The Intrinsic Dimension of Collider Events and Model-Independent Searches in 100 Dimensions

Abstract

The phase space of hadron collider events spans hundreds of dimensions, generating an intricate geometry that we are just starting to explore. The number of possible new physics signals is exponential in the number of dimensions and detecting all of them is currently impossible for any human or artificial intelligence. In this work we introduce a method to search for new physics model-independently in this high-dimensional space. It is based on the measurement of the most basic property of the manifold of collider events, its dimensionality. Our proposed technique does not suffer from a look-elsewhere effect that grows exponentially with the number of dimensions of the dataset, and by construction is insensitive to energy scale uncertainties. We illustrate its potential by finding new physics in simulated events with hundreds of phase space dimensions, taking as input single particles rather than jets. This study sets the stage for new model-independent search strategies based on global properties of collider data manifolds.

Figures (19)

• Figure 1: Sketch of a Swiss-Roll manifold.
• Figure 2: A comparison of the correlation dimension $d_C$ (solid lines) and the NNID (dotted lines) for a Swiss-Roll. The NNID is computed at $i = 1$ and $j=2$ and by definition is insensitive to cutting the largest distances in the dataset. The parameter $\delta$, defined in the text, quantifies the thickness of the Swiss Roll. The shaded areas give the $95\%$ C.L. interval for the two estimators.
• Figure 3: The intrinsic dimension of a Swiss-Roll for different choices of the noise $\delta$, i.e. its thickness. On the $x$-axis we show the average distance of the $i$-th neighbor, on the y-axis the NNID calculated at $j=2i$. The shaded areas give the $95\%$ C.L. interval for the estimator. We truncate our lines at the value of $\overline{r}_i$ below which there are no more neighbors.
• Figure 4: Leading diagram for the leptonic MSSM signal in Section \ref{['sec:MSSM_lep']}.
• Figure 5: Parton level NNID curves as a function of $2i/N$ (left panel) and the average distance to the $i$-th neighbor (right panel) in the SM (black) and in three MSSM-like benchmark models described in the text. The curves are obtained from 100 samples. In the left panel the central line represents the median, while the band is the $68\%$ confidence interval. In the right panel we show the $68\%$ confidence interval for both axes as error bars.