Measurement of the top-quark mass using decays with a $J/\psi$ meson at $\sqrt{s}=$13 TeV with the ATLAS detector

Using 140 fb$^{-1}$ of 13 TeV proton-proton collision data collected by the ATLAS detector, the top-quark mass is measured to be 172.17 $\pm$ 1.56 GeV by analyzing the invariant mass distribution of systems comprising an isolated lepton and a $J/\psi$ meson from top-quark decays.

The Gist

Imagine the universe is a giant, high-speed car race. In this race, the top quark is the heaviest, most powerful car on the track. Because it is so heavy, it is incredibly unstable; the moment it is created, it instantly crashes and breaks apart into smaller pieces.

For decades, physicists have been trying to weigh this "race car" (the top quark) to see if our understanding of the universe's rules (the Standard Model) is correct. The problem is, since the car explodes so fast, you can't just put it on a scale. You have to weigh the pieces it leaves behind.

The New Way to Weigh the Car

In the past, scientists tried to weigh the top quark by looking at the "debris" (jets of particles) it leaves behind. But measuring debris is messy; it's like trying to guess the weight of a car by weighing the scattered pieces of metal and glass after a crash, where some pieces might be missing or distorted.

This paper describes a new, cleaner approach used by the ATLAS experiment at CERN's Large Hadron Collider (LHC). Instead of looking at the messy debris, they looked for a very specific, rare "signature" left behind: a $J/\psi$ meson.

Think of the $J/\psi$ meson as a perfectly wrapped gift box that only appears when a specific part of the top quark's crash happens. This box is made of two muons (a type of particle) that are very easy to track and measure with high precision. Because this "gift box" is made of clean, well-behaved particles, it acts like a high-precision ruler, avoiding the messiness of the other debris.

How They Did It

1. The Collision: They smashed protons together at nearly the speed of light (13 TeV energy) using the LHC. This created millions of top quarks.
2. The Hunt: They sifted through 140 "years" worth of data (an integrated luminosity of 140 fb⁻¹) looking for events where a top quark decayed into:
   • A standard "isolated" particle (an electron or muon) from the main crash.
   • The special "gift box" ($J/\psi$ meson) made of two muons.
3. The Measurement: They measured the combined weight (invariant mass) of the isolated particle and the two muons from the gift box. Because this combination is sensitive to the original top quark's mass, they could work backward to figure out how heavy the top quark was.

The Result

After running a complex statistical "fit" (like finding the best-fitting curve through a cloud of data points), they found:

• The Weight: The top quark weighs 172.17 GeV.
• The Precision: They are very confident in this number, with a total uncertainty of 1.56 GeV.

The "Recoil" Problem

The paper highlights one specific source of uncertainty called the "recoil scheme."

Imagine the top quark is a cannon firing a shell. When the shell flies out, the cannon kicks back (recoils). In the computer simulations used to predict what should happen, physicists have to decide what absorbs that kick.

• Option A: The kick is absorbed by the heavy $b$-quark (the "gift box" maker).
• Option B: The kick is absorbed by the top quark itself before it fully decays.

The paper found that changing this assumption in their computer models changed the calculated mass by about 1.07 GeV. This is the largest single source of uncertainty in their result. It's like saying, "We know the car weighs 172.17, but depending on whether we think the engine or the wheels absorbed the crash impact, the weight could be slightly different."

Why This Matters

This measurement is important because:

1. It's a Different Angle: It uses a method that doesn't rely on measuring messy "jets" of particles, which usually causes the biggest errors in other measurements.
2. It Checks the Rules: The result (172.17 GeV) agrees well with previous measurements from other experiments (like CMS and earlier ATLAS runs). This consistency helps confirm that our current "rulebook" of particle physics is correct.
3. Future Improvements: The paper notes that the main limitation right now is the amount of data (statistical uncertainty). If they collect more data in the future, they can shrink the uncertainty even further, making the "scale" even more precise.

In short, the ATLAS team used a rare, clean "gift box" signature to weigh the universe's heaviest particle, confirming previous results while highlighting a specific area where our computer simulations of particle crashes could still be tweaked for even better accuracy.

Technical Summary

1. Problem and Motivation

The top-quark mass ($m_{top}$) is a fundamental parameter of the Standard Model (SM) and plays a critical role in testing the consistency of the SM, particularly regarding vacuum stability and electroweak precision observables. While $m_{top}$ has been measured with high precision (total uncertainty $\sim 0.33$ GeV) by combining results from the Tevatron and LHC (ATLAS and CMS), these measurements predominantly rely on reconstructing the full top-quark decay products, including jets.

Key Challenges in Current Measurements:

• Jet Energy Scale (JES) Uncertainty: The dominant systematic uncertainties in traditional measurements arise from the calibration of jet energies and $b$-jet energy scales.
• Theoretical Ambiguities: The definition of the mass parameter in Monte Carlo (MC) simulations is scheme-dependent, and different reconstruction methods probe different aspects of the mass definition.

Motivation for this Analysis:
This paper presents a measurement using a partial reconstruction method that exploits the decay chain $t \to W b$, followed by $b \to J/\psi + X \to \mu^+\mu^- + X$. The observable used is the invariant mass of the system composed of the isolated lepton ($\ell = e, \mu$) from the $W$ boson decay and the muon pair from the $J/\psi$ decay: $m(\ell \mu^+\mu^-)$.

• Advantage: This observable consists entirely of leptons, offering superior momentum resolution and significantly reducing sensitivity to jet energy calibration uncertainties.
• Goal: To provide a complementary measurement with a distinct set of systematic uncertainties to test the consistency of the theoretical interpretation of the top-quark mass.

