Efficient tau-pair invariant mass reconstruction with simplified matrix element techniques

TL;DR

This work presents fastMTT, a fast matrix-element–based method for reconstructing the di-tau invariant mass at hadron colliders. By combining the collinear approximation with simplified matrix elements and analytic phase-space integration, fastMTT achieves roughly two orders of magnitude speedup over prior ME approaches while maintaining mass resolution comparable to SVfit. The framework yields event-by-event mass uncertainties from full likelihood maps and supports additional mass constraints, enhancing its utility for Higgs CP studies and searches for di-tau resonances. The approach scales with vectorized Python implementations and batch processing, enabling practical use on large data samples without sacrificing interpretability or precision.

Abstract

The quality of the invariant mass reconstruction of the di-τ system is crucial for searches and analyses of di-τ resonances. Due to the presence of neutrinos in the final state, the τ τ invariant mass cannot be calculated directly at hadron colliders, where the longitudinal momentum sum constraint cannot be applied. A number of approaches have been adopted to mitigate this issue. The most general one uses Matrix Element (ME) integration for likelihood estimation, followed by invariant mass reconstruction as the value maximizing the likelihood. However, this method has a significant computational cost due to the need for integration over the phase space of the decay products. We propose an algorithm that reduces the computational cost by two orders of magnitude, while maintaining the resolution of the invariant mass reconstruction at a level comparable to the ME-based method. Moreover, we introduce additional features to estimate the uncertainty of the reconstructed mass and the kinematics of the initial τ leptons (e.g., their momenta).

Figures (8)

• Figure 1: Example of tau decay in electron channel $\tau^- \rightarrow e^- \nu_\tau \bar{\nu}_e$. The top picture shows the division of decay products -- invisible products (neutrinos) are marked with red, while visible products are marked with blue. Light-grey color marks the $\tau^-$ decay cone. Bottom picture shows the definition of Gottfried-Jackson $\theta_{GJ}$ and the $\phi$ angles.
• Figure 2: The likelihood map on the ($x_1, x_2$) plane for a single event. The red cross marks the position of the likelihood maximum, while the blue contour limits the area in which there is $\sim 68\%$ (1 $\sigma$) probability to choose the true mass.
• Figure 4: Time needed to calculate the masses for a given number of cases. The figure shows a comparison between the NumPy implementation (blue line), using batch processing (orange line), and both batch and multiprocessing (green line).
• Figure 5: Reconstruction of the $Z^0$ (left) and Higgs (right) bosons' mass with the fastMTT algorithm. The x-axis represents the invariant mass of the reconstructed di-tau system, while the y-axis represents event density.
• Figure 6: Relative resolution of $\tau\tau$ reconstruction for $Z^0$ (left) and Higgs (right) bosons. The x-axis represents the relative resolution of the mass reconstruction, while the y-axis represents event density.