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Subjet analysis and ${e^+ e^-}~$ mode Once the hadronic final state has been decomposed into jets, the structure of the jets themselves can be investigated. This is commonly known as a subjet analysis. The procedure is physically (and practically) identical to that employed in the analysis of an ${e^+ e^-}~$ event. In the ${e^+ e^-}~$case, all final state objects are used as input to the algorithm. In a subjet analysis on a particular jet, only the particles within that jet are used as input. The steps are as follows; Define a resolution parameter $$y_\mathit{cut}= Q_0^2 / E_\mathit{cut}^2.$$ (4) The parameter $E_\mathit{cut}^2$ may be chosen by the user, but is conventionally taken to be the square of the total energy of the ${e^+ e^-}~$event (or the $p_t$ of the jet) in the frame in which the algorithm is run. These are the default settings in KtJet. For each pair of objects $h_k$ and $h_l$, construct the rescaled resolution variable $y_{kl}$ $$y_{kl}=d_{kl}/E_\mathit{cut}^2$$ (5) where $d_{kl}$ is defined as in section 2.1. Find $y_{min}$, the smallest of the $y_{kl}$. If $y_\mathit{min} < y_\mathit{cut}$, $h_k$ and $h_l$ are combined into a single object with momentum $p_{(kl)}$ according to a user specified recombination scheme (parameter recom). Repeat the procedure until all pairs of objects have $y_{kl} > y_\mathit{cut}$. The remaining objects are called subjets. As described in section 2.2, one can choose to stop merging when a given number of jets is reached, instead of specifying the stopping scale $y_\mathit{cut}$.