Precision measurement of the $B^{0}$ meson lifetime using $B^{0} \rightarrow J/ψK^{*0}$ decays with the ATLAS detector

Using 140 fb$^{-1}$ of 13 TeV proton-proton collision data collected by the ATLAS detector, this paper presents the most precise measurement to date of the $B^0$ meson effective lifetime and its associated decay width parameters, all of which are consistent with theoretical predictions and results from other experiments.

The Gist

Imagine the universe as a giant, high-speed racetrack where particles zoom around at nearly the speed of light. In this paper, the scientists from the ATLAS experiment at CERN (the European Organization for Nuclear Research) act like ultra-precise race officials. Their job was to time a very specific type of "race car" called the $B^0$ meson to see exactly how long it survives before it crashes (decays) into other particles.

Here is the breakdown of their findings in simple terms:

1. The Race Car and the Track

The "race car" they studied is a particle called the $B^0$ meson. It's unstable, meaning it doesn't last long. It quickly breaks apart into other particles, specifically a $J/\psi$ (which looks like a heavy, short-lived pair of muons) and a $K^{*0}$ (which looks like a kaon and a pion).

To catch these cars, the scientists used the ATLAS detector, which is essentially a massive, 3D digital camera and stopwatch wrapped around the Large Hadron Collider (LHC). They analyzed data from 2015 to 2018, looking at 140 "years" of collision data (measured in a unit called femtobarns inverse). That's a huge amount of data, giving them a very clear picture.

2. The Stopwatch Challenge

Measuring the life of a particle this small is incredibly hard. It's like trying to time a firefly that flashes for a split second while it's flying through a hurricane.

• The Problem: The particle moves so fast and decays so quickly that you can't just watch it. You have to reconstruct its path backward from where it ended up to where it started.
• The Solution: The team used a sophisticated statistical method (a "maximum-likelihood fit"). Imagine you have a pile of photos showing where the car ended up and a pile of photos showing where it started. They used math to figure out the most likely time it took to get from A to B, while filtering out all the "noise" (other particles that weren't the real race car).

3. The Big Result: The New Record Time

After all the calculations, they found the effective lifetime of the $B^0$ meson to be:
1.5053 picoseconds.

To put that in perspective:

• A picosecond is one-trillionth of a second.
• If one second were the age of the universe, a picosecond would be less than a blink of an eye.
• The scientists measured this with incredible precision. Their uncertainty is only about 0.0035 picoseconds. This is like measuring the distance from New York to London and being off by less than the width of a human hair.

This is the most precise measurement of this particle's life ever recorded.

4. Why Does This Matter? (The "Rulebook" Check)

In the world of particle physics, there is a theoretical "rulebook" called the Heavy-Quark Expansion (HQE). It predicts how long these particles should live based on the laws of the weak force (one of the four fundamental forces of nature).

• The Check: The scientists compared their new, super-precise stopwatch result against the rulebook's prediction.
• The Verdict: The result matches the rulebook perfectly. The measured lifetime and the calculated "decay width" (how fast the car is falling apart) fit right where the theory said they would.

They also compared the $B^0$ meson's life to its cousin, the $B^0_s$ meson. They found the ratio of their lifetimes is almost exactly 1 (specifically 0.9910). This means they are practically twins in terms of how long they survive, which again, matches what the theory predicts.

5. How They Did It (The "Magic" Tools)

To get this result, they had to overcome several hurdles:

• The "Noise": In the detector, there are millions of particles flying around. The team had to distinguish the real $B^0$ mesons from "fake" ones created by random collisions. They used the mass of the particles as a fingerprint to separate the real signal from the background noise.
• The "Blur": The detector isn't perfect; it has a tiny bit of "blur" (uncertainty) in how it measures time. They used computer simulations to understand exactly how blurry their "camera" was and mathematically corrected for it.
• The "Alignment": The detector is made of millions of sensors. If even one is slightly out of place, the measurements are wrong. The team checked the alignment of the entire machine using other known particles (like the $Z$ boson) to ensure their "ruler" was straight.

Summary

The ATLAS collaboration has set a new gold standard for measuring how long a $B^0$ meson lives. They found it lives for 1.5053 picoseconds. This measurement is so precise that it confirms our current understanding of the universe's "rulebook" (the Standard Model) is still correct. It's like checking a very expensive, very complex watch against the atomic clock and finding that they agree down to the nanosecond. No new physics was found (which is actually good news for confirming our current theories), but the precision of the measurement itself is a major achievement.

Technical Summary

Technical Summary: Precision measurement of the $B^0$ meson lifetime using $B^0 \to J/\psi K^{*0}$ decays with the ATLAS detector

Problem and Motivation
The lifetime of elementary particles, or equivalently their decay width, is a fundamental property essential for testing the Standard Model, particularly the weak interaction. In the context of $b$-hadrons, theoretical predictions for absolute lifetimes are challenging due to non-perturbative QCD effects. However, the Heavy-Quark Expansion (HQE) framework allows for systematic calculations of lifetime ratios, where certain theoretical uncertainties cancel out. Specifically, differences in $b$-hadron lifetimes are attributed to corrections for Pauli interference and weak annihilation, which are enhanced by phase space factors entering at the order of $m_b^{-3}$.

While previous measurements of the $B^0$ meson lifetime have been reported by ATLAS, LHCb, CMS, and various $e^+e^-$ experiments (BaBar, Belle, CDF, D0), there remains a need for higher precision to constrain theoretical models and improve the determination of the average decay width $\Gamma_d$. This paper presents a new measurement of the $B^0$ effective lifetime using the decay channel $B^0 \to J/\psi K^{*0}$, aiming to provide the most precise result to date.

