Differential decay rate of $B^+ \to J/\psi K^+$ with the LHCb Upgrade I experiment

Using a 1.1 fb$^{-1}$ data sample from the LHCb Upgrade I detector collected in October 2024, this paper measures the normalised decay rate and angular coefficients of the $B^+ \to J/\psi K^+$ process, demonstrating that the upgraded detector's response is sufficiently understood to reliably extract parameters for rare $b \to s \mu^+\mu^-$ and $b \to d \mu^+\mu^-$ transitions sensitive to physics beyond the Standard Model.

The Gist

The Big Picture: A High-Speed Camera Check

Imagine the Large Hadron Collider (LHC) as a massive, ultra-fast racetrack where protons zoom around at nearly the speed of light. The LHCb experiment is like a specialized camera team standing on the side of the track, trying to take pictures of very rare, short-lived particles called "B-mesons" as they zoom by and fall apart.

In 2022, this camera team got a massive upgrade (called Upgrade I). They replaced almost all their lenses and sensors to handle traffic that is five times heavier than before. But before they could trust these new, super-fast cameras to take pictures of the most mysterious particles in the universe, they needed to make sure the cameras weren't distorting the images.

This paper is the "quality control report" for that new camera system.

The Test Subject: The "Gold Standard" Particle

To test the camera, the scientists didn't look at the most mysterious particles yet. Instead, they looked at a very well-known, predictable decay: $B^+ \to J/\psi K^+$.

Think of this particle decay like a perfectly choreographed dance.

• The $B^+$ particle is the lead dancer.
• It spins and splits into a $J/\psi$ (which immediately splits into two muons, like a pair of dancers) and a $K^+$ (a kaon).
• Because we know the rules of physics (the "choreography") so well for this specific dance, we know exactly how the dancers should move. If the camera is working right, the video of the dance should look exactly like the choreography. If the camera is broken or biased, the video will look weird.

The Measurement: Checking the Angles

The scientists focused on one specific thing: the angle at which the muons (the two dancers) fly apart. They call this the "helicity angle."

They measured two main things about this angle:

1. Forward-Backward Asymmetry ($A_{FB}$): Do the dancers lean more toward the front or the back? (Theory says: No, it should be perfectly balanced, like a seesaw in the middle).
2. Flatness ($F_H$): Is the distribution of angles perfectly smooth and flat? (Theory says: Yes).

In the "Standard Model" of physics (the rulebook for how the universe works), these two numbers should be zero. If the camera is perfect, the measurements should be zero. If the camera is tilted or biased, the numbers will be off.

The Results: The Camera is Perfect

The scientists analyzed data collected in October 2024. They looked at the data in two different ways:

• MagDown & MagUp: The LHCb detector uses a giant magnet to bend particle paths. They tested the camera with the magnet pointing up and with it pointing down to ensure the magnet itself wasn't causing any bias.
• Different Conditions: They checked the data under different "traffic" conditions (how crowded the track was) and for particles moving at different speeds.

The Verdict:
The measurements came out to be zero, right within the margin of error.

• The "dance" looked exactly as the choreography predicted.
• The camera didn't favor the left side over the right, or the front over the back.
• Even when the track was super crowded (high "pile-up"), the camera still took clear, unbiased pictures.

Why This Matters (According to the Paper)

The paper explains that this specific test is a rehearsal for the real show.

The scientists are preparing to study rare decays (like $b \to s\mu^+\mu^-$) that might reveal "new physics" beyond our current rulebook. These rare decays are like finding a dancer who breaks the rules. But to spot a rule-breaker, you have to be 100% sure your camera isn't accidentally making a normal dancer look like a rule-breaker.

By proving that the Upgrade I camera measures the "perfect dance" ($B^+ \to J/\psi K^+$) with extreme precision, the team is saying:

"We have calibrated our new high-speed cameras. We know exactly how they see the world. Now, when we look at the mysterious, rule-breaking particles, we can trust that any weirdness we see is real physics, not a glitch in our camera."

Summary

This paper is a success story for the LHCb Upgrade I. It confirms that the new, faster detector is working exactly as intended, handling heavy traffic without distorting the angles of particle decays. It gives the scientists the green light to start hunting for new physics with confidence.

Technical Summary

Technical Summary: Differential Decay Rate of $B^+ \to J/\psi K^+$ with the LHCb Upgrade I Experiment

Problem and Motivation
The LHCb experiment underwent a major upgrade (Upgrade I) for the start of LHC Run 3, enabling operation at an instantaneous luminosity five times greater than previous periods and a fully software-based trigger system at 40 MHz. While this upgrade promises enhanced sensitivity to rare $b \to s\mu^+\mu^-$ and $b \to d\mu^+\mu^-$ transitions—processes highly sensitive to physics beyond the Standard Model (SM)—it necessitates a rigorous validation of the detector's response under these new, high-pile-up conditions.

