Evidence for the decay $B^0_s\to\phi\eta'$

Using LHCb data from proton-proton collisions collected between 2011 and 2018, the paper reports evidence for the decay $B^0_s\to\phi\eta'$ with a significance of $3.5\sigma$ and determines its branching fraction to be $(0.66 \pm 0.15 \pm 0.03 \pm 0.02) \times 10^{-6}$.

The Gist

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful particle smasher. It fires tiny protons at each other at nearly the speed of light, creating a chaotic explosion of new particles. Most of these particles are boring and short-lived, but occasionally, something rare and interesting happens: a heavy particle called a $B_s^0$ meson is created, and it decays (breaks apart) into a specific, unusual combination of lighter particles.

This paper is a report from the LHCb collaboration, a team of scientists who built a giant, high-tech camera (the LHCb detector) to take pictures of these collisions. Their goal was to catch a glimpse of a very rare "ghost" event: the decay of a $B_s^0$ meson into a $\phi$ meson and an $\eta'$ meson.

Here is the story of their discovery, explained simply:

1. The Hunt for the "Ghost"

In the world of particle physics, some decay paths are like busy highways, while others are like hidden backroads that almost no one travels. The decay $B_s^0 \to \phi\eta'$ is one of those hidden backroads.

• The Theory: Scientists have theories (based on the Standard Model of physics) that predict this decay should happen, but they aren't sure exactly how often. It's like trying to guess how many times a specific bird flies through a specific tree in a massive forest.
• The Problem: In the past (using data from 2011–2012), the LHCb team looked for this bird but didn't see it. They could only say, "It's probably not happening more than X times."
• The New Data: This paper uses a much larger dataset, collected between 2011 and 2018 (a total of 9 "inverse femtobarns" of data, which is a fancy way of saying "a huge number of collisions"). It's like returning to that forest with a better camera and staying there for twice as long.

2. The Detective Work: Finding the Needle in the Haystack

Finding this decay is incredibly hard because the "haystack" (background noise from other particle collisions) is massive.

• The Signal: The scientists are looking for a specific pattern: a $B_s^0$ meson breaking into a $\phi$ (which itself breaks into two kaons) and an $\eta'$ (which breaks into a rho meson and a photon).
• The Noise: There are millions of other particle crashes that look almost like this signal. For example, a different particle might break apart in a way that mimics the mass of the signal, or a photon might be missed by the detector.
• The Filter: To find the signal, the team used a "digital sieve." They built a computer program (a machine learning algorithm) trained to spot the subtle differences between the real signal and the background noise. They also used strict rules: the particles must come from a specific point in space, have specific speeds, and match specific mass calculations.

3. The Discovery: A "3.5 Sigma" Whisper

After sifting through the data, the team found something exciting.

• The Result: They found evidence of the decay happening 46 times (give or take a few).
• The Significance: In science, finding a signal is like hearing a whisper in a noisy room.
  • If you hear it once, it might be a trick of the ear.
  • If you hear it clearly, it's a "discovery."
  • This team heard a 3.5 sigma whisper. In the language of particle physics, "sigma" is a measure of confidence. A 3.5 sigma result means there is a very small chance (about 1 in 2,000) that this signal is just random noise. It is strong "evidence," though not quite the "gold standard" 5 sigma (1 in 3.5 million) required to officially claim a "discovery."
• The Analogy: Imagine flipping a coin 100 times. If you get 55 heads, that's normal. If you get 90 heads, you'd suspect the coin is rigged. This result is like getting 85 heads—it's very suspicious that the coin is rigged, but you'd want to flip it a few more times to be absolutely sure.

4. Measuring the Rarity

The team didn't just count the events; they calculated how rare this event is compared to a known, common event.

• The Comparison: They compared the rare $B_s^0 \to \phi\eta'$ decay to a more common decay called $B_s^0 \to \phi\phi$ (where the meson breaks into two $\phi$ particles).
• The Ratio: They found that for every 100 times the common decay happens, the rare decay happens about 3.5 times.
• The Final Number: This translates to a branching fraction (a probability) of about 0.66 in a million. This means if you produced one million of these specific particles, you would expect to see this specific decay pattern about 0.66 times.

5. Why Does This Matter?

This isn't just about counting particles; it's about testing the rules of the universe.

