Search for Z' bosons decaying into charginos in final states with two oppositely charged leptons and missing transverse momentum in pp collisions at $\sqrt{s}$ = 13 TeV

Using 138 fb$^{-1}$ of proton-proton collision data at 13 TeV, the CMS experiment searched for massive leptophobic Z' bosons decaying into charginos in final states with two oppositely charged leptons and missing transverse momentum, finding no evidence of new physics and setting upper limits that exclude Z' boson masses up to approximately 3.5 TeV.

The Gist

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful particle smasher. It takes two beams of protons and smashes them together at nearly the speed of light, creating a chaotic explosion of energy that briefly recreates conditions similar to the Big Bang.

This paper is a report from the CMS experiment (one of the giant detectors watching the crash), and it's essentially a cosmic treasure hunt. The scientists are looking for a specific, elusive type of "gold" hidden in the debris: a heavy, invisible particle called a $Z'$ boson.

Here is the story of the hunt, broken down into simple concepts:

1. The Target: The "Ghost" Particle ($Z'$)

Physicists have a theory called the Standard Model, which is like a rulebook for how the universe works. But they suspect there are missing pages. One idea is that there is a new, heavy force-carrier particle called a $Z'$ boson.

• The Twist: Usually, when scientists look for new heavy particles, they expect them to decay into pairs of electrons or muons (light, charged particles), which are easy to spot.
• The Sneaky Part: This specific paper looks for a "leptophobic" $Z'$. "Leptophobic" means "fear of leptons." This particle hates decaying into electrons or muons. Instead, it prefers to decay into charginos.

2. The Suspects: Charginos and Neutralinos

If the $Z'$ is the mastermind, the charginos are its henchmen.

• The Chargino: A heavy, charged particle that is a cousin to the electron but much heavier.
• The Neutralino: A stable, invisible particle that is a top candidate for Dark Matter (the invisible stuff holding galaxies together).

The Chain Reaction:

1. The $Z'$ boson is created in the collision.
2. It instantly splits into two charginos.
3. Each chargino immediately decays into a W boson (which turns into a visible electron or muon) and a Neutralino.
4. The Neutralino is invisible. It escapes the detector without leaving a trace, taking energy with it.

The Signature:
Because the Neutralinos escape, the detector sees a "missing" amount of energy. So, the scientists are looking for a very specific crime scene:

• Two visible suspects: Two oppositely charged particles (like an electron and a positron, or a muon and an antimuon) flying out.
• One missing piece: A huge amount of "missing transverse momentum" (energy that vanished into the dark).

3. The Detective Work: The "Parametrized Neural Network"

The problem is that the background noise is deafening. Every second, the LHC produces billions of collisions that look almost like the signal (e.g., top quarks decaying). It's like trying to find a specific needle in a haystack, but the haystack is made of millions of other needles that look 99% identical.

To solve this, the team didn't just use a simple ruler. They built a super-smart AI detective called a Parametrized Neural Network (PNN).

• How it works: Imagine a human detective who has to learn a new case for every single suspect's height and weight. It would take forever.
• The PNN Advantage: This AI is trained to learn the pattern of the crime, not just one specific suspect. It takes the mass of the $Z'$ and the chargino as "inputs" (like telling the detective, "Look for a suspect who is 2 meters tall"). It learns the relationships between the angles, speeds, and missing energy of the particles.
• The Result: It can scan through millions of collisions and say, "This event looks 95% like our specific $Z'$ scenario," even if the $Z'$ has a slightly different mass than the one it was trained on.

4. The Verdict: "No New Gold Found (Yet)"

The team analyzed data from 2016, 2017, and 2018, covering a massive amount of collisions (138 "inverse femtobarns"—a unit that represents a huge number of crashes).

• The Outcome: They looked at the data, ran it through their AI, and compared it to what the Standard Model predicts.
• The Result: Everything matched the Standard Model. They found no evidence of the $Z'$ boson or the charginos.
• The Silver Lining: Even though they didn't find the particle, they learned something valuable. They can now say with 95% confidence: "If this $Z'$ boson exists, it must be heavier than 3.5 TeV (about 3,500 times the mass of a proton)."