The $B^+ \to J/\psi K^+$ decay mode serves as a critical benchmark for this validation. Unlike $B^0 \to J/\psi K^{*0}$, which involves complex interference with exotic contributions, $B^+ \to J/\psi K^+$ is a tree-level $b \to s c \bar{c}$ decay with a large branching fraction and a precisely known angular distribution. In the SM, within the $J/\psi$ resonance region, the angular observables associated with this decay are expected to be zero due to angular momentum conservation. Consequently, any measured deviation would primarily indicate detector-induced asymmetries or mismodeling rather than new physics. Validating the detector's ability to correctly reconstruct the lepton helicity angle ($\theta_\ell$) in this channel is essential for calibrating efficiency estimates and cross-checking analysis strategies for the rare $b \to s\mu^+\mu^-$ modes, which share similar final states and angular functional forms.

Methodology
The analysis utilizes a data sample corresponding to an integrated luminosity of $1.1 \text{ fb}^{-1}$ collected in October 2024 at a center-of-mass energy of 13.6 TeV. The dataset includes configurations with both magnetic field polarities (MagDown and MagUp).

1. Candidate Selection: Events are selected using the online trigger system (HLT1 and HLT2) and offline reconstruction. Selection criteria require a displaced vertex formed by two oppositely charged muons and a kaon. Particle identification (PID) is applied using artificial neural networks ($PNN_i$), and a loose Boosted Decision Tree (BDT) classifier is employed to suppress combinatorial background, mimicking the selection strategies used for rare decay analyses.
2. Efficiency Modeling: To correct for detector acceptance and reconstruction effects, simulated samples of $B^+ \to J/\psi K^+$ are calibrated using data-driven weights. These weights correct for PID efficiency, trigger efficiency, detector occupancy, and production kinematics. The efficiency as a function of $\cos \theta_\ell$, denoted $\epsilon(\cos \theta_\ell)$, is parameterized using a 12th-order Legendre polynomial.
3. Fit Model: A two-dimensional unbinned extended maximum-likelihood fit is performed on the invariant mass $m(K^+\mu^+\mu^-)$ and $\cos \theta_\ell$. The signal is modeled by the theoretical differential decay rate (Eq. 1) multiplied by the efficiency function. Backgrounds from $B^+ \to J/\psi \pi^+$ and combinatorial sources are modeled using Chebyshev polynomials and exponential functions.
4. Systematic Evaluation: Systematic uncertainties are assessed using ensembles of pseudoexperiments. Dominant sources include the finite size of simulation samples used for efficiency parameterization and variations in the weighting schemes for kinematic corrections.
5. Differential Analysis: The angular coefficients are measured differentially across 17 kinematic and detector-response variables (e.g., primary vertex count, transverse momentum, impact parameter $\chi^2$) to identify potential trends or biases.

Key Contributions and Results
The paper presents the first complete physics analysis of a $b$-hadron decay using the LHCb Upgrade I detector. The primary results are the measurements of the forward-backward asymmetry ($A_{FB}$) and the flatness parameter ($F_H$).

• Integrated Measurements: The combined results for the full dataset are:
  • $A_{FB} = 0.19 \pm 0.48 \text{ (stat)} \pm 0.33 \text{ (syst)} \times 10^{-3}$
  • $F_H = 0.5 \pm 1.1 \text{ (stat)} \pm 1.4 \text{ (syst)} \times 10^{-3}$
    These values are consistent with the SM prediction of zero within approximately 1.2 standard deviations. The results for MagDown and MagUp polarities agree with each other at the level of 1.5$\sigma$.
• Differential Stability: The analysis reveals no significant trends in $A_{FB}$ or $F_H$ across the 17 tested variables. Linear fits to the differential measurements show no coherent deviations from zero, and "pull" distributions (comparing binned results to the integrated value) are consistent with statistical fluctuations.
• Pile-up Robustness: The signal purity remains stable (varying by less than 10%) across a wide range of primary vertex counts (1 to 14), and the $B^+$ mass resolution shows little degradation, demonstrating the detector's resilience under high-luminosity conditions.

Significance and Claims
The paper claims that these measurements demonstrate the LHCb Upgrade I detector response is understood to the precision required for reliable extraction of angular coefficients in rare $b \to s\mu^+\mu^-$ and $b \to d\mu^+\mu^-$ transitions.

Specifically, the authors state that:

1. The systematic uncertainties of this measurement are significantly smaller than the statistical uncertainties expected for future $b \to s\mu^+\mu^-$ analyses in the same kinematic region.
2. The stability of the results across various detector-response variables and selection criteria (including tighter PID and BDT cuts) validates the analysis strategy for rare decay searches.
3. The detector performs robustly under the high instantaneous luminosity ($2 \times 10^{33} \text{ cm}^{-2}\text{s}^{-1}$) characteristic of Run 3, confirming that the upgraded system can handle the increased pile-up without introducing significant biases in angular observables.

The work serves as a crucial validation step, ensuring that the LHCb Upgrade I is ready to probe potential deviations from the Standard Model in rare decays with high confidence.