Measurement of the top-quark production cross-section and charge asymmetry at LHCb

Using 13 TeV proton-proton collision data corresponding to 5.4 fb⁻¹ of integrated luminosity, the LHCb experiment presents the first measurements of differential and total top- and antitop-quark production cross-sections and the top-quark charge asymmetry in the forward region, finding results consistent with next-to-leading-order Standard Model predictions.

The Gist

Imagine the Large Hadron Collider (LHC) as the world's most powerful particle smasher. Usually, when scientists look at the debris from smashing protons together, they look straight ahead or slightly to the sides. But the LHCb experiment is like a specialized camera perched on the side of the track, looking far down the "forward" tunnel.

This paper is about the LHCb team finally taking a close-up photo of the top quark, the heaviest and most massive particle in the Standard Model of physics. Think of the top quark as the "king" of the particle world—it's so heavy it's almost like a tiny, unstable planet that falls apart the moment it's born.

Here is what the scientists did and found, broken down into simple concepts:

1. The Hunt in the "Forward" Zone

Most other experiments at the LHC (like ATLAS and CMS) look at the center of the collision. The LHCb experiment, however, looks at the "forward" region—the area where particles fly off at a sharp angle, almost parallel to the beam.

• The Analogy: Imagine a cannon firing cannonballs. ATLAS and CMS are standing right in front of the cannon, catching the balls that fly straight out. LHCb is standing off to the side, catching the ones that ricochet or fly out at an angle.
• Why it matters: In this forward zone, the rules of how particles are made are slightly different. It's like looking at a crowd from the back of a stadium versus the front; you see different patterns. This specific view helps scientists understand the "glue" (gluons) that holds the protons together, especially when that glue is carrying a lot of energy.

2. The "Top" and "Anti-Top" Dance

When protons smash, they can create a pair of top quarks: a top ($t$) and an anti-top ($\bar{t}$).

• The Measurement: The team counted how many tops and anti-tops were created. They found that for every 100 tops created, there were about 85 anti-tops.
• The Result: They calculated the "production cross-section," which is a fancy physics way of saying "how big a target the top quark presents to the collision." They found the top quark is produced slightly more often than the anti-top quark in this forward region.

3. The Charge Asymmetry (The "Left-Right" Bias)

This is the most exciting part of the paper. In a perfectly symmetrical world, you would expect to see exactly the same number of tops flying left as anti-tops flying left. But the universe isn't always perfectly symmetrical.

• The Analogy: Imagine a dance floor where the music is slightly off-beat. If you ask everyone to spin, you might find that the men spin slightly more to the left, while the women spin slightly more to the right, even though the music is the same for everyone.
• The Finding: The LHCb team measured a "charge asymmetry." They found that top quarks tend to fly in one direction (forward) slightly more often than anti-top quarks do. The measurement was 0.08, which means there is a small but noticeable bias.
• Why it's a big deal: This is the first time this specific bias has been measured in the forward region at the LHC. Previous experiments had seen hints of it, but LHCb's unique angle provided a fresh, clearer view. The result matches the predictions of the Standard Model (our current best theory of physics), which is a good sign that our theory is working correctly.

4. How They Did It (The Detective Work)

Top quarks don't last long enough to be seen directly. They decay instantly into other particles. The team looked for a specific "signature" left behind:

• The Clue: They looked for a muon (a heavy electron) and a b-jet (a spray of particles coming from a bottom quark).
• The Filter: The detector is like a sieve. They had to filter out millions of "junk" events (like random sparks or other particles) to find the few thousand real top quark events. They used a sophisticated computer brain (a Deep Neural Network) to act like a bouncer, checking IDs to make sure the particles were actually what they claimed to be.
• The Data: They analyzed data from 2015 to 2018, equivalent to 5.4 "inverse femtobarns" of collisions (a unit of how much data they collected).

5. The Conclusion

The paper concludes that:

1. They successfully measured the top quark production rates in the forward region for the first time.
2. They measured the charge asymmetry (the slight preference for tops over anti-tops) and found it to be 0.08.
3. These numbers line up perfectly with the predictions made by the Standard Model.

In short: The LHCb team looked at the side of the particle collision track, caught the heaviest particle in the universe, and confirmed that it behaves exactly as our best theories predict, with a tiny, measurable preference for flying in one direction over the other. It's a victory for precision physics and a confirmation that our understanding of the subatomic world is still holding up.

Technical Summary

Technical Summary: Measurement of the top-quark production cross-sections and charge asymmetry at LHCb

Problem and Motivation
The top quark, as the most massive fundamental particle in the Standard Model (SM), plays a central role in electroweak symmetry breaking and Higgs boson interactions. Its production cross-section is highly sensitive to the gluon parton distribution function (PDF), particularly in the high-Bjorken-$x$ region where constraints remain weak. While the Large Hadron Collider (LHC) experiments ATLAS and CMS have extensively measured top-quark production in central rapidity regions, the forward region offers a unique kinematic regime. In this region, the SM predicts that approximately 80% of top quarks originate from $t\bar{t}$ pair production, while the remaining 20% are dominated by $t$-channel single-top production. Furthermore, while $t\bar{t}$ production is intrinsically charge symmetric at leading order, next-to-leading-order (NLO) QCD effects induce a small charge asymmetry. In proton-proton collisions, single-top production exhibits a significant intrinsic charge asymmetry (approx. 40%) due to the higher $u$-quark density relative to $d$-quarks. The LHCb detector, with its unique forward acceptance ($2 < \eta < 5$), provides a complementary environment to probe these kinematic regimes and potentially observe the top-quark charge asymmetry with enhanced sensitivity due to reduced dilution from gluon fusion.

