Search for light scalar particles produced in Higgs boson decays in exclusive final states with two muons and two hadrons in proton-proton collisions at $\sqrt{s}$ = 13 TeV

Using 138 fb$^{-1}$ of 13 TeV proton-proton collision data from the CMS experiment, this study searches for exotic Higgs boson decays into pairs of light scalar particles (0.4–2.0 GeV) that decay into collimated muon and hadron pairs, setting upper limits on the branching fraction at the $\mathcal{O}(10^{-4})$ level for proper decay lengths up to $\sim$1 mm.

The Gist

The Big Picture: Hunting for Invisible Ghosts in a Giant Machine

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful, high-speed car crash simulator. Scientists smash protons together at nearly the speed of light to see what tiny pieces fly out. Usually, they look for heavy, famous particles like the Higgs boson (often called the "God particle" because it gives other particles mass).

This paper is about a specific, tricky hunt: looking for light, invisible "ghost" particles that might be hiding inside the debris of a Higgs boson crash.

The Story: The Higgs and its Secret Children

Think of the Higgs boson as a fragile, heavy egg. When it breaks (decays), it usually splits into known, heavy ingredients. But physicists suspect that sometimes, instead of breaking into known pieces, it might split into two light, secret children (called scalar particles, or $S$).

These "children" are very light (about the weight of a few atoms) and are very shy. They might:

1. Disappear immediately (decay right where they are born).
2. Run a short distance before disappearing (decay a few millimeters away).

The paper focuses on a very specific scenario:

• The Higgs splits into two of these light particles ($S$).
• One $S$ turns into a pair of muons (heavy cousins of electrons).
• The other $S$ turns into a pair of light hadrons (either pions or kaons, which are like tiny, lightweight bricks).

The Challenge: Finding a Needle in a Haystack

The problem is that the "haystack" (background noise) is massive. Every time the LHC smashes protons, it creates millions of random particles that look exactly like the signal we want. It's like trying to find two specific red marbles in a stadium full of people throwing red, blue, and green marbles everywhere.

To solve this, the CMS team (the scientists) used a clever strategy:

1. The "Flashlight" Trigger: They decided to only look at crashes where one of the "children" ($S$) immediately turns into muons. Muons are easy to spot, like a bright flashlight in a dark room. This helps the computer decide which crashes to save for later analysis.
2. The "Twin" Check: They looked for a second pair of particles (the pions or kaons) that appeared at the exact same time and had the exact same mass as the muon pair. If you find two pairs of particles that are perfect twins, it's very unlikely to be a random accident. It's like finding two identical, rare coins in a pile of junk; it suggests they came from the same source.
3. The "Displacement" Test: Some of these light particles might travel a tiny distance before vanishing. The scientists checked if the particles appeared slightly away from the center of the crash. This is like checking if a firework exploded right where the fuse was lit, or if it flew a few feet away before popping.

What They Did

• The Data: They analyzed 138 "years" of data (technically 138 inverse femtobarns, a unit of collision volume) collected between 2016 and 2018.
• The Search: They looked for these specific "twin pairs" (muons + hadrons) in the debris.
• The Filter: They built a digital sieve to filter out the millions of fake signals, keeping only the events that looked like the Higgs breaking into these specific light particles.

The Results: No Ghosts Found (Yet)

After looking through all the data, they did not find any evidence of these light particles.

However, this is still a huge success for science. Here is what they learned:

• Setting the Limits: They can now say with 95% confidence that if these light particles do exist, they are much rarer than previously thought. Specifically, the Higgs boson cannot turn into these particles more than about 1 in 10,000 times (a branching fraction of $10^{-4}$).
• Covering New Ground: They checked a mass range (0.4 to 2.0 GeV) and a distance range (up to 100 mm) that hadn't been thoroughly explored before. It's like mapping a new continent and saying, "We looked everywhere here, and we didn't find the treasure, but now we know exactly where it isn't."

The Takeaway

This paper is a "negative result" in the best possible way. It didn't find new particles, but it successfully ruled out a large area of possibilities. It tells physicists: "If you are looking for these light, shy particles that decay into muons and pions, you won't find them here. You'll have to look in a different place or with different tools."

It's like a detective saying, "We checked the entire basement and found no footprints. The thief didn't go down there." This helps narrow the search for the next big discovery in physics.

Technical Summary

Technical Summary: Search for Light Scalar Particles in Exclusive Higgs Decays

Problem and Motivation
The discovery of the Higgs boson confirmed the Standard Model (SM) of particle physics, yet significant gaps remain regarding its couplings and potential decays into invisible or exotic states. Theoretical extensions, such as the "Higgs portal" scenario involving a real singlet scalar field $S$ mixing with the SM Higgs field $H$, predict the existence of light scalar bosons ($m_S \sim \mathcal{O}(\text{GeV})$). These particles are relevant to models of dark matter, cosmic inflation, and the hierarchy problem.

While searches for heavy scalar bosons are well-established, the low-mass region ($m_S \lesssim 2$ GeV) presents unique challenges. In this regime, hadronic decays of the scalar boson do not produce collimated jets but rather exclusive final states of light hadrons (pions or kaons). Previous searches in this mass window have been limited by SM resonances or overwhelmed by QCD backgrounds in inclusive production modes. This paper addresses the search for the process $H \to SS$, where one scalar decays to a muon pair ($S \to \mu^+\mu^-$) and the other to a pair of charged hadrons ($S \to h^+h^-$, where $h = \pi, K$), covering scalar masses between 0.4 and 2.0 GeV and proper decay lengths ($c\tau$) up to 100 mm.

