Study of Low Mass Long Lived Particles Decaying in the Muon System

Author: Gabrielle Dituri
Mentors: Maria Spiropulu, Christina Wang, Cristian Pena, and Si Xie
Editor: Stephanie Chen

The God Particle and Why it is Troublesome

The Higgs boson (nicknamed the “God Particle”) was discovered in 2012 at the Large Hadron Collider (LHC) by ATLAS and CMS¹. This nickname arrived due to a hilarious publishing decision in which the author of a book about the Higgs particle decided to shorten the original title (“the Goddamn Particle”) into a title that would appeal to a wider range of audiences (“the God Particle”). The original title was named to comedically highlight the difficulty in finding proof of the particle’s existence, which took about 50 years and an expensive particle accelerator. Despite this decision to shorten the name, the God Particle nickname accurately emphasizes the importance of the Higgs discovery to modern physics. The discovery of the particle provided credence to the Standard Model (SM), which is a model describing all the elementary particles and their interactions. The Higgs is an elementary particle previously predicted by the SM, but never before seen until 2012. The discovery of the particle confirmed that the Standard Model was able to correctly predict the existence of a particle before any data was collected. This is extremely important to particle physics as this shows that unknown particles can be predicted before we have the technology to find physical proof of them. According to the Standard Model, the Higgs can decay into fermions and massive gauge bosons (Fig. 1).

The SM dictates that the Higgs boson decays into SM particles including fermions, which are elementary particles with half odd integer spin (1/2, 3/2, etc.) that obey the Pauli Exclusion Principle.  However, we are looking to provide credence to an alternative theory³ which  suggests that the Higgs decays first into a pair of long lived particles (LLPs). These particles then decay into SM particles which are measured in the Cathode Strip Chamber (CSC), the endcap Muon System in CMS. The Higgs has a 20% probability of decaying into invisible particles, such as neutrinos or beyond the standard model (BSM) particles. Therefore, there is a possibility that the Higgs can decay to LLPs, which then decay back to decay modes that can be detected, like fermions⁴. LLPs are BSM particles, meaning they are extremely important to study as they could help solve many current problems in physics, such as the matter/antimatter asymmetry problem⁵. My research aims to verify the theory that the Higgs decays into LLPs by looking for this signature of the LLPs decaying back to SM particles in the CSC system. The decayed LLPs generally create a large cluster of RecHits (reconstructed hits in the detector) in the CSC thus allowing us to accurately study them.  Furthermore, we would like to understand if the number of RecHits are related to mass and the decay mode of the LLPs, and how the distribution is different from that of background. The background mostly consists of particles such as pions and kaons that are produced at the interaction point (the point where the protons collide) instead of particles produced from the displaced decays. 

Methods and Results

For this study, we utilized 10 simulated samples (Fig. 3, col. 1). Here, k is a kaon, pi is a pion, d is down quark, τ is tau lepton, e is an electron, and b is bottom quark. These particles were used as they represent a broad spectrum of particles, including some charged/neutral, quarks/leptons, etc.

Acceptance vs Lifetime

We were able to plot a graph of acceptance (the number of events that have at least 1 LLP decay in CSC) vs proper lifetime (Fig. 2). The larger the number of signal events, the more sensitive the detector is to a decay. From this graph, we could clearly see that the most sensitive lifetime is highly dependent on the LLP mass and that the Muon System is sensitive to low mass LLP with shorter lifetime.

Acceptance and Clustering Efficiency

We then calculated the acceptance for events pertaining to LLPs with differing lifetimes (Fig. 3). We also looked at how many of those events had a cluster matched to LLP, where a cluster has 50 or more RecHits. The cluster matched simply means that a cluster was produced from a specific LLP.  By analyzing these two percentages, we were able to conclude the Clustering Efficiency in RecHitCluster. The Clustering Efficiency is defined as the number of events with a cluster matched to LLP/ number of events that have at least 1 LLP decay in CSC. This is important as it tells us if the formation of clusters is related to the LLP mass and the type of particles that they decay to.

Decay Particles, ms (GeV), cτ (mm)	% Acceptance	% Events with a Cluster Matched to LLP	Clustering Efficiency (%)
ee, 0.5, 500	3.04	0.90	29.50
ee, 1, 100	15.65	5.00	31.94
ee, 1, 500	6.59	1.95	29.67
pi0pi0, 1, 100	15.65	5.00	31.98
pi0pi0, 1, 500	6.58	1.99	30.18
pi+pi–, 1, 500	6.55	4.05	61.90
k+k–, 1.5, 500	8.80	5.70	64.83
dd, 1, 1000	3.74	1.96	52.43
ττ, 7, 1000	14.15	6.45	45.58
bb, 15, 1000	16.35	11.94	73.04

Relationship Between Number of Events and Mass

We wanted to find the relationship between the number of events/hits and the lifetime and mass of the LLP the particles decayed from. This gave us insight into how sensitive the detector is concerning these factors. One of the ways we did this was by analyzing the relationship between events and X Spread (how much the clusters are spread in the X direction of the detector) , Y Spread (how much the clusters are spread in the Y direction of the detector), N Station (station in the detector where the hits are detected), Cluster Size (number of RecHits in the clusters), pseudorapidity of the cluster (represents the angle of the particle relative to the z axis), and Avg Station (average of the station number of the RecHits, 4 stations for the CSC).

