Studies of Z $\to$ 4$\ell$ decays in proton-proton collisions at $\sqrt{s}$ = 8 and 13 TeV

This paper presents a study of Z boson decays into four charged leptons using proton-proton collision data at 8 and 13 TeV collected by the CMS detector, reporting precise measurements of inclusive and individual branching fractions, differential decay rates, and triple-product asymmetries that are consistent with Standard Model predictions and used to set limits on new gauge bosons.

The Gist

The Big Picture: Catching a Rare Bird in a Storm

Imagine the Large Hadron Collider (LHC) as a massive, high-speed train station where particles are smashed together billions of times a second. Most of the time, these collisions produce common, predictable results. But occasionally, a very rare event happens: a "Z boson" (a heavy particle that acts like a messenger of the weak force) decays into four charged leptons (electrons or muons) all at once.

Think of the Z boson as a magician. Usually, it pulls out two rabbits (two particles). But in this incredibly rare trick, it pulls out four rabbits simultaneously. The paper reports on a massive study by the CMS collaboration to catch this specific magic trick in action.

They looked at data from two different "seasons" of the LHC:

1. 2012: A smaller dataset (like a short summer vacation).
2. 2016–2018: A much larger dataset (like a long, productive work year).

By combining these, they caught 1,877 of these rare four-lepton events. This is a huge number for such a rare trick, allowing them to measure it with extreme precision.

The Main Goal: Measuring the "Magic Trick" Rate

The scientists wanted to answer a simple question: How often does the Z boson do this four-rabbit trick?

In the world of physics, this is called the "branching fraction." It's like asking, "If a magician performs 1 million tricks, how many times will they pull out four rabbits instead of two?"

• The Result: They found that this happens about 4.67 times out of every million Z boson decays.
• The Precision: They are very confident in this number, with an error margin of only about 3%.
• The Comparison: They compared their result to the "Standard Model" (the rulebook of how the universe should work). The rulebook predicted 4.70. The scientists measured 4.67. They match perfectly. This means the current rulebook is still working correctly; no new "magic" was found that breaks the rules.

Breaking It Down: The Different Rabbit Colors

The four rabbits (leptons) can be different colors (types):

• 4 Muons: All four are muons.
• 4 Electrons: All four are electrons.
• 2 Muons + 2 Electrons: A mix.

The paper is special because it measured the frequency of each specific combination separately for the first time with this level of detail. Just like checking if the magician is better at pulling out red rabbits vs. blue rabbits, they found that the rates for all combinations match the Standard Model predictions.

Looking for Hidden Clues: The "Dance Floor"

The scientists didn't just count the rabbits; they watched how they danced.

When the Z boson splits into four particles, those particles fly out in specific directions. The team mapped out the "dance moves" (kinematic and angular quantities) of these particles.

• The Analogy: Imagine a spinning top that breaks into four pieces. The pieces fly off in a pattern. If there were a hidden force or a new invisible particle involved, the pieces might fly off in a weird, lopsided pattern.
• The Finding: The "dance" looked exactly like the Standard Model predicted. The particles spun and flew in the expected, symmetrical ways.

The "Mirror Test": Checking for Time-Travel Violations

One of the most fascinating parts of the paper is a test for CP violation (Charge-Parity violation).

• The Concept: In physics, there's a rule that says if you look at a process in a mirror (parity) and swap particles for anti-particles (charge), the laws of physics should look the same. Sometimes, nature breaks this rule.
• The Test: The scientists looked at the "triple-product asymmetry." Imagine the four particles forming a shape in 3D space. They checked if the shape had a "handedness" (like a left hand vs. a right hand) that favored one direction over the other.
• The Result: The shape was perfectly balanced. There was no "handedness" bias. The universe passed the mirror test; no new physics was found that breaks this symmetry in this specific decay.

The "Ghost Hunter": Searching for New Particles

Finally, the scientists asked: "Could there be a new, invisible particle (let's call it a 'U boson') that helps the Z boson do this trick?"

• The Analogy: Imagine you see a magician pull a rabbit out of a hat. You suspect there might be a second, invisible assistant helping them. If that assistant existed, the magician would pull the rabbit out slightly more often or in a slightly different way.
• The Hunt: The team used their precise measurements to set limits on how heavy or how "strongly coupled" this invisible assistant could be.
• The Result: They ruled out a wide range of possibilities for this new particle. If this "U boson" exists, it must be very weak or very heavy, because the data didn't show the "extra help" the scientists were looking for.

Summary

In short, this paper is a masterclass in precision measurement.

1. They counted a very rare event (Z → 4 leptons) with record-breaking accuracy.
2. They confirmed that the universe behaves exactly as the Standard Model predicts.
3. They checked for subtle "glitches" in the laws of physics (CP violation) and found none.
4. They used these precise measurements to say, "If there is a new, light particle helping these decays, it's not hiding in the places we looked."

It's a victory for the current theory of physics, showing that our understanding of the subatomic world is still incredibly solid, even as we look for cracks in the foundation.

