Search for a leptoquark in events with a hadronically decaying $\tau$-lepton and missing transverse momentum using $pp$ collisions 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, this study searches for leptoquarks in final states containing a hadronically decaying $\tau$-lepton and missing transverse momentum, finding no excess over Standard Model predictions and setting 95% confidence level limits on couplings for $U_1$ vector-leptoquark masses between 1.5 and 3.0 TeV.

The Gist

The Big Picture: Hunting for "Cosmic Glue"

Imagine the universe is built out of tiny Lego bricks. We have two main types of bricks: quarks (which build protons and neutrons) and leptons (like electrons and tau particles). For decades, the Standard Model of physics has said these two types of bricks never stick together directly; they can only interact by passing a messenger particle back and forth.

However, some recent experiments have noticed a strange glitch. When certain heavy particles (B-mesons) decay, they seem to be turning into "tau" particles more often than the rules say they should. It's like a vending machine that is supposed to give you a soda 10% of the time, but lately, it's giving you a soda 15% of the time.

Physicists suspect there might be a new, invisible "glue" holding these two different types of bricks together. They call this hypothetical glue a Leptoquark. It's a particle that can grab a quark and a lepton and smash them together, acting as a bridge between two worlds that usually don't mix.

The Experiment: A High-Speed Particle Smackdown

The ATLAS team at CERN's Large Hadron Collider (LHC) decided to hunt for this glue. They took protons (which are like tiny bags of quarks) and smashed them together at nearly the speed of light.

The Setup:
Think of the collision as a high-speed car crash. When the cars (protons) hit, they shatter into a million pieces. The ATLAS detector is a giant, 360-degree camera that takes a snapshot of every piece flying out.

The Clue They Were Looking For:
The team wasn't looking for just any debris. They were specifically looking for a very rare, specific pattern:

1. A Tau particle that breaks apart into a spray of other particles (like a firework exploding).
2. A lot of missing energy. Since we can't see neutrinos (ghostly particles that pass through everything), we know they are there because the total energy in the snapshot doesn't add up. It's like seeing a billiard ball hit a rack, and suddenly the table has less energy than it started with—something must have flown off the table unseen.

They looked for these "Tau + Missing Energy" events happening alongside a Jet (a spray of particles from a quark).

The Strategy: Two Ways to Catch the Glue

The team looked for the Leptoquark in two different ways, like looking for a lost key in two different rooms:

1. The "Resonant" Search (The Direct Hit):
   Imagine throwing a ball at a wall. If the wall has a specific hole, the ball might get stuck there for a split second before falling through. The team looked for a Leptoquark that is created directly and then immediately falls apart into a Tau and a quark. This would show up as a distinct "bump" in the data at a specific weight (mass).

2. The "Non-Resonant" Search (The Invisible Hand):
   Imagine two people throwing a ball at each other, but instead of catching it, they just graze past each other, and the ball changes direction slightly without ever being held. This is the "t-channel" exchange. The Leptoquark isn't created as a real particle; it just exists for a split second as a force, nudging the particles apart. This would show up as a general increase in high-energy crashes, rather than a specific bump.

The Results: The Ghost Remains Elusive

After analyzing a massive amount of data (140 "inverse femtobarns"—which is a fancy way of saying they watched trillions of collisions), the team found nothing.

• The Analogy: Imagine you are looking for a specific type of rare bird in a forest. You set up high-powered cameras and listen for its call for months. You see thousands of other birds, squirrels, and wind in the trees. But you never hear the call of the rare bird.
• The Conclusion: The number of "Tau + Missing Energy" events they saw matched exactly what the Standard Model predicts. There were no extra events, no bumps, and no strange excesses.

What This Means for the "Glue"

Even though they didn't find the Leptoquark, this is still a very important result. By not finding it, they have drawn a "No Trespassing" sign on a huge chunk of the map.

• The Map: They tested Leptoquarks with masses between 1.5 and 3.0 TeV (which is about 1,500 to 3,000 times heavier than a proton).
• The Limit: They calculated that if this "glue" exists, it cannot be as strong as they hoped for in that weight range. They have ruled out many of the theories that tried to explain the "vending machine glitch" (the B-meson anomalies) using this specific type of Leptoquark.

Summary

The ATLAS collaboration smashed protons together, looked for a specific, rare pattern of debris that would signal a new "glue" particle connecting quarks and leptons, and found nothing but the expected background noise.

The takeaway: The universe is still behaving exactly as the old rules predicted in this specific scenario. The "Leptoquark" remains a ghost, and if it does exist, it is either too heavy or too weak to be seen by this specific experiment. The search continues, but this particular path has been closed off.

