Electroweak physics and long-lived particles at LHCb

This paper presents LHCb's first measurements of $W$ and top quark production cross-sections and charge asymmetries using 5.1–5.4 fb$^{-1}$ of data to probe electroweak physics and parton distribution functions, while also discussing recent searches for long-lived particles such as axion-like particles and heavy neutral leptons.

The Gist

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful particle microscope. Inside the LHCb detector, scientists are like detectives sifting through billions of tiny cosmic collisions to solve two main mysteries: How well does our current rulebook (the Standard Model) hold up? and Are there hidden characters (new particles) lurking in the shadows?

This paper, presented by Felicia Volle from the University of Birmingham, reports on two major investigations the LHCb team has recently completed.

1. The Precision Check: Weighing the Cosmic Giants

Think of the Standard Model as a giant, complex machine. To make sure it's working perfectly, the scientists need to measure the "weight" and "behavior" of its biggest gears: the Z boson, the W boson, and the top quark.

• The Z-Boson (The Heavy Hitter):
  The team measured the mass of the Z boson (a particle that carries the weak force) by looking at how it splits into two muons (heavy cousins of electrons). It's like trying to weigh a speeding train by measuring the speed and angle of the two cars it breaks apart into. Because the LHCb detector is positioned at the "front" of the collision (looking forward rather than straight down the middle), they had to be incredibly precise with their calibration. They used known "anchors" (like the J/ψ particle) to ensure their rulers were straight.

  • The Result: They got a very precise weight for the Z boson. This is the first time this specific measurement has been done at the LHC, acting as a new, independent check on the machine's accuracy.

• The W-Boson (The Trickster):
  The W boson is harder to measure because it disappears instantly into a "ghost" (a neutrino) that detectors can't see. Usually, scientists have to guess how the ghost behaves based on theory.

  • The New Trick: The team tried a clever, "model-independent" approach. Instead of guessing the ghost's behavior, they measured the W boson's production rate first, then used that data to back-calculate its mass. It's like weighing a magician by measuring how much air they displace before they vanish, rather than trying to catch the ghost.
  • The Result: They successfully demonstrated this new method works, providing a fresh way to check the W boson's mass without relying too heavily on theoretical guesses.

• The Top Quark and the "Charge Asymmetry":
  The top quark is the heaviest known particle. The LHCb team measured how often these particles are created in the forward direction.

  • The Analogy: Imagine a busy highway where cars (particles) are created. The team noticed that slightly more "positive" cars are driving one way, and "negative" cars are driving the other. This imbalance is called charge asymmetry.
  • Why it matters: Because the LHCb detector looks at the "forward" lane of the highway (which other detectors miss), they found new details about how the "fuel" inside the proton (called Parton Distribution Functions) is distributed. This helps refine the map of how protons are built.

2. The Treasure Hunt: Looking for Hidden Mediators

The second part of the paper is a direct search for "Dark Sector" particles. Imagine the visible world (us, stars, atoms) and a "Dark World" that doesn't talk to us directly. For them to interact, they need a mediator—a translator that can speak both languages.

• Axion-Like Particles (The Invisible Messengers):
  Scientists looked for a specific type of mediator called an Axion-Like Particle (ALP). They imagined these particles being created in the collision and then instantly turning into two photons (particles of light).

  • The Search: They scanned the data for a "bump" in the energy spectrum—a sudden spike that would indicate a new particle appeared and vanished.
  • The Result: No bumps were found. This is actually good news for setting boundaries; it means these specific mediators don't exist in the mass range they looked at, or they are even more elusive than expected. This sets the tightest limits yet for this specific type of particle.

• Heavy Neutral Leptons (The Long-Lived Ghosts):
  These are heavy cousins of neutrinos that might explain why neutrinos are so light. The key feature here is that they are "long-lived."

  • The Analogy: Most particles created in the collision die instantly, right at the starting line. But these Heavy Neutral Leptons (HNLs) are like marathon runners; they might travel a few meters (or even several meters!) before they finally decay.
  • The Search: The team looked for these particles decaying inside the detector (short run) and even outside the main tracking area (long run). They used a new "AI brain" (a deep neural network) to spot the specific tracks left by these runners.
  • The Result: They didn't find any HNLs, but they improved the search limits by a factor of ten compared to previous runs. They also highlighted that with more data and better tracking of these "long-distance runners," the chances of finding them in the future are very promising.

The Bottom Line

This paper is a report card on the LHCb detector's performance.

1. Precision: They successfully weighed and measured the behavior of the universe's heavy particles (Z, W, Top) in a new "forward" direction, providing a unique perspective that complements other detectors.
2. Innovation: They introduced new tools, like AI-based tagging to spot heavy particles and new ways to measure mass without relying on old theories.
3. Discovery Potential: While they didn't find the "Dark Sector" mediators this time, they proved that their new methods (like looking for particles that travel far before decaying) are powerful enough to find them if they are there.

In short, the LHCb team has tightened the screws on our current understanding of physics and sharpened the tools needed to find the next big discovery.