Methodology
The analysis utilizes proton-proton collision data collected by the CMS experiment at $\sqrt{s} = 13$ TeV during 2016–2018, corresponding to an integrated luminosity of 138 fb$^{-1}$.

• Signal Topology: The search targets the exclusive final state $\mu^+\mu^- h^+h^-$. Due to the large mass difference between the Higgs boson (125 GeV) and the light scalars, the decay products are highly boosted and collimated.

• Event Selection:

  • Trigger: Events are selected using isolated single-muon triggers ($p_T > 24$ or $27$ GeV) and, for the 2018 dataset, displaced dimuon triggers to enhance sensitivity to long-lived particles.
  • Reconstruction: Offline, events require two muons and two charged hadrons. Muons must have $p_T > 5$ GeV and $|\eta| < 2.4$, with the leading muon satisfying higher thresholds to ensure trigger efficiency. Hadrons are identified via the particle-flow algorithm, with mass hypotheses assigned based on the scalar mass ($m_S \le 1.0$ GeV uses pions; $m_S \ge 1.1$ GeV uses kaons).
  • Vertexing: Oppositely charged pairs are fitted to secondary vertices. The analysis categorizes events based on the transverse displacement significance ($L_{xy}/\sigma_{xy}$) of the dimuon and dihadron vertices, creating four categories: prompt, displaced $\mu\mu$, displaced $hh$, and fully displaced.
  • Mass Constraints: A crucial background suppression technique involves a two-dimensional mass selection in the $(m_{\mu\mu}, m_{hh})$ plane. Since the signal involves two identical scalars, the invariant masses of the two pairs are expected to be approximately equal ($m_{\mu\mu} \approx m_{hh}$). A diagonal mass window is defined around the signal hypothesis, rejecting the majority of QCD multijet backgrounds.
  • Isolation: Relative isolation requirements are applied to muons and hadrons, with looser criteria for displaced categories to recover signal efficiency.

• Background Estimation: The dominant background arises from QCD multijet events and $t\bar{t}$ production. The background in the signal region (SR) is estimated directly from data in a control region (CR) defined by the Higgs boson mass sidebands ($110 < m_{\mu\mu hh} < 122.5$ GeV and $127.5 < m_{\mu\mu hh} < 140$ GeV). An exponential fit to the CR distribution is extrapolated into the SR. For non-prompt categories with low statistics in the CR, a "loose" CR is defined by relaxing isolation criteria, and transfer factors are applied to correct the yield.

• Systematic Uncertainties: Major uncertainties include the statistical limitation of the control region, the modeling of the Higgs boson $p_T$ spectrum (17%), secondary vertex reconstruction efficiency (5–40%), and trigger/reconstruction efficiencies.

Key Contributions

1. Novel Search Strategy: The paper demonstrates a novel approach to probing hadronic decays of light scalar bosons by requiring one scalar to decay to muons. This bypasses the overwhelming hadronic backgrounds that typically plague fully hadronic searches in inclusive Higgs production.
2. Exclusive Final State Reconstruction: The analysis fully reconstructs the exclusive $H \to \mu^+\mu^- h^+h^-$ final state, utilizing the kinematic correlation between the two scalar decay products to suppress background.
3. Extended Parameter Space: The search covers a previously under-explored parameter space of light ($0.4–2.0$ GeV) and long-lived ($c\tau$ up to 100 mm) scalar particles, specifically targeting the region where hadronic decays result in exclusive two-body final states rather than jets.

Results
No significant excess of events over the expected background was observed in any of the four displacement categories or across the mass range. Consequently, upper limits on the branching fraction $\mathcal{B}(H \to SS)$ were set at the 95% confidence level (CL).

• Sensitivity: For scalar masses between 0.4 and 2.0 GeV, the analysis sets upper limits on $\mathcal{B}(H \to SS)$ at the level of $\mathcal{O}(10^{-4})$ for proper decay lengths up to $\sim 1$ mm.
• Mass Dependence: Sensitivity improves at higher masses due to lower backgrounds, though a dip in sensitivity is observed near 1 GeV, attributed to the smaller branching fraction of $S \to \mu^+\mu^-$ in that region.
• Decay Length Dependence: Limits are strongest for prompt-like signatures ($c\tau \lesssim 0.1$ mm) where reconstruction and trigger efficiencies are highest. Sensitivity decreases for larger decay lengths ($c\tau > 10$ mm) as vertices become more displaced, reducing trigger efficiency and reconstruction quality.

Significance
The paper claims to provide unique, complementary sensitivity to the BSM process $H \to SS$ in the low-mass regime. By successfully reconstructing exclusive final states with light hadrons and muons, the analysis excludes branching fractions greater than $10^{-4}$ for a wide range of scalar masses and lifetimes. This result covers a largely unexplored parameter space for light, long-lived particles, offering stringent constraints on minimal Higgs portal scenarios and motivating further exploration of light scalar sectors in future collider experiments.