Methodology
This analysis utilizes proton-proton collision data collected by the LHCb experiment at a center-of-mass energy of $\sqrt{s} = 13$ TeV, corresponding to an integrated luminosity of 5.4 fb$^{-1}$. The measurement focuses on the decay channel $t \to W^+ b$, where the $W$ boson decays leptonically to a muon ($W^+ \to \mu^+ \nu_\mu$).

• Fiducial Region: The analysis is performed within a specific fiducial phase space defined by:
  • Muon: $p_{T,\mu} > 25$ GeV and $2.0 < \eta_\mu < 4.5$.
  • $b$-jet: Reconstructed using the anti-$k_T$ algorithm ($R=0.5$) with $p_{T,jet} > 50$ GeV and $2.2 < \eta_{jet} < 4.0$.
  • System: The muon and $b$-jet system must satisfy $p_T(\mu + \text{jet}) > 20$ GeV.
• Event Selection and Background Suppression:
  • Candidates are formed from well-separated muon-jet pairs ($\Delta R > 0.5$).
  • Semileptonic heavy-flavor backgrounds are suppressed by requiring the muon impact parameter to be $< 0.04$ mm.
  • Hadron misidentification is suppressed via calorimeter energy deposit cuts.
  • $Z/\gamma^* \to \mu^+\mu^-$ contamination is rejected by vetoing events with a second high-$p_T$ muon.
  • $b$-jet identification utilizes a Deep Neural Network (DNN) classifier trained on simulated samples. A working point of $P_b > 0.65$ and $P_q < 0.05$ is selected. A template fit to the $P_b$ distribution in data is used to extract the $b$-jet fraction, yielding a purity of approximately 74%.
  • QCD multijet backgrounds are suppressed using kinematic criteria on the total transverse momentum of the $\mu+b$-jet system and muon isolation ($I_\mu > 0.9$). The residual QCD background is estimated using a data-driven ABCD method in the ($p_{T,total}$, $I_\mu$) plane.
  • Electroweak backgrounds ($Z+b$-jet and $W+b$-jet) are estimated using simulation and data-driven corrections.
• Correction and Efficiency:
  • Signal yields are corrected for detector effects, including muon reconstruction and selection efficiencies, jet reconstruction efficiency, and $b$-tagging efficiency.
  • Muon efficiencies are determined via a tag-and-probe method using $Z \to \mu^+\mu^-$ data.
  • Migration corrections for detector resolution effects are evaluated using simulation; bin-to-bin migrations in $\eta_\mu$ are found to be negligible.
  • An acceptance factor is applied to correct for the mismatch between the fiducial definition (vector sum $p_T$) and the signal region definition (muon-containing jet $p_T$).

Key Contributions and Results
The paper presents the first measurements of the differential production cross-sections for top ($t$) and antitop ($\bar{t}$) quarks as a function of muon pseudorapidity ($\eta_\mu$) in the forward region, along with the corresponding charge asymmetry ($A_C^t$).

• Integrated Cross-Sections:
  The total production cross-sections within the fiducial region are measured as:

  • $\sigma_t = 0.95 \pm 0.04 \text{ (stat)} \pm 0.08 \text{ (syst)} \pm 0.02 \text{ (lumi)}$ pb.
  • $\sigma_{\bar{t}} = 0.81 \pm 0.03 \text{ (stat)} \pm 0.07 \text{ (syst)} \pm 0.02 \text{ (lumi)}$ pb.
    The systematic uncertainties are correlated at the level of 96%.

• Charge Asymmetry:
  The inclusive top-quark charge asymmetry is measured to be:

  • $A_C^t = 0.08 \pm 0.03 \text{ (stat)} \pm 0.01 \text{ (syst)}$.
    This corresponds to a significance of 2.64$\sigma$ deviation from zero.

• Differential Measurements:
  Differential cross-sections and asymmetries are provided in bins of $\eta_\mu$ (ranging from 2.0 to 4.5). The results show good agreement with NLO Standard Model predictions from Powheg-BOX (using CT18 and NNPDF3.1 PDFs) and MadGraph (using NNPDF3.1).

Significance and Claims
The authors state that these results represent the most precise top-quark production cross-section measurements in the forward region to date. The measurement of the charge asymmetry is claimed to be the first significant observation of this observable at the LHC. The results are consistent with NLO Standard Model predictions. The paper notes that the measured asymmetry receives contributions from both $t\bar{t}$ and single-top production; in future analyses with larger datasets, the authors suggest that the measured asymmetry should be decomposed through a fit incorporating the expected asymmetries from both processes. The work provides complementary constraints to ATLAS and CMS, particularly for probing the gluon PDF at high $x$.