Measurement of the dineutrino system kinematic variables in dileptonic top quark pair production in proton-proton collisions at$\sqrt{s}$ = 13 TeV

Using 138 fb$^{-1}$ of proton-proton collision data at $\sqrt{s}$ = 13 TeV collected by the CMS detector, this study measures differential top quark pair production cross sections in dilepton final states as a function of dineutrino system kinematic variables, finding results consistent with Standard Model predictions.

The Gist

Imagine the Large Hadron Collider (LHC) at CERN as a massive, high-speed particle racetrack. Scientists smash protons together at nearly the speed of light to create a chaotic explosion of new particles. Among the most famous "race cars" produced in these crashes are top quarks, the heaviest known elementary particles. They are so unstable that they immediately break apart (decay) into other particles, much like a fragile glass vase shattering the moment it hits the floor.

This paper is a detailed report from the CMS Collaboration, a team of scientists using a giant detector called CMS to study what happens when two top quarks are created and then break apart in a specific way: the "dileptonic" channel.

Here is a breakdown of what they did and found, using simple analogies:

1. The Mystery of the "Invisible Ghosts"

When top quarks decay, they often produce neutrinos. Neutrinos are like ghosts: they have almost no mass, carry no electric charge, and pass right through the Earth (and the detector) without leaving a trace. You cannot see them directly.

However, physics has a rule called conservation of momentum. Imagine a billiard table where you know exactly how hard the cue ball was hit. If you see the other balls flying in certain directions, you can calculate where the "missing" momentum went, even if you can't see the ball that took it.

In this experiment, the scientists looked for the "ghosts" (neutrinos) by measuring the missing momentum in the event. Since the top quarks decay into W bosons, which then decay into charged leptons (electrons or muons) and neutrinos, the scientists could track the visible leptons and infer the path of the invisible neutrinos.

2. The Two Clues They Measured

Instead of just counting how many top quarks were made, the scientists measured how they moved. They focused on two specific clues regarding the pair of neutrinos (the "dineutrino system"):

• The "Speed" of the Ghosts ($p_T^{\nu\nu}$): How much transverse momentum (sideways speed) did the pair of neutrinos have?
• The "Angle" of the Ghosts ($\min[\Delta\phi]$): How far apart was the direction of the neutrinos from the direction of the visible charged particles (leptons)?

Think of it like a crime scene investigation. If you see two suspects running away, you want to know: How fast were they running, and were they running in the same direction or scattering in different directions?

3. The Problem: A Foggy Lens

The scientists faced a major problem: the detector isn't perfect. Just like trying to see a ghost through a foggy window, the measurement of the "missing momentum" was often blurry. This "fog" was caused by:

• Pileup: The LHC doesn't just smash one pair of protons at a time; it smashes many bunches at once. It's like trying to hear a whisper in a crowded stadium.
• Measurement Errors: The detector sometimes miscalculates the energy of other particles, throwing off the calculation of the missing neutrinos.

4. The Solution: An AI "De-Fogger"

To clear up the fog, the scientists developed a Deep Neural Network (DNN). Think of this as a highly trained AI detective.

• They fed the AI millions of simulated crash events where they knew the "true" answer (the actual neutrino path).
• The AI learned to spot patterns in the "noise" (the foggy data) and correct the measurements.
• The Result: The AI acted like a high-tech image stabilizer, sharpening the picture of the neutrinos' path and speed by about 15%. This allowed the scientists to measure the neutrinos with much greater precision than ever before.

5. The Big Test: Is the Standard Model Right?

The main goal was to see if the Standard Model of physics (our current best theory of how the universe works) could accurately predict these neutrino movements.

• The Comparison: They compared their real-world measurements against predictions from complex computer simulations (Monte Carlo) and advanced mathematical formulas.
• The Verdict: The measurements matched the predictions perfectly. The data and the theory were in "agreement."

6. Why This Matters (The "New Physics" Hunt)

Why measure invisible ghosts so precisely? Because sometimes, the Standard Model isn't the whole story.

The paper mentions a hypothetical scenario involving Supersymmetry (a theory suggesting every known particle has a heavier "super-partner"). If these super-partners existed, they might produce extra invisible particles (like neutralinos) that would mess up the neutrino measurements, making the "ghosts" scatter in weird angles or move at unexpected speeds.

By measuring the neutrinos so precisely, the scientists are essentially checking the "shadow" of the event. If the shadow looked weird, it would be a sign of new, unknown physics. Since the shadow looked exactly as the Standard Model predicted, no new physics was found in this specific search, but the team has proven they can measure these invisible effects with incredible accuracy.

Summary

• What they did: Measured the speed and direction of invisible neutrino pairs created when top quarks collide.
• How they did it: Used a massive dataset from 2016–2018 and a new AI tool to fix blurry measurements.
• What they found: The invisible particles behaved exactly as the Standard Model predicted.
• The takeaway: The "ghosts" are behaving normally, and our current map of the subatomic world is holding up under this new, high-precision scrutiny.

Technical Summary

Technical Summary: Measurement of the Dineutrino System Kinematic Variables in Dileptonic Top Quark Pair Production

Problem and Motivation
Precision measurements of top quark pair ($t\bar{t}$) production serve as stringent tests of the Standard Model (SM) and are crucial for searching for new phenomena. While previous differential cross-section measurements have focused on visible kinematic observables (jets, leptons) or intermediate particles ($W$ bosons, top quarks), certain Beyond-the-SM (BSM) scenarios primarily modify the invisible sector of the event. Specifically, processes involving undetected particles, such as supersymmetric top squarks decaying to top quarks and neutralinos, can mimic the dileptonic $t\bar{t}$ signature but alter the kinematics of the missing transverse momentum ($\vec{p}^{\text{miss}}_T$).