The Bottom Line

Think of this paper as a negative search warrant. The scientists went into the forest with a very specific map and a high-tech metal detector. They didn't find the treasure, but they successfully proved that the treasure isn't buried anywhere in the first 3.5 kilometers of the forest.

This narrows the search for the next generation of physicists. They now know exactly where not to look, allowing them to focus their energy on even heavier, more elusive particles in the future. The hunt for the "Ghost" continues!

Technical Summary

Here is a detailed technical summary of the CMS paper CMS-SUS-23-006, titled "Search for Z′ bosons decaying into charginos in final states with two oppositely charged leptons and missing transverse momentum in pp collisions at √s = 13 TeV."

1. Problem and Physics Motivation

The search targets a specific Beyond the Standard Model (BSM) scenario involving leptophobic $Z'$ bosons within the $U(1)'$-extended Minimal Supersymmetric Standard Model (UMSSM).

• Theoretical Context: The UMSSM, derived from the $E_6$ grand unified theory, introduces an extra gauge boson ($Z'$). In specific charge scenarios, this $Z'$ is "leptophobic," meaning its decays to Standard Model (SM) leptons are suppressed. This allows it to evade stringent limits from traditional dilepton resonance searches ($Z' \to \ell^+\ell^-$).
• Signal Process: Instead of decaying to SM particles, the $Z'$ decays into a pair of charginos ($\tilde{\chi}^\pm_1$). These charginos subsequently decay into a $W$ boson and the lightest neutralino ($\tilde{\chi}^0_1$, the dark matter candidate). The $W$ bosons decay leptonically.
• Final State Signature: The process $pp \to Z' \to \tilde{\chi}^+_1 \tilde{\chi}^-_1 \to (W^+ \tilde{\chi}^0_1) (W^- \tilde{\chi}^0_1) \to \ell^+ \nu \tilde{\chi}^0_1 \ell^- \nu \tilde{\chi}^0_1$ results in:
  • Two oppositely charged high-momentum leptons ($e^\pm, \mu^\pm$).
  • Significant missing transverse momentum ($p^{\text{miss}}_T$) from the neutrinos and neutralinos.
• Gap in Previous Searches: Previous $Z'$ searches focused on dilepton resonances (ignoring $p^{\text{miss}}_T$), while direct chargino searches assumed direct production (ignoring the kinematic constraints of a heavy parent $Z'$). This analysis bridges that gap.

2. Methodology

Data and Simulation

• Dataset: Proton-proton collision data at $\sqrt{s} = 13$ TeV collected by the CMS experiment in 2016, 2017, and 2018.
• Integrated Luminosity: $138 \text{ fb}^{-1}$.
• Signal Generation: Generated using MADGRAPH5_aMC@NLO at Leading Order (LO). The $Z'$ and chargino masses were scanned ($m_{Z'}$: 1.7–4.1 TeV; $m_{\tilde{\chi}^\pm_1}$: 345–1845 GeV). The neutralino mass was fixed at half the chargino mass ($m_{\tilde{\chi}^0_1} = 0.5 m_{\tilde{\chi}^\pm_1}$).
• Background Simulation: SM backgrounds ($t\bar{t}$, single top, $WZ$, $ZZ$, $WW$, Drell-Yan, etc.) were simulated using POWHEG (NLO) and MADGRAPH5_aMC@NLO (NLO), interfaced with PYTHIA 8 for parton showering and hadronization.

Object Reconstruction and Selection

• Leptons: Electrons and muons with $p_T > 25$ GeV and $|\eta| < 2.5$ (excluding transition regions).
• Event Selection Criteria:
  • Exactly two oppositely charged leptons ($e^+e^-$, $\mu^+\mu^-$, or $e^\pm\mu^\mp$).
  • Leading lepton $p_T > 80$ GeV; trailing lepton $p_T > 40$ GeV.
  • Dilepton invariant mass $m_{\ell\ell} > 100$ GeV (to suppress on-shell $Z$ bosons).
  • Missing transverse momentum $p^{\text{miss}}_T > 100$ GeV.
  • Veto: Events with $b$-tagged jets are rejected to suppress $t\bar{t}$ background.

