[Paper Review] Determining masses of supersymmetric particles

B. K. Gjelsten, D.J. Miller+1 more|ArXiv.org|Nov 1, 2005

Particle physics theoretical and experimental studies8 references3 citations

TL;DR

This paper presents a method to determine supersymmetric particle masses at the LHC using invariant mass distribution endpoints from cascade decays, particularly in the mSUGRA model. By analyzing kinematic edges in dilepton and quark-lepton invariant masses, the authors show that mass differences can be measured with high precision, though absolute masses suffer from ambiguities and lower accuracy, which can be resolved by combining LHC data with Linear Collider measurements of the lightest supersymmetric particle mass.

ABSTRACT

If supersymmetric particles are produced at the Large Hadron Collider it becomes very important not only to identify them, but also to determine their masses with the highest possible precision, since this may lead to an understanding of the SUSY-breaking mechanism and the physics at some higher scale. We here report on studies of how such mass measurements are obtained, and how the precision can be optimized.

Motivation & Objective

• To develop a robust method for measuring supersymmetric particle masses at the LHC despite the presence of invisible decay products.
• To address the challenge of reconstructing full decay chains when the lightest supersymmetric particle (LSP) escapes detection.
• To quantify the precision of mass measurements, particularly distinguishing between mass differences and absolute masses.
• To investigate the existence of multiple viable mass solutions from endpoint data and assess their compatibility with experimental data.
• To propose a strategy—combining LHC endpoint measurements with Linear Collider data—to resolve mass ambiguities and improve absolute mass accuracy.

Proposed method

• Uses invariant mass distributions (e.g., $m_{ll}$, $m_{ql({ m low})}$, $m_{ql({ m high})}$, $m_{qll}$) from cascade decays such as $ ilde{q} \to \tilde{\chi}^0_2 \to \tilde{l} \to \tilde{\chi}^0_1$ to extract kinematic endpoints.
• Applies analytical expressions for composite functions describing the shape of invariant mass distributions, which exhibit abrupt slope changes at endpoints.
• Performs numerical $\chi^2$ fits to endpoint data to extract particle masses, comparing multiple competing solutions.
• Identifies and evaluates mass solution ambiguities by comparing $\chi^2$ values of different mass configurations, with a threshold of $\Delta\chi^2 < 1$ or $3$ to define acceptable alternatives.
• Proposes combining LHC endpoint data with a direct measurement of the LSP mass from a Linear Collider to fix the absolute mass scale and resolve degeneracies.
• Uses benchmark points SPS 1a (α) and SPS 1a (β) to validate the method and quantify precision and ambiguity levels.

Experimental results

Research questions

• RQ1 How can supersymmetric particle masses be extracted from invariant mass distributions in cascade decays when the LSP is undetected?
• RQ2 What is the precision of mass difference measurements versus absolute mass measurements using endpoint techniques?
• RQ3 To what extent do multiple mass solutions exist that are consistent with the same set of measured endpoints?
• RQ4 How does the probability of selecting a non-nominal mass solution depend on the experimental uncertainty and the number of measured endpoints?
• RQ5 Can combining LHC endpoint data with a Linear Collider measurement of the LSP mass resolve mass ambiguities and significantly improve absolute mass accuracy?

Key findings

• Mass differences (e.g., $m_{\tilde{l}_R} - m_{\tilde{\chi}^0_1}$) are measured with much higher precision than absolute masses, with errors about an order of magnitude smaller.
• For the SPS 1a (α) benchmark, the nominal solution (1,1) region has a 12% probability of being mixed with a competing solution in the (1,2) region when $\Delta\chi^2 < 1$ is allowed.
• In SPS 1a (α), the root-mean-square deviation for $m_{\tilde{q}_L}$ is 6.0 GeV in the nominal solution, but only 5.0 GeV in the (1,2) solution, indicating that alternative solutions are not easily ruled out.
• The mass difference $m_{\tilde{\chi}^0_2} - m_{\tilde{\chi}^0_1}$ is measured with a precision of 0.18 GeV in the nominal solution, compared to 0.29 GeV in the competing solution.
• The SPS 1a (β) scenario exhibits three competing minima, with the nominal solution having significant admixture from other solutions, highlighting the challenge of solution degeneracy.
• Combining LHC endpoint data with a Linear Collider measurement of the LSP mass is shown to drastically improve the accuracy of absolute masses by fixing the mass scale and resolving ambiguities.