2. Methodology

Data and Simulation:

• Dataset: Proton-proton collision data collected by the ATLAS detector during LHC Run 2 ($\sqrt{s} = 13$ TeV), corresponding to an integrated luminosity of 140 fb$^{-1}$.
• Signal Processes: Top-quark pair ($t\bar{t}$) and single-top-quark production.
• Simulation: Signal events were simulated using Powheg Box v2 (NLO QCD) interfaced with Pythia 8 (parton shower and hadronisation). Alternative samples using Herwig 7 and variations in parton shower parameters were used to estimate systematic uncertainties. Backgrounds (e.g., $W/Z$+jets, dibosons) were modeled using Sherpa and MadGraph5_aMC@NLO.

Object Definition and Selection:

• Leptons: Events require exactly one isolated high-$p_T$ lepton ($e$ or $\mu$) from the $W$ decay ($p_T > 25$ GeV).
• $J/\psi$ Reconstruction: Reconstructed via the decay $J/\psi \to \mu^+\mu^-$. The muons are "soft" ($p_T > 3$ GeV) and non-isolated, originating from $b$-hadron decays.
• Selection Criteria:
  • At least one $b$-tagged jet.
  • $J/\psi$ invariant mass in the range $2.9\text{--}3.3$ GeV.
  • $J/\psi$ transverse momentum $p_T > 8$ GeV.
  • System transverse momentum $p_T(\ell \mu^+\mu^-) > 25$ GeV.
  • Invariant mass of the system $10 < m(\ell \mu^+\mu^-) < 160$ GeV.
• Yield: Approximately 12,165 events passed the final selection. The signal fraction (events with a true $b \to J/\psi$ decay) is $\sim 73\%$.

Analysis Technique:

• Template Fit: An unbinned maximum-likelihood fit is performed on the $m(\ell \mu^+\mu^-)$ distribution.
• Templates:
  • $m_{top}$-dependent: Constructed from $t\bar{t}$ and single-top samples generated with various input masses ($169$ to $176$ GeV). These are parameterized using a sum of a Gaussian and a LogNormal function.
  • $m_{top}$-independent: Constructed from background processes ($W/Z$+jets, dibosons, etc.) and fitted with a Chebyshev polynomial.
• Calibration: The relationship between the generated mass ($m_{gen}$) and the reconstructed mass ($m_{rec}$) was verified to be linear and unbiased using pseudo-experiments.

3. Key Contributions

1. Novel Observable: The first ATLAS measurement of $m_{top}$ using the $m(\ell \mu^+\mu^-)$ observable, which bypasses the dominant jet energy scale uncertainties affecting previous measurements.
2. Systematic Uncertainty Characterization: A detailed breakdown of uncertainties specific to this channel, highlighting the sensitivity to:
   • Parton Shower and Hadronisation: Modeling of the $b$-quark fragmentation and gluon recoil.
   • $b$-quark Fragmentation: The specific modeling of how the $b$-quark turns into a $b$-hadron and subsequently a $J/\psi$.
   • Recoil Scheme: The ambiguity in the dipole parton shower regarding which particle recoils against secondary gluon emissions from the $b$-quark.
3. Data-Driven Background Estimation: Utilization of the "matrix method" for non-prompt/fake leptons and sideband checks for combinatorial backgrounds.

4. Results

The measured top-quark mass is:
$$m_{top} = 172.17 \pm 0.80 \text{ (stat)} \pm 0.81 \text{ (syst)} \pm 1.07 \text{ (recoil)} \text{ GeV}$$

• Total Uncertainty: 1.56 GeV.
• Breakdown of Uncertainties:
  • Statistical: 0.80 GeV (dominated by the limited number of signal events due to the small branching ratio of $b \to J/\psi$).
  • Systematic (excluding recoil): 0.81 GeV. Major contributors include parton shower/hadronisation modeling (0.40 GeV), $W$+jets background modeling (0.40 GeV), and final-state radiation (0.21 GeV).
  • Recoil Uncertainty: 1.07 GeV. This arises from the ambiguity in the dipole parton shower gluon-recoil scheme (choosing between the $b$-quark or the top quark as the recoil particle). This is the largest single source of uncertainty.
• Comparison: The result is in good agreement with previous ATLAS measurements, the ATLAS+CMS Run 1 combination ($172.52 \pm 0.33$ GeV), and the CMS measurement in the same channel ($173.5 \pm 3.0$ GeV).

5. Significance

• Complementarity: This measurement provides a crucial cross-check for the top-quark mass using a method with a completely different systematic error profile. While traditional measurements are limited by jet energy scales, this method is limited by theoretical modeling of the $b$-quark fragmentation and parton showers.
• Theoretical Insight: The large uncertainty associated with the gluon-recoil scheme (1.07 GeV) highlights a significant gap in the theoretical understanding of how parton showers handle color coherence and recoil in top-quark decays. This suggests that future improvements in $m_{top}$ precision using this channel depend heavily on refining QCD shower models rather than just collecting more data.
• Future Prospects: The statistical uncertainty (0.80 GeV) indicates that with the full High-Luminosity LHC dataset, the statistical precision could be significantly improved, potentially making this a competitive method for future $m_{top}$ determinations once the modeling uncertainties are better constrained.

In summary, this paper establishes a robust, jet-independent method for measuring the top-quark mass, yielding a result consistent with the Standard Model but exposing specific areas in QCD modeling (recoil and fragmentation) that require further theoretical and experimental attention.