• The "QCD" Puzzle: The decay involves complex interactions called "penguin diagrams" (a term physicists use for specific loop-like interactions in quantum mechanics). Theoretical models predict this decay should happen, but the predictions have a huge range of uncertainty (from 0.05 to 20 in their units).
• The Constraint: By measuring the actual rate (0.66), the scientists have narrowed down the possibilities. It's like having a map that says the treasure is somewhere between a mile north and a mile south. This new measurement says, "Actually, it's right here, 0.2 miles north." This helps physicists refine their mathematical models of how quarks (the building blocks of matter) interact.

Summary

The LHCb team used a massive amount of data from the Large Hadron Collider to find strong evidence (3.5 sigma) of a very rare particle decay that had never been seen before. They measured exactly how often it happens and found it matches the predictions of the Standard Model of physics, helping to solve a puzzle about how the fundamental forces of nature work. They didn't find "new physics" (like a new force or particle), but they confirmed that our current understanding of the universe is on the right track, even in its most complex corners.

Technical Summary

Technical Summary of CERN-EP-2026-104: Evidence for the decay $B^0_s \to \phi\eta'$

Problem and Motivation
In the Standard Model (SM), decays of $b$-hadrons to charmless final states are highly suppressed due to the structure of the Cabibbo-Kobayashi-Maskawa (CKM) matrix. Consequently, these decays serve as sensitive probes for potential contributions from physics beyond the SM. Theoretical predictions for such charmless modes, specifically the $B^0_s \to \phi\eta'$ decay, rely on frameworks such as perturbative QCD (pQCD), soft collinear effective theory (SCET), and QCD factorisation. However, these predictions carry large uncertainties due to the complexity of calculating electroweak loop (penguin) contributions, form factors, and $\omega-\phi$ mixing.

The $B^0_s \to \phi\eta'$ decay proceeds via a $b \to s\bar{s}s$ transition. A specific challenge in modeling this mode arises because the spectator $s$ quark can hadronise into either the vector meson $\phi$ or the pseudoscalar meson $\eta'$. Depending on the $B^0_s \to \phi$ form factor, strong cancellations between different $P-V$ and $V-P$ amplitudes may occur, a feature not present in vector-vector modes like $B^0_s \to \phi\phi$. Previous searches by the LHCb collaboration using Run 1 data (2011–2012) found no signal, setting an upper limit of $\mathcal{B}(B^0_s \to \phi\eta') < 0.82 \times 10^{-6}$ at 90% confidence level. This paper presents an updated analysis using the full Run 1 and Run 2 dataset to search for this decay and constrain QCD models.

Methodology
The analysis utilizes a dataset corresponding to an integrated luminosity of $9 \text{ fb}^{-1}$ collected by the LHCb experiment in proton-proton collisions between 2011 and 2018 at center-of-mass energies of $\sqrt{s} = 7, 8,$ and $13 \text{ TeV}$.

• Event Selection: The signal decay chain is reconstructed as $B^0_s \to \phi(\to K^+K^-)\eta'(\to \rho^0\gamma \to \pi^+\pi^-\gamma)$. Candidates are selected based on high-quality charged tracks displaced from the primary vertex (PV). The $\phi$ candidate is formed from oppositely charged kaons with an invariant mass within $15 \text{ MeV}/c^2$ of the known $\phi$ mass. The $\eta'$ candidate is reconstructed from a $\rho^0$ (identified via $\pi^+\pi^-$) and a photon, with the $\eta'$ mass constrained between $920$ and $1000 \text{ MeV}/c^2$.
• Background Suppression: Specific backgrounds are suppressed through kinematic and topological requirements. For instance, the contribution from $B^0_{(s)} \to \phi\pi^+\pi^-$ with a random photon is reduced by requiring the four-particle invariant mass to be below $5250 \text{ MeV}/c^2$. A multivariate analysis using a gradient-boosted decision tree (XGBoost) is employed to suppress residual combinatorial background, optimizing for a $5\sigma$ significance figure of merit.
• Normalization: The branching fraction is determined relative to the normalisation channel $B^0_s \to \phi\phi$ ($\phi \to K^+K^-$), which shares similar kinematic properties and detector acceptance.
• Fit Strategy: A simultaneous unbinned maximum-likelihood fit is performed on the invariant mass distribution of the selected candidates. The signal shape is modeled by a double-sided Crystal Ball (DSCB) function. Backgrounds, including the partially reconstructed $B^0_s \to \phi\phi$ and the rare decay $\Lambda^0_b \to pK^-\eta'$ (with misidentified proton), are modeled using bifurcated Gaussians and wide DSCB functions, respectively. Combinatorial background is described by an