Topology Class
In order to treat the UL and EM map results on the same footing, SModelS applies a trivial binary efficiency to elements for UL-type results as will be explained in detail later.↩