[Paper Review] An improved mass reconstruction technique for a heavy resonance decaying to $ au^+ au^-$

L. Xia|arXiv (Cornell University)|Jan 11, 2016

Particle physics theoretical and experimental studies3 references3 citations

TL;DR

This paper proposes a novel mass reconstruction technique for heavy resonances decaying to $\tau^+\tau^-$, using only the magnitude of the invisible momentum $|\vec{p}_{\text{inv}}|$ and the masses of visible/invisible decay products ($m_{\text{vis}}, m_{\text{inv}}$), reducing unknowns from eight to four. By sampling these variables via Monte Carlo simulations and selecting the mass with maximal likelihood, the method achieves a mass resolution of 14% relative to the nominal mass, outperforming traditional methods without relying on neutrino momentum assumptions or solving complex equations.

ABSTRACT

For a resonance decaying to $ au^+ au^-$, it is difficult to reconstruct its mass accurately because of the presence of neutrinos in the decay products of the $ au$ leptons. If the resonance is heavy enough, we show that its mass can be well determined by the magnitude of the momentum of the invisible decay products, $|\vec{p}_{inv}|$, and the mass of the visible/invsible decay products, $m_{vis/inv}$, for $ au$ decaying to hadrons/leptons (4 unknowns in total). We do not need to know all the components of $\vec{p}_{inv}$s and $m_{vis/inv}$s (8 unknonws in total). By sampling all kinematically allowed values of $|\vec{p}_{inv}|$ and $m_{vis/inv}$ according to their distributions in the MC simulations, the mass of the mother resonance is assumed to lie at the postion with the maximal probability. This new mass reconstruction technique inherits the similar idea from the Missing Mass Calculator Technique (MMCT). It has a better performance, since it neither relies on the assumption that only the neutrinos from the tau leptons contribute to the missing transverse energy, nor requires to solve a set of equations. The method is tested using the MC simulations of the reaction $pp o Z/h(125)/h'(750) o au au$ at 13~TeV. The reconstructed mass resolution divided by the nominal mass is found to be about 14\%.

Motivation & Objective

• To address the challenge of accurate mass reconstruction for heavy resonances decaying to $\tau^+\tau^-$ when neutrinos in the decay products obscure momentum balance.
• To reduce reliance on full momentum reconstruction of invisible neutrinos, which is impractical in experimental data.
• To improve mass resolution compared to existing techniques like the Missing Mass Calculator Technique (MMCT), especially in high-mass resonance scenarios.
• To develop a method that avoids assumptions about neutrino contributions to missing transverse energy and eliminates the need to solve systems of equations.

Proposed method

• The method uses only the magnitude of the invisible momentum $|\vec{p}_{\text{inv}}|$ and the masses $m_{\text{vis}}$ and $m_{\text{inv}}$ as kinematic variables, reducing the number of unknowns from eight to four.
• It samples all kinematically allowed values of $|\vec{p}_{\text{inv}}|$ and $m_{\text{vis/inv}}$ based on Monte Carlo simulation distributions.
• The resonance mass is determined by identifying the value that maximizes the likelihood of the observed kinematic configuration.
• The approach inherits the core idea of the Missing Mass Calculator Technique (MMCT) but improves it by avoiding assumptions about neutrino momentum and eliminating equation solving.
• The method is validated using Monte Carlo simulations of $pp \to Z/h(125)/h'(750) \to \tau^+\tau^-$ at $\sqrt{s} = 13$ TeV.
• It assumes the resonance mass lies at the peak of the probability distribution derived from the sampled variables.

Experimental results

Research questions

• RQ1 Can the mass of a heavy resonance decaying to $\tau^+\tau^-$ be reconstructed with improved accuracy by reducing reliance on full neutrino momentum reconstruction?
• RQ2 Does using only $|\vec{p}_{\text{inv}}|$ and $m_{\text{vis/inv}}$ as variables yield better mass resolution than traditional methods?
• RQ3 To what extent does eliminating the assumption that only $\tau$-neutrinos contribute to missing transverse energy improve reconstruction performance?
• RQ4 Can the method avoid solving complex systems of equations while maintaining high resolution in mass reconstruction?
• RQ5 What is the achievable mass resolution using this technique in high-mass $\tau^+\tau^-$ resonance decays?

Key findings

• The proposed method achieves a reconstructed mass resolution of approximately 14% relative to the nominal resonance mass.
• The resolution is obtained without assuming that only $\tau$-neutrinos contribute to the missing transverse energy, improving robustness.
• The method avoids solving a system of equations, simplifying implementation and reducing computational cost.
• By sampling $|\vec{p}_{\text{inv}}|$ and $m_{\text{vis/inv}}$ from Monte Carlo distributions, the method effectively captures the kinematic likelihood of the resonance mass.
• The technique outperforms traditional approaches by reducing the number of unknowns from eight to four, enhancing precision.
• The method is validated in $pp \to Z/h(125)/h'(750) \to \tau^+\tau^-$ simulations at 13 TeV, confirming its feasibility and performance.