Theory Definitions

The so-called theory module contains the basic tools necessary for decomposing the input model (either in LHE or SLHA format) into SMS topologies and using the output of the decomposition to compute the theoretical prediction for a given experimental analysis.

We start by explaining the basic components: vertices, Z2-even and Z2-odd states shown in the scheme below. The construction of a global topology and the bracket notation used in SModleS are explained further below on this page.

_images/topScheme.png

Vertices

Each Z2-odd state appearing in a topology ends with a vertex (see scheme above) In most cases vertices correspond to the decay of the Z2-odd state. The only exceptions are topologies ending with a stable Z2-odd state. In this case the last vertex contains no outgoing final states and indicates the stability of the last Z2-odd particle appearing in the branch.

Final States (Z2-even)

Final states indicate all Z2-even states coming out of a vertex (see scheme above). 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

Intermediate States (Z2-odd)

The Z2-odd states are always assumed to consist of BSM particles with Z2 conserving decays of the form: (Z2-odd state) \(\rightarrow\) (Z2-odd state’) + Final States. The only information kept from the intermediate states are their masses (see scheme above). 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

Branches

A branch is the basic substructure of a topology. It represents a series of cascade decays of a single initial Z2-odd state. The figure below shows an example of a branch.

_images/branchTop.png

Each branch is fully defined by its number of vertices and the number of Final States (Z2-even) coming out of each vertex. The particle labels for the final states may or may not be specified. If the particle labels of the final states are not specified (such as in the figure above), the branch belongs to a global topology. However, if it is dressed with its final states as in the figure below, the branch belongs to an element.

_images/branchEl.png

Topologies

Topologies describe the basic structure of an element. Each global topology corresponds to a cascade decay chain without the final Z2-even states or Z2-odd masses specified. Therefore the global topology is fully determined by its number of branches, number of vertices in each branch and number of final states coming out of each vertex. As as example consider the following topology:

_images/globTop.png

It contains 2 branches. The first (topmost) branch contains 3 vertices with 1 final state each in the first two vertices and zero in the third. On the other hand, the second branch contains 2 vertices with two final states coming out of the first vertex and zero coming out of the second. Notice that, for topologies ending with stable Z2 -odd states, there are no final states coming out of the last vertex in the branch.

Topologies are also a useful way to group elements. In this way, topologies represent a list of elements sharing a common basic structure (same number of branches, vertices and final states in each vertex).

Elements

Elements are dressed global topologies, where both the final state (Z2-even) particles and the BSM (Z2-odd) masses appearing in the topology have been defined. An element may also hold information about its corresponding weight (cross-section times branching ratio). An element is defined by its global topology properties (number of branches, vertices and particles in each vertex) plus its final states, and a mass array containing the ordered Z2-odd masses appearing in the element. Below we show an example of an element and the information it contains.

_images/element.png

Bracket Notation

The structure and final states of elements 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:

_images/bracketNotation.png

The brackets are ordered and nested in the following way. The outermost brackets correspond to the branches of the element. The ordering for the branches is arbitrary and each branch contains an ordered list of vertices and each vertex contains an unordered list of the final states coming out of the vertex. Schematically, for the example in the figure above, we have:

element = [branch1, branch2]
   branch1 = [vertex1,vertex2]
      vertex1 = [l+]
      vertex2 = [nu]
   branch2 = [vertex1]
      vertex1 = [l+,l-]

Using the above scheme it is possible to unambiguously describe each element with a simple list of nested brackets. However, in order to fully specify all the information relative to a single element, we must also include the list of intermediate state masses and the element weight. The intermediate state masses can also be represented by a mass array for each branch, as shown below:

_images/massNotation.png

Table Of Contents

Previous topic

Basic Concepts and Definitions

Next topic

Database Definitions

This Page