Technical Summary

Technical Summary: Electroweak Physics and Long-Lived Particles at LHCb

Problem and Scope
This proceeding addresses two primary avenues for testing the Standard Model (SM) of particle physics: precision measurements of SM observables to probe for indirect Beyond the Standard Model (BSM) effects, and direct searches for BSM particles. The LHCb Collaboration focuses on the electroweak sector, specifically the properties of the $Z$ boson, $W$ boson, and top quark, as well as searches for mediators between the visible and dark sectors, namely axion-like particles (ALPs) and heavy neutral leptons (HNLs). A central theme is leveraging the forward acceptance of the LHCb detector to access low and high Bjorken-$x$ values, providing complementary constraints on parton distribution functions (PDFs) compared to central rapidity measurements.

Methodology and Analysis Strategies
The analysis utilizes proton-proton ($pp$) collision data collected by the LHCb experiment at center-of-mass energies of $\sqrt{s} = 5.02$ TeV and $13$ TeV, with integrated luminosities ranging from $100$ pb$^{-1}$ to $5.4$ fb$^{-1}$.

• Electroweak Precision Measurements:

  • $Z$-boson Mass: Reconstructed from $Z \to \mu^+\mu^-$ decays using the 2016 dataset ($1.7$ fb$^{-1}$). Momentum calibration relies on $\Upsilon(1S)$ and $J/\psi$ resonances and the pseudomass method at the $Z$ peak to minimize systematic uncertainties.
  • $W$-boson Mass: A model-independent approach is employed using a 2017 dataset ($100$ pb$^{-1}$ at $5.02$ TeV). This method factorizes experimental effects from signal modeling, extracting the mass from differential cross-sections of $W \to \mu\nu$ decays as a function of muon transverse momentum ($p_T$) without assuming a signal shape in $p_T$.
  • Cross-sections and Asymmetries: Differential production cross-sections for $W$ and top quarks are measured using datasets of $5.1$ fb$^{-1}$ and $5.4$ fb$^{-1}$ respectively. Signal separation utilizes template fits to muon isolation variables and $b$-jet probabilities. A novel multiclass neural network is used for $b$- and $c$-tagging, improving efficiency over secondary vertex-based algorithms. Charge asymmetries are extracted by separating differential cross-sections by muon charge.

• BSM Searches:

  • Axion-like Particles (ALPs): A search for $ALP \to \gamma\gamma$ decays is performed on 2018 data. The analysis assumes gluon-gluon fusion as the dominant production mode and employs multivariate methods to suppress combinatorial backgrounds and merged $\pi^0$ decays.
  • Heavy Neutral Leptons (HNLs): Searches target $B$-meson decays ($B^+_{(c)} \to \mu^+ N$ and $B \to \mu^+ N X$) in the $2016-18$ dataset ($5.0$ fb$^{-1}$). The HNL decay mode $\mu^\pm \pi^\mp$ is reconstructed. The analysis distinguishes between Dirac-like and Majorana-like HNLs based on charge combinations and categorizes tracks based on decay location (inside or outside the vertex locator).

Key Contributions and Results

1. First LHC $Z$-boson Mass Measurement: The Collaboration reports the first dedicated measurement of the $Z$-boson mass at the LHC, yielding $m_Z = 91185.7 \pm 8.3(\text{stat}) \pm 3.9(\text{sys})$ MeV.
2. Model-Independent $W$-boson Mass: A proof-of-concept measurement of $m_W = 80369 \pm 130(\text{exp}) \pm 33(\text{th})$ MeV is presented. While not superseding the $13$ TeV result, it demonstrates a novel factorization approach to reduce dependence on theoretical signal modeling.
3. First Forward $W$ and Top Cross-sections:
   • The first measurements of $W$ production cross-sections and muon charge asymmetries in the forward region are presented using $5.1$ fb$^{-1}$ of data. These represent the most precise muon asymmetry determinations in the forward region to date.
   • The first measurement of top-quark production cross-sections in the forward region is reported using $5.4$ fb$^{-1}$ of data. This includes the first extraction of top charge asymmetry in this kinematic region.
   • These measurements provide complementary constraints on PDFs due to the forward coverage.
4. BSM Search Limits:
   • ALPs: No candidates were found. Upper limits on the cross-section times branching fraction are set at 95% confidence level, representing the best limits on the decay constant $f_a$ for ALP masses in the $[4.9, 10]$ GeV range. This is the first search for a fully neutral final state by LHCb.
   • HNLs: No candidates were found in the $1.5$ to $5.5$ GeV mass range. The resulting upper limits on the coupling $|U_{\mu N}|^2$ improve upon previous LHCb Run 1 results by an order of magnitude.

Significance and Claims
The paper claims that these results significantly enhance the LHCb program's capability to probe the Standard Model and search for new physics. The forward coverage of the detector is highlighted as a unique asset for constraining PDFs and measuring charge asymmetries with high precision.

Methodologically, the work introduces and validates new tools and strategies:

• The use of deep neural networks for $b$- and $c$-tagging is shown to improve efficiency by $11-53\%$, with broad applicability to other analyses including Higgs searches.
• The model-independent extraction of the $W$-boson mass offers a pathway to decouple experimental measurements from theoretical modeling uncertainties.
• New tracking strategies, such as the reconstruction of "T-tracks" for particles decaying after traveling $2.5-8$ m, are identified as promising avenues for enhancing sensitivity to long-lived signatures.

The authors conclude that the combination of improved analysis tools, novel strategies (such as using fully neutral final states), and the statistical power of the upgraded detector's Run 3 dataset positions the LHCb experiment to significantly advance the discovery potential for BSM physics.