Multivariate Analysis (Parametrized Neural Network)

To distinguish the signal from irreducible backgrounds (primarily $t\bar{t}$, $WW$, and $tW$), the analysis employs a Parametrized Neural Network (PNN).

• Innovation: Unlike standard NNs trained on fixed mass points, the PNN includes the signal model parameters ($m_{Z'}$ and $m_{\tilde{\chi}^\pm_1}$) as inputs during training. This allows a single model to be applied across the entire mass grid without retraining.
• Input Variables:
  • Kinematic: $p_T$ of leading/trailing leptons, $m_{\ell\ell}$, $p^{\text{miss}}_T$.
  • Derived: Transverse mass ($m_T$), stransverse mass ($M_{T2}$), vector sums of momenta.
  • Angular: $\Delta\phi$ and $\Delta R$ between leptons and $p^{\text{miss}}_T$.
• Training Strategy: The PNN is trained on half the simulated events (signal + backgrounds) and validated on the other half. The training is performed independently for each search channel ($ee$, $\mu\mu$, $e\mu$).

Statistical Interpretation

• Control Regions (CRs): Three CRs are defined to constrain background normalizations:
  • $t\bar{t}$ CR: Requires $\ge 1$ $b$-jet.
  • $WW$ CR: Requires $40 < m_{\ell\ell} < 100$GeV (only in$e\mu$ channel).
  • DY CR: Requires $30 < p^{\text{miss}}_T < 100$GeV (only in$ee$and$\mu\mu$ channels).
• Fit: A binned likelihood fit is performed on the PNN score distributions in the Signal Region (SR) and CRs simultaneously. Systematic uncertainties (luminosity, JES, $b$-tagging, PDFs, etc.) are treated as nuisance parameters.
• Limits: Upper limits on the production cross-section are set at 95% Confidence Level (CL) using the CLs method.

3. Key Contributions

1. First Search of its Kind: This is the first LHC search specifically targeting leptophobic $Z'$ bosons decaying to chargino pairs in the dilepton + $p^{\text{miss}}_T$ channel.
2. Parametrized Neural Network: Demonstrates the effectiveness of PNNs in high-energy physics for scanning large parameter spaces (mass grids) with a single, flexible model, avoiding the computational cost of training separate networks for every mass point.
3. Comprehensive Background Control: Utilizes a multi-channel approach with dedicated control regions for $t\bar{t}$, $WW$, and Drell-Yan processes to robustly constrain SM backgrounds in a signal-rich region.

4. Results

• Observation: The measured data distributions in the Signal Regions are consistent with Standard Model expectations. No significant excess was observed.
  • A mild excess (2–3$\sigma$ local significance) was noted in the $\mu^+\mu^-$ channel in the signal-like bin, but it is not statistically significant enough to claim a discovery.
  • The $e^\pm\mu^\mp$ channel showed a mild deficit.
• Exclusion Limits:
  • Cross-Section Limits: Upper limits on $\sigma(pp \to Z') \times \text{BR}(Z' \to \tilde{\chi}^+_1 \tilde{\chi}^-_1)$ were set as a function of $m_{Z'}$ and $m_{\tilde{\chi}^\pm_1}$.
  • Mass Exclusions:
    • For a chargino mass of $m_{\tilde{\chi}^\pm_1} \approx 1.8$ TeV, $Z'$ boson masses up to 3.5 TeV are excluded.
    • Assuming a $Z'$ mass of 2.9 TeV decaying exclusively to charginos, chargino masses in the range 400–1400 GeV are excluded.
  • The sensitivity is driven primarily by the $e^\pm\mu^\mp$ channel due to higher signal and background yields.

5. Significance

This analysis significantly expands the reach of SUSY and $Z'$ searches at the LHC. By targeting a "leptophobic" scenario, it probes a region of parameter space that is invisible to traditional dilepton resonance searches. The successful application of the PNN technique sets a precedent for future searches involving complex, multi-parameter BSM models where scanning the full mass space with traditional methods would be computationally prohibitive. The results constrain the UMSSM parameter space, ruling out specific combinations of heavy $Z'$ and chargino masses up to the multi-TeV scale.