Methodology
The analysis utilizes proton-proton collision data collected by the ATLAS detector at the LHC at a center-of-mass energy of $\sqrt{s} = 13$ TeV, corresponding to an integrated luminosity of 140 fb$^{-1}$ recorded between 2015 and 2018.

• Event Reconstruction and Selection:

  • $B^0$ candidates are reconstructed via the decay chain $B^0 \to J/\psi K^{*0}$, with $J/\psi \to \mu^+\mu^-$ and $K^{*0} \to K^+\pi^-$.
  • Muons are required to satisfy "Tight" identification criteria and form a common vertex with a reduced $\chi^2 < 10$. The $J/\psi$ mass is constrained to the world average value during the vertex fit.
  • $K^{*0}$ candidates are formed from tracks satisfying specific transverse momentum ($p_T$) and pseudorapidity ($|\eta|$) requirements, with an invariant mass window of 846–946 MeV.
  • The $B^0$ candidate vertex is fitted with the $J/\psi$ mass constrained. Events with multiple candidates are resolved by selecting the one with the lowest $\chi^2$/ndof.
  • The proper decay time $t$ is calculated using the transverse decay length $L_{xy}$ and the reconstructed transverse momentum $p_T^B$: $t = L_{xy} m_B / p_T^B$. The primary vertex (PV) is selected based on the smallest three-dimensional impact parameter relative to the $B^0$ flight direction.

• Statistical Analysis:

  • A two-dimensional unbinned maximum-likelihood fit is performed on the invariant mass ($m$) and proper decay time ($t$) distributions.
  • Signal Model: The mass distribution is modeled by a Johnson $SU$-distribution. The proper decay time follows an exponential function convolved with a resolution function (modeled as a sum of three Gaussians).
  • Background Model: Backgrounds are categorized as "prompt" (combinatorial $J/\psi$ with random $K^{*0}$) and "combinatorial" (real $b$-hadron decays). The prompt background mass is modeled by a polynomial plus a sigmoid function; the time distribution is a delta function convolved with the resolution. The combinatorial background mass uses a similar polynomial/sigmoid sum, while its time distribution is a sum of three exponentials convolved with the resolution.
  • Efficiency Corrections: Trigger and reconstruction efficiencies, which bias the decay time distribution (particularly at large $t$), are corrected using weights derived from Monte Carlo (MC) simulations. These weights are parameterized using an error function and applied to the likelihood fit.

• Systematic Uncertainties:

  • Sources include inner detector (ID) alignment, choice of mass window, primary vertex selection, time efficiency modeling, candidate selection, mass fit model variations (including kinematic reflections from other $b$-hadron decays), mass-time correlations, and resolution model choices.
  • Uncertainties are estimated by comparing nominal fits with alternative models or by performing pseudo-experiments.

Key Contributions and Results
The analysis yields the following primary results:

1. $B^0$ Effective Lifetime:
   The measured effective lifetime is:
   $$\tau = 1.5053 \pm 0.0012 \text{ (stat.)} \pm 0.0035 \text{ (syst.) ps}$$
   This result is based on approximately 2.45 million signal events. The systematic uncertainty is dominated by mass-time correlations and the mass fit model.

2. Average Decay Width ($\Gamma_d$):
   Using the measured lifetime and the normalized width difference parameter $y = \Delta\Gamma_d / (2\Gamma_d)$ from HFLAV ($y = 0.001 \pm 0.010$), the average decay width is extracted:
   $$\Gamma_d = 0.6643 \pm 0.0005 \text{ (stat.)} \pm 0.0016 \text{ (syst.) ps}^{-1}$$
   The uncertainty from the external parameter $y$ is negligible at this precision.

3. Decay Width Ratio ($\Gamma_d / \Gamma_s$):
   Combining the new $\Gamma_d$ with the previously measured ATLAS value for the $B_s^0$ average decay width ($\Gamma_s = 0.6703 \pm 0.0014 \text{ (stat.)} \pm 0.0018 \text{ (syst.) ps}^{-1}$), the ratio is determined:
   $$\frac{\Gamma_d}{\Gamma_s} = 0.9910 \pm 0.0022 \text{ (stat.)} \pm 0.0036 \text{ (syst.)}$$

Significance and Comparison

• Precision: This measurement represents the most precise determination of the $B^0$ effective lifetime to date. Compared to the previous ATLAS measurement at $\sqrt{s}=7$ TeV, the systematic uncertainty is reduced by a factor of 4.7. This improvement is attributed to the Insertable B-Layer (IBL), which provides superior vertexing and time resolution, improved ID alignment in Run 2, and the larger dataset allowing for better modeling of decays.
• Theoretical Consistency: The measured $\Gamma_d$ is compatible with the HQE theoretical prediction of $0.63^{+0.11}_{-0.07}$ ps$^{-1}$ within $0.3\sigma$. The ratio $\Gamma_d/\Gamma_s$ is consistent with HQE predictions ($1.003 \pm 0.006$) and Lattice QCD predictions ($1.00 \pm 0.02$) within $1.6\sigma$ and $0.4\sigma$, respectively.
• Experimental Consistency: The result is generally compatible with other experimental measurements, including those from LHCb, CMS, and Belle II. While some LHCb measurements in specific channels differ by up to $2.3\sigma$, the current result aligns well with the $B^0 \to J/\psi K_S^0$ channel measurement from LHCb. The value differs from the 2024 world average ($1.517 \pm 0.004$ ps) by $2.1\sigma$.

The paper concludes that the measurement provides a stringent test of the HQE framework and the understanding of non-perturbative QCD effects in $b$-hadron decays, confirming the consistency of the Standard Model description of $b$-hadron lifetimes.