This paper addresses the need to validate the modeling of the SM $t\bar{t}$ process in a phase space sensitive to such BSM signatures. The analysis focuses on the dileptonic final states ($e^+e^-$, $\mu^+\mu^-$, and $e^\pm\mu^\mp$), where the two neutrinos from the $W$ boson decays constitute the primary source of $\vec{p}^{\text{miss}}_T$. The study measures differential cross sections as functions of:

1. The transverse momentum of the dineutrino system ($p^{\nu\nu}_T$).
2. The minimum azimuthal distance between the dineutrino system and a charged lepton ($\min[\Delta\phi(\vec{p}^{\nu\nu}_T, \vec{p}^\ell_T)]$).
3. A two-dimensional (2D) distribution of both observables.

Methodology
The analysis utilizes proton-proton collision data recorded by the CMS detector at $\sqrt{s} = 13$ TeV between 2016 and 2018, corresponding to an integrated luminosity of $138 \text{ fb}^{-1}$.

• Event Selection: Events are selected requiring two oppositely charged leptons ($p_T > 25/20$ GeV for leading/subleading), at least two jets (one $b$-tagged), and specific missing transverse momentum requirements. Same-flavor channels require $p^{\text{miss}}_T > 40$ GeV and a veto on the dilepton invariant mass near the $Z$ boson mass to suppress Drell-Yan backgrounds.
• Missing Transverse Momentum Resolution: A critical component of the analysis is the reconstruction of the dineutrino system's kinematics via $\vec{p}^{\text{miss}}_T$. To improve resolution, particularly at high $p^{\text{miss}}_T$, a dedicated Deep Neural Network (DNN) regression is developed. This DNN corrects the $\vec{p}^{\text{miss}}_T$ vector (initially reconstructed using the PUPPI algorithm) by predicting the difference between the reconstructed and generated $\vec{p}^{\text{miss}}_T$ based on 17 input observables, including jet and lepton kinematics. This method improves the resolution of the magnitude and azimuthal angle of $\vec{p}^{\text{miss}}_T$ by approximately 15% and 12%, respectively, compared to standard reconstruction.
• Unfolding: Differential cross sections are extracted at the particle level using an unregularized least-squares unfolding method (TUNFOLD). The procedure involves subtracting background contributions (dominated by $t\bar{t}$ with non-dileptonic decays, single top, and Drell-Yan) and unfolding detector-level distributions to a fiducial phase space defined by detector acceptance and specific kinematic cuts.
• Systematic Uncertainties: Uncertainties are categorized into experimental (jet energy scale/resolution, lepton reconstruction, $b$-tagging, luminosity, pileup) and theoretical (renormalization/factorization scales, parton distribution functions, matching schemes, top quark mass, and background normalizations).

Key Contributions

• First Measurement: This work presents the first differential cross-section measurements of $t\bar{t}$ production as a function of the dineutrino system kinematic variables ($p^{\nu\nu}_T$ and $\min[\Delta\phi]$).
• DNN Application: The development and application of a DNN-based regression to correct $\vec{p}^{\text{miss}}_T$ specifically for dileptonic $t\bar{t}$ events, significantly enhancing the resolution required for precise kinematic reconstruction.
• 2D Analysis: The provision of a two-dimensional differential measurement, offering a more granular view of the phase space correlations between the neutrino system and the leptons.
• BSM Sensitivity: The analysis includes closure tests using a top squark pair production scenario (stop mass 525 GeV, neutralino mass 350 GeV) to demonstrate that the measurement and unfolding procedure can correctly reproduce deviations from the SM assumption used in the response matrix construction.

Results
The measured absolute and normalized differential cross sections are compared against five theoretical predictions:

1. POWHEG+PYTHIA (NLO)
2. POWHEG+HERWIG (NLO)
3. MC@NLO+PYTHIA (NLO)
4. Fixed-order NLO QCD
5. Fixed-order NNLO QCD

• Agreement: The measured results are generally in agreement with all theoretical predictions. The data and simulation distributions for $p^{\text{miss}}_{T,\text{DNN}}$ and $\min[\Delta\phi]$ show good consistency.
• Statistical Compatibility: $\chi^2$ tests indicate that all predictions describe the data well. For the one-dimensional absolute measurements, the POWHEG predictions provide the best overall description. For the 2D absolute measurement, the NNLO fixed-order calculation shows the best agreement.
• Shape Differences: Small shape differences are observed in the $\min[\Delta\phi]$ distribution, consistent with previous measurements of the azimuthal angle between the two leptons. These differences are within the range of theoretical uncertainties.
• Uncertainty Dominance: For the $p^{\nu\nu}_T$ measurement, the jet energy scale (JES) is the dominant experimental uncertainty. For the angular measurement, lepton reconstruction uncertainties become significant at large angles. Theoretical uncertainties related to the $tW$-$t\bar{t}$ overlap removal scheme dominate at high $p^{\nu\nu}_T$.

Significance
The paper claims that these results constitute the first differential cross-section measurements based on dineutrino kinematic properties in top quark pair production. The measurements validate the modeling of the SM $t\bar{t}$ process in a phase space specifically sensitive to BSM scenarios that introduce additional sources of undetected particles. The observed agreement between data and various theoretical calculations (including NNLO) confirms the robustness of current SM descriptions in the dileptonic channel. While no significant deviations were found, the precision of these measurements and the improved resolution of the missing transverse momentum provide a refined baseline for future searches for new physics in the invisible sector of top quark events.