Based on the table (Fig. 3) and the graphs above, the initial conclusion was that the detector is sensitive to the branching ratio (the ratio of Higgs decaying to LLP) of similar order of magnitude for LLPs with different masses. We concluded this because the Clustering Efficiency and the RecHits distribution are similar for the different signal samples. Additionally, we can see that the detector is sensitive to decay particles since pi⁺pi^– and pi⁰pi⁰ have extremely different Clustering Efficiencies despite being produced from LLPs with the same mass and lifetime.

Clustering Efficiency and Geometry

We plotted the Clustering Efficiency with respect to several factors, including the LLP decay position and the energy of the LLP. This shows us how the Clustering Efficiency varies in the detector and which showers penetrate the stations (Fig. 10-12).

The LLP decay vertex Z/R plots clearly show the shape of the detector: when the LLP decays in the sensitive detector volume the Clustering Efficiency increases. Fig. 13 directly demonstrates why the Clustering Efficiency fluctuates – the iron/steel in the detector prevents a high Clustering Efficiency while the sensitive detector region encourages a high Efficiency. There also seems to be a small increase of Clustering Efficiency with LLP energy, but it is not highly dependent. As all these graphs exhibit the same general shape, we concluded that the detector is sensitive to different particles. More specifically, we can see from Fig. 10-12 that Clustering Efficiency is dependent on the type of shower – a particle shower is a cascade of particles produced from a particle collision. Hadronic shower particles like bb tend to have a higher Clustering Efficiency, and electromagnetic (EM) shower particles like ee tend to have a lower Clustering Efficiency. Because the Clustering Efficiency is higher for hadronic shower particles, we know that the level of sensitivity is different depending on the type of shower.

2D Clustering Efficiency

Finally, we wanted to analyze the 2D Clustering Efficiency plots, which would help to further show the difference between hadronic and EM showers. We knew from the previous graphs that the Clustering Efficiency changed according to the type of shower due to the geometry of the detector (Fig. 13). However, we wanted to visualize the dependence on detector geometry in both the R and Z direction of the detector. Below are the 2D Clustering Efficiency graphs, with the red boxes representing the detector volume.

In a Nutshell (more like Particle Detector)

In summary, we saw that the Muon System is sensitive to all LLP decay modes – ee, bb, dd, ττ, pi⁰pi⁰, pi⁺pi^–, k⁺k^–, but that the level of sensitivity is different between these decay modes. Also, our preliminary study shows that Clustering Efficiency and Cluster Size are correlated with the LLP energy and momentum. Furthermore, we found that hadronic showers have more penetration than EM showers. Most importantly, we found that the Muon System is sensitive to LLPs with mass as low as 0.4 GeV; this is the first study at the CMS to set limits on the sensitivity of low mass LLPs.

Why Does This (anti)Matter?

Dark matter may be comprised of these BSM particles which is why this field is important to study: dark matter makes up most of the universe, and we still do not know exactly what it is. In the future, I hope to continue my research on this topic and find the exact level of sensitivity to LLP mass and decay mode. I additionally hope to research the lowest mass that the detector is sensitive to, which would help in looking for BSM particles. In general, conducting studies like this one, not bound by the SM, brings us physicists closer than ever to finding a unifying theory to describe the world around us.

Acknowledgements

Thank you so much to my SURF supervisor, Maria Spiropulu. Without her mentorship, I never would have undertaken such an amazing project. Also thank you to Cristian Pena and Si Xie who constantly reviewed my work and gave me great feedback. Special thanks to Christina Wang who guided me through every aspect of the project and helped me realize my passion for this field!

References

1. Gray, Heather, and Bruno Mansoulié, “The Higgs Boson: the Hunt, the Discovery, the Study and Some Future Perspectives.” ATLAS Experiment at CERN, 4 July 2018.
2. Particles of the Standard Model of particle physics (Image: Daniel Dominguez/ CERN).
3. Craig, Nathaniel, et al. “Naturalness in the Dark at the LHC.” Journal of High Energy Physics, vol. 2, 23 Mar. 2015, doi:10.1007/jhep07(2015)105.
4. Blas, J. De, et al. “Higgs Boson Studies at Future Particle Colliders.” Journal of High Energy Physics, vol. 1, 9 May 2019, doi:10.1007/jhep01(2020)139.
5. The Matter-Antimatter Asymmetry Problem. CERN, home.cern/science/physics/matter-antimatter-asymmetry-problem.