By Kyle Cranmer, Lukas Heinrich

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:
$$p_0(x)=\int\,p_0(z)W(x|z)dz\hspace{.5cm}\Longrightarrow\hspace{.5cm}p_1(x)=\int\,p_1(z)W(x|z)dz$$

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 $$p_1(x)=\int p_1(z)W(x|z)dz=\int\,p_0(z)\underbrace{\frac{p_1(z)}{p_0(z)}}_{\textrm{reweighting}}W(x|z)dz$$ This approach does not require simulating new events or the approximations used in unfolding. Note, sample variance becomes a problem if $r(z_i)\gg\,1$.