[Paper Review] Stochastic mass-reconstruction: a new technique to reconstruct resonance masses of heavy particles decaying into tau lepton pairs

S. Maruyama|arXiv (Cornell University)|Dec 15, 2015

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper introduces stochastic mass-reconstruction, a novel technique to improve resonance mass reconstruction for heavy particles decaying into tau lepton pairs at colliders. By modeling the momentum distribution of tau decay products using a beta function and combining transverse momenta of two taus, the method achieves better mass resolution than traditional approaches, especially when taus are collimated, and provides a new, independent variable for Higgs and exotic particle analyses without relying on missing transverse momentum.

ABSTRACT

The invariant mass of tau lepton pairs turns out to be smaller than the resonant mass of their mother particle and the invariant mass distribution is stretched wider than the width of the resonant mass as significant fraction of tau lepton momenta are carried away by neutrinos escaping undetected at collider experiments. This paper describes a new approach to reconstruct resonant masses of heavy particles decaying to tau leptons at such experiments. A typical example is a Z or Higgs boson decaying to a tau pair. Although the new technique can be used for each tau lepton separately, I combine two tau leptons to improve mass resolution by requiring the two tau leptons are lined up in a transverse plane. The method is simple to implement and complementary to the collinear approximation technique that works well when tau leptons are not lined up in a transverse plane. The reconstructed mass can be used as another variable in analyses that already use a visible tau pair mass and missing transverse momentum as these variables are not explicitly used in the stochastic mass-reconstruction to select signal-like events.

Motivation & Objective

• Address the challenge of poor mass resolution in resonance decays to tau pairs due to undetected neutrinos carrying away momentum.
• Develop a new kinematic variable that reconstructs resonant masses without relying on missing transverse momentum or collinear approximations.
• Improve mass resolution in di-tau final states by combining transverse momenta of two taus when they are aligned in the transverse plane.
• Provide a complementary technique to existing methods like the collinear approximation, particularly effective in low-boost, transverse-collimated configurations.
• Enable precise measurements of SM Higgs and exotic particles like Z' bosons in tau+tau final states using a new, analytically tractable reconstruction method.

Proposed method

• Model the momentum distribution of daughter particles in n-body decays using a beta distribution: f(x)_{n-body} = (n-1)(1-x)^{n-2}, where x is the momentum fraction of the first daughter.
• Use the expectation value of momentum fractions, ⟨x⟩ = 1/n, to estimate the average momentum per daughter particle in the rest frame of the mother particle.
• Combine transverse momenta of two taus in events where they are aligned in the transverse plane to reconstruct a stochastic mass via a sum of momentum fractions.
• Apply kinematic selection cuts (e.g., pT thresholds) and correct for biases in the mean momentum using simulated samples, especially for low-n decay modes.
• Validate the method on Z, Higgs, Z', and QCD di-jet events, showing that the reconstructed mass peak aligns with the true resonance mass.
• Avoid dependence on E_T^miss by relying solely on visible tau decay products, making it orthogonal to standard missing energy-based variables.

Experimental results

Research questions

• RQ1 Can a new mass reconstruction technique be developed that improves resolution in di-tau final states without relying on missing transverse momentum?
• RQ2 How does the stochastic mass-reconstruction method perform in comparison to the collinear approximation in transverse-collimated tau pair configurations?
• RQ3 What is the impact of kinematic selection cuts (e.g., pT thresholds) on the reconstructed mass, and how can biases be corrected?
• RQ4 To what extent can this method be applied to both SM Higgs and exotic Z' boson searches in tau+tau final states?
• RQ5 Can the method be extended to reconstruct individual tau momenta in single-tau final states, such as W→τν decays?

Key findings

• The stochastic mass-reconstruction method achieves improved mass resolution by combining transverse momenta of two taus when they are aligned in the transverse plane.
• The momentum distribution of daughter particles in n-body decays follows a beta distribution: f(x)_{n-body} = (n-1)(1-x)^{n-2}, with an expected momentum fraction of ⟨x⟩ = 1/n.
• For 1-1 pion decay modes, kinematic thresholds (e.g., 1 GeV) induce a ~5% shift in the mean momentum relative to zero threshold, which can be corrected using simulated samples.
• The method is most effective in low-Lorentz-boosted, transverse-collimated configurations where the collinear approximation fails, and it provides a complementary variable to E_T^miss.
• The reconstructed mass peak aligns well with the true resonance mass in Z, Higgs, Z', and QCD di-jet simulations, validating its use in precision measurements.
• The technique is independent of missing transverse momentum and can be used as an additional variable in conventional di-tau analyses, enhancing signal discrimination.