[Paper Review] Cracking the dark matter code at the LHC

Won‐Sang Cho, Doojin Kim+2 more|arXiv (Cornell University)|Jun 7, 2012

Particle physics theoretical and experimental studies7 citations

TL;DR

This paper proposes a method to decode dark matter particle properties at the LHC by analyzing the invariant mass distribution of two visible particles produced in resonance decays involving invisible particles. By studying the shape—endpoint, peak, and curvature—of these distributions, the method can identify decay topologies and measure particle masses, with some cases allowing full reconstruction of the mass spectrum.

ABSTRACT

We consider the decay of a generic resonance to two visible particles and any number of invisible particles. We show that the shape of the invariant mass distribution of the two visible particles is sensitive to both the mass spectrum of the new particles, as well as the decay topology. We provide the analytical formulas describing the invariant mass shapes for the nine simplest topologies (with up to two invisible particles in the final state). Any such distribution can be simply categorized by its endpoint, peak location and curvature, which are typically sufficient to discriminate among the competing topologies. In each case, we list the effective mass parameters which can be measured by experiment. In certain cases, the invariant mass shape is sufficient to completely determine the new particle mass spectrum, including the overall mass scale.

Motivation & Objective

• To develop a model-independent method for probing the mass spectrum and decay topology of new particles decaying into visible and invisible final states at the LHC.
• To identify how the shape of the invariant mass distribution of two visible particles encodes information about the invisible particle masses and decay structure.
• To provide analytical formulas for the invariant mass shapes across the nine simplest decay topologies involving up to two invisible particles.
• To determine which effective mass parameters can be measured experimentally from these distributions.
• To assess whether the invariant mass shape alone can fully reconstruct the new particle mass spectrum, including the overall mass scale.

Proposed method

• The study analyzes the invariant mass distribution of two visible particles produced in the decay of a resonance, with any number of invisible particles in the final state.
• Analytical formulas are derived for the invariant mass shapes in the nine simplest decay topologies, considering up to two invisible particles.
• The shape of each distribution is characterized by three key features: the endpoint, peak location, and curvature, which are used to classify and distinguish topologies.
• The method relies on kinematic constraints and phase space integration to compute the differential decay rate as a function of the visible invariant mass.
• The analysis identifies measurable effective mass parameters—such as the endpoint and peak mass—that can be extracted from experimental data.
• The approach enables discrimination among competing topologies based on the functional form of the invariant mass distribution.

Experimental results

Research questions

• RQ1 Can the shape of the invariant mass distribution of two visible particles uniquely identify the decay topology involving invisible particles?
• RQ2 Which features of the invariant mass distribution (e.g., endpoint, peak, curvature) are most sensitive to the underlying particle mass spectrum?
• RQ3 To what extent can the full mass spectrum of new particles, including the overall mass scale, be reconstructed from the invariant mass shape alone?
• RQ4 Which effective mass parameters can be reliably measured in experiments from the observed invariant mass distributions?
• RQ5 How do different topologies (with up to two invisible particles) produce distinct invariant mass shapes that allow for discrimination?

Key findings

• The invariant mass distribution's shape—specifically its endpoint, peak location, and curvature—is sufficient to discriminate among the nine simplest decay topologies involving up to two invisible particles.
• In certain cases, the invariant mass shape alone allows complete determination of the new particle mass spectrum, including the overall mass scale.
• The method provides analytical formulas that describe the invariant mass distributions for all nine topologies with up to two invisible particles.
• The endpoint of the distribution is directly related to the mass of the parent resonance and the masses of the invisible particles.
• The peak location and curvature provide additional constraints that help distinguish between topologies with similar endpoints.
• Effective mass parameters such as the endpoint and peak mass can be measured experimentally and used to constrain the underlying particle physics model.