Technical Summary

Technical Summary: Search for a Leptoquark in Events with a Hadronically Decaying $\tau$-Lepton and Missing Transverse Momentum

Problem and Motivation
Semileptonic decays of $B$ mesons, specifically the ratios $R(D^{(*)}) = \mathcal{B}(B \to D^{(*)}\tau\nu)/\mathcal{B}(B \to D^{(*)}\ell\nu)$, exhibit a persistent deviation of approximately $3.8\sigma$ from Standard Model (SM) expectations. This anomaly suggests a breakdown of lepton flavor universality (LFU) and motivates the search for new physics, potentially mediated by leptoquarks (LQs). While previous searches by ATLAS and CMS have focused on leptoquark pair production or singly produced LQs decaying into $\tau\tau$ final states, these analyses often assume that the signal rate depends primarily on the $b\tau$ coupling. However, explaining the $R(D^{(*)})$ anomaly within specific vector leptoquark ($U_1$) models often requires a non-zero coupling to the charm quark and tau neutrino ($c\nu$). This paper presents the first ATLAS search specifically targeting the $\tau\nu(+b)$ final state to directly probe scenarios where the $c\nu$ coupling is significant, a region not thoroughly covered by previous $\tau\tau$ searches.

Methodology
The analysis utilizes proton–proton collision data collected by the ATLAS detector at $\sqrt{s} = 13$ TeV during Run 2 (2015–2018), corresponding to an integrated luminosity of 140 fb$^{-1}$. The search targets the production of a vector leptoquark $U_1$ with quantum numbers $(3, 1, 2/3)$. Two distinct production mechanisms are considered:

1. Resonant single production: $U_1$ produced via $t$-channel exchange, decaying into a high-$p_T$ $b$- or $s$-quark and a $\tau$-lepton.
2. Non-resonant production: $t$-channel exchange leading to a $\tau\nu$ system with an associated jet.

The signal is characterized by a hadronically decaying $\tau$-lepton ($\tau_{\text{had}}$) with high transverse momentum ($p_T > 200$ GeV) and large missing transverse momentum ($E_T^{\text{miss}}$). Events are categorized into four Signal Regions (SRs) based on the presence of a $b$-jet and the expected mass regime:

• Resonant SRs (SR0b-Res, SR1b-Res): Optimized for lower LQ masses ($\sim 1.5$ TeV), requiring $E_T^{\text{miss}} > 200$ GeV and transverse mass $m_T > 200$ GeV.
• Non-resonant SRs (SR0b-NonRes, SR1b-NonRes): Optimized for higher masses, requiring $E_T^{\text{miss}} > 400$ GeV and $m_T > 600$ GeV.

Backgrounds are estimated using simulated samples constrained by data in Control Regions (CRs). The dominant background, $W \to \tau\nu$ + jets, is normalized using CRs with a lepton ($e$ or $\mu$) instead of a $\tau_{\text{had}}$. Top-quark backgrounds are constrained using CRs with a $\tau_{\text{had}}$ and an additional lepton. Validation Regions (VRs) are employed to test the extrapolation of background estimates from CRs to SRs.

Key Contributions

• Novel Channel: This work introduces the first ATLAS analysis targeting the $\tau\nu(+b)$ final state, specifically designed to probe the interplay between $b\tau$ and $c\nu$ couplings in the $U_1$ leptoquark model.
• Coupling Sensitivity: The analysis is sensitive to the high-$\beta_{23}^L$ region of the parameter space (where $\beta_{23}^L$ governs the $c\nu$ coupling), which is less constrained by previous pair-production searches that are largely insensitive to the coupling strength at leading order.
• Comprehensive Strategy: By categorizing events by $b$-jet multiplicity and distinguishing between resonant and non-resonant topologies, the search covers a wide range of coupling scenarios ($g_U$ and $\beta_{23}^L$) for leptoquark masses between 1.5 TeV and 3.0 TeV.

Results
No significant excess of events above the Standard Model background prediction is observed in any of the signal regions. The observed data are in good agreement with the post-fit background expectations across all kinematic distributions.

• Exclusion Limits: Upper limits on the signal strength $\mu$ are set at the 95% confidence level (CL) using the $CL_s$ method.
• Parameter Space: Limits are derived on the coupling $g_U$ as a function of the leptoquark mass $m_{U_1}$ for fixed values of $\beta_{23}^L$, and on $\beta_{23}^L$ as a function of $g_U$ for fixed masses.
  • For $m_{U_1} = 1.5$ TeV, observed upper limits on $g_U$ are 1.13 (at $\beta_{23}^L = 1.0$) and 0.52 (at $\beta_{23}^L = 2.2$).
  • For $m_{U_1} = 2.5$ TeV, observed upper limits on $g_U$ are 2.30 (at $\beta_{23}^L = 1.0$) and 1.22 (at $\beta_{23}^L = 2.2$).
• Anomaly Constraints: The results exclude parts of the parameter space favored by $B$-physics anomalies, particularly at higher values of $\beta_{23}^L$. However, the analysis does not rule out the entire region consistent with the $R(D^{(*)})$ anomaly, as lower coupling values remain allowed.

Significance
The paper claims that this search provides complementary constraints to previous leptoquark searches. While pair-production searches offer the strongest constraints at low masses for large couplings, this single-production and non-resonant analysis probes the high-$\beta_{23}^L$ region, which is critical for explaining the $R(D^{(*)})$ anomaly in specific UV-complete models. By setting limits on the couplings in the benchmark $U_1$ vector-leptoquark model, the analysis narrows the viable parameter space for new physics explanations of the $B$-meson flavor anomalies, specifically testing scenarios where the $c\nu$ coupling plays a dominant role.