.. index:: Missing Topologies
The constraints provided by SModelS are obviously limited by its |database| and the available set of simplified model interpretations provided by the experimental collaborations or computed by theory groups. Therefore it is interesting to identify classes of missing simplified models (or missing topologies) which are relevant for a given input model, but are not constrained by the SModelS |database|. This task is performed as a last step in SModelS, once the |decomposition| and the |theory predictions| have been computed.
During the computation of the |theory predictions|, each |element| from the |decomposition| which matches at least one of the simplified models in the |database| is marked as "covered by" the corresponding type of |ExpRes|. Currently the |ExpRess| are either of type prompt or displaced.[1] If the same |element| is covered by both types of |ExpRess|, it will be marked as covered by displaced and prompt results. If, in addition to being covered, the |element| also has a non-zero efficiency or upper limit (i.e. its properties fall inside the data grid for any result), it will be marked as "tested by" the corresponding type of result (prompt or displaced). Hence, after the |theory predictions| have been computed, the |elements| store information about their experimental coverage and can be classified and group into :ref:`coverage <coverageGroups>`.
- The coverage tool is implemented by the Uncovered class
The coverage algorithm groups all the |elements| into coverage groups which can be easily defined by the user (see the coverage module). Each group must define a criterium for selecting |elements| after the |theory predictions| have been computed. The default coverage groups implemented in SModelS are:
- missing (prompt): not covered by prompt-type results. This group corresponds to all |elements| which did not match any of the simplified models contrained by prompt |ExpRess|.
- missing (displaced): not covered by displaced-type results. This group corresponds to all |elements| which did not match any of the simplified models contrained by displaced |ExpRess|.
- missing (all): not covered by any type of result. This group corresponds to all |elements| which did not match any of the simplified models contrained by the |database|.
- outsideGrid (all): covered by at least one type of |ExpRes| and not tested by any type of result. This group corresponds to all |elements| which matched at least one the simplified models constrained by the |database|, but were not tested (e.g. their masses and/or widths fall outside the efficiency or upper limit grids).
The :ref:`figure below <coverA>` schematically represents the grouping performed in coverage:
Besides defining which |elements| should be selected, each coverage group can also specify a reweighting function for the |element|'s cross section. This is useful for the cases where the coverage group aims to represent missing topologies with prompt (or displaced) decays, so only the fraction of prompt (displaced) cross section should be extracted. The reweighting functions defined will be applied to the selected |elements| in order to extract the desirable fraction of signal cross section for the group. For instance, for the default groups listed above, the following reweighint functions are defined:
- missing (prompt): \sigma \to \xi \times \sigma,\;\; \xi = \prod_{i=1,N-2} \mathcal{F}_{prompt}^{i} \times \prod_{i=N-2,N} \mathcal{F}_{long}^{i}
- missing (displaced): \sigma \to \xi \times \sigma,\;\; \xi = \mathcal{F}_{displaced}(any) \times \prod_{i=N-2,N} \mathcal{F}_{long}^{i}
- missing (all): \sigma \to \xi \times \sigma,\;\; \xi = 1
- outsideGrid (all): \sigma \to \xi \times \sigma,\;\; \xi = 1
The definition for the fraction of long-lived (\mathcal{F}_{long}) and prompt (\mathcal{F}_{prompt}) decays can be found in :ref:`lifetime reweighting <dbReweighting>`. The fraction \mathcal{F}_{displaced}(any) corresponds to the probability of at least one displaced decay taking place, where the probability for a displaced decay is given by 1-\mathcal{F}_{long}-\mathcal{F}_{prompt}.
If :ref:`mass <massComp>` or :ref:`invisible compression <invComp>` are turned on, |elements| generated by :ref:`compression <elementComp>` and their ancestors (original/uncompressed |element|) could both fall into the same coverage group. Since the total missed cross section in a given group should equal the total signal cross section not covered or tested by the corresponding type of |ExpRess|, one has to avoid double counting |elements|. In addition, a compressed |element| belonging to a given coverage group could combine cross sections from more than one uncompressed (original) |element|. If one of the original |elements| do not belong to this coverage group (i.e. it has been covered and/or tested by the |ExpRess|), its contribution to the compressed |element| cross section should be subtracted. SModelS deals with the above issues through the following steps:
- an effective "missing cross section" is computed for each |element|, which corresponds to the |element| weight subtracted of the weight of its ancestors which do not belong to the same coverage group. The effective cross section also includes the reweighting :ref:`discussed above <coverReweight>`.
- All |elements| belonging to the same group which have a common ancestor are removed (only the |element| with largest missing cross section is kept).
Usually the list of |elements| in each group can be considerably long, due to distinct intermediate BSM states and final SM states. In order to make the list more compact, all |elements| are further combined according to their |topology| and final state |particles| (i.e. all properties of intermediate BSM states are ignored). By default, the SM |particles| are grouped according to the definitions below:
- W^+,W^- \to \mbox{W}
- \tau^+,\tau^- \to \mbox{ta}
- e^+,e^-,\mu^+,\mu^- \to \mbox{l}
- t,\bar{t} \to \mbox{t}
- u,d,s,c,\bar{u},\bar{d},\bar{s},\bar{c},g,pions \to \mbox{jet}
- \nu_{e},\nu_{\mu},\nu_{\tau},\bar{\nu}_{e},\bar{\nu}_{\mu},\bar{\nu}_{\tau} \to \mbox{nu}
while the final ( Z2-odd) BSM |particles| are grouped by their signature:
- color and electrically neutral states \to \mbox{MET}
- color neutral states with electric charge +-1 \to \mbox{HSCP}
- color triplet states with electric charge +-2/3 or +-1/3 \to \mbox{RHadronQ}
- color octates states with zero electric charge \to \mbox{RHadronG}
The :ref:`figure below <coverB>` schematically represents the combination of elements according to the grouping of similar final states:
- Coverage groups are implemented by the UncoveredGroup class
| [1] | Prompt results are all those which assumes all decays to be prompt and the last BSM particle to be stable (or decay outside the detector). Searches for heavy stable charged particles (HSCPs), for instance, are classified as prompt, since the HSCP is assumed to decay outside the detector. Displaced results on the other hand require at least one decay to take place inside the detector. |