Recasting through reweighting

By Kyle Cranmer, Lukas Heinrich

physics reinterpretation lhc

Recasting refers to reinterpreting the results of searches for new particles or standard model measurements in the context of different theoretical models [1]. The fundamental task is to replace the original hypothesis $p_0(x)$ with a new hypothesis $p_1(x)$, where $x$ is some observed quantity. The effect of the detector response and analysis cuts can be encoded in a folding operator $\int,W(x|z)dz$ acting on the truth-level distribution $p(z)$. By keeping the analysis fixed, $W(x|z)$ does not change, thus recasting amounts to:
\begin{equation}p_0(x)=\int,p_0(z)W(x|z)dz\hspace{.5cm}\Longrightarrow\hspace{.5cm}p_1(x)=\int,p_1(z)W(x|z)dz\end{equation}

There are two primary approaches:

• folding: Samples from $p_1(z)$ are run through a detector simulation and analysis chain to estimate $p_1(x)$ [2]. This is common when $z$ is high-dimensional, $p_0(z)$ and $p_1(z)$ are very different, or $W(x|z)$ is sensitive to experimental details.
• unfolding: An alternate theory $p_1(z)$ is compared directly to an unfolded distribution $\hat{p}(z)$ obtained from applying an approximate inverse operation to the observed data. Typically, unfolding is restricted to low-dimensional $x, z$ and Gaussian uncertainties.

We point out a third option

• reweighting: Reweight pre-folded events $(x_i,z_i)~\sim,p_0(x,z)$ by the factor $r(z_i)=p_1(z_i)/p_0(z_i)$, as in
  \begin{equation}p_1(x)=\int p_1(z)W(x|z)dz=\int,p_0(z)\underbrace{\frac{p_1(z)}{p_0(z)}}_{\textrm{reweighting}}W(x|z)dz\end{equation}
  This approach does not require simulating new events or the approximations used in unfolding. Note, sample variance becomes a problem if $r(z_i)\gg,1$.

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