Technical Summary

Technical Summary: Studies of Z → 4ℓ decays in proton-proton collisions at √s = 8 and 13 TeV

Problem and Motivation
Decays of on-shell Z bosons into four charged leptons (electrons and muons, $Z \to 4\ell$) are predicted by the Standard Model (SM) to be rare, with a branching fraction on the order of $10^{-6}$. While these decays offer a unique window to observe physics beyond the Standard Model (BSM)—such as the existence of new light gauge bosons coupling to leptons—they have historically been difficult to study in detail due to their low rate. Previous measurements by the CMS and ATLAS collaborations at the LHC have agreed with SM predictions, but with limited precision. This paper addresses the need for a more precise and detailed study of the $Z \to 4\ell$ process to improve sensitivity to BSM physics, specifically constraining the production of new neutral scalar or vector bosons ($U$) that couple to electrons and/or muons.

Methodology
The analysis utilizes proton-proton collision data collected by the CMS detector at center-of-mass energies of $\sqrt{s} = 8$ TeV (2012, 19.7 fb$^{-1}$) and $\sqrt{s} = 13$ TeV (2016–2018, 138 fb$^{-1}$).

• Event Selection: Events are selected requiring exactly four tightly-identified leptons (electrons or muons) satisfying specific kinematic and topological criteria. The phase space is defined by a four-lepton invariant mass $80 < m_{4\ell} < 100$ GeV and a dilepton invariant mass $m_{\ell^+\ell^-} > 4$ GeV for any same-flavor, opposite-sign pair to suppress low-mass resonances like $J/\psi$.
• Normalization Strategy: To minimize systematic uncertainties associated with luminosity and cross-section measurements, the branching fraction $B(Z \to 4\ell)$ is extracted relative to the well-measured dilepton branching fraction $B(Z \to \ell^+\ell^-)$. The ratio of observed yields, corrected for acceptance and efficiency ($A\epsilon$), is used to infer the inclusive and flavor-specific branching fractions.
• Background Estimation: The dominant backgrounds arise from nonprompt leptons in $Z \to \ell^+\ell^-$ and $t\bar{t} \to 2\ell 2\nu$ processes. These are estimated using a "same-sign" control region in data, where one lepton pair is same-flavor and same-sign. Other prompt backgrounds (diboson, triboson, Higgs, $t\bar{t}Z$) are estimated using Monte Carlo simulations.
• Differential and Asymmetry Measurements: Differential decay rates are measured as functions of nine kinematic and angular quantities defined in the Z boson rest frame (e.g., invariant masses of lepton pairs, lepton momenta, and decay angles). Additionally, triple-product asymmetries ($A_{\sin \phi}$) are measured to test for violations of charge conjugation (C) and parity (P) invariance.
• BSM Constraints: Limits are set on a new light boson $U$ (scalar or vector) mediating the $Z \to 4\ell$ decay. The analysis considers cases where $U$ couples equally to electrons and muons, or exclusively to one flavor.

Key Contributions and Results

1. Precision Branching Fraction Measurement:
   The paper reports the most precise measurement of the inclusive branching fraction to date:
   $$B(Z \to 4\ell) = [4.67 \pm 0.11 \text{ (stat)} \pm 0.10 \text{ (syst)}] \times 10^{-6}$$
   This result has a total precision of approximately 3.2%, which is significantly more precise than previous CMS and ATLAS results and twice as precise as the latest ATLAS measurement. The measurement is consistent with the SM prediction of $(4.70 \pm 0.03) \times 10^{-6}$.

2. Flavor-Specific Branching Fractions:
   For the first time, CMS reports individual branching fractions for the distinct channels:

   • $B(Z \to 4\mu) = [1.25 \pm 0.04 \text{ (stat)} \pm 0.03 \text{ (syst)}] \times 10^{-6}$
   • $B(Z \to 2\mu 2e) = [2.17 \pm 0.08 \text{ (stat)} \pm 0.06 \text{ (syst)}] \times 10^{-6}$
   • $B(Z \to 4e) = [1.16 \pm 0.09 \text{ (stat)} \pm 0.06 \text{ (syst)}] \times 10^{-6}$
     All values are consistent with SM expectations.

3. Differential Decay Rates:
   Nine differential decay rates ($d\Gamma/dx$) are presented as functions of kinematic variables in the Z rest frame. These distributions, unfolded to the dressed lepton level and scaled to the full phase space, show good agreement with SM predictions based on POWHEG and MADGRAPH simulations.

4. CP Invariance Test:
   The triple-product asymmetry $A_{\sin \phi}$, a probe for C, P, and CP violation, is measured for all channels. The results are consistent with zero (e.g., $A_{\sin \phi} = -4.0 \pm 2.3\%$ for the inclusive sample), providing no evidence for CP violation in $Z \to 4\ell$ decays, as expected in the SM.

5. New Physics Constraints:
   Using the measured branching fractions, the paper sets 95% confidence level upper limits on the production of a new light boson $U$. These limits are more stringent than previous constraints derived from world-average branching fractions. Specifically, the analysis excludes regions in the $(m_U, g_\ell)$ parameter space for scalar and vector bosons coupling to leptons, complementing direct searches for narrow-width resonances.

Significance
The paper claims that this analysis represents the most precise determination of the $Z \to 4\ell$ branching fraction to date, reducing the uncertainty to the percent level. By providing flavor-specific measurements and detailed differential distributions, the work significantly improves the understanding of this rare decay process. The results serve as robust constraints on BSM models involving light gauge bosons with lepton couplings, particularly those relevant to leptophilic dark matter and $L_\mu - L_\tau$ symmetry models. The high statistical precision achieved allows for sensitive probes of CP invariance and sets the stage for future searches for new physics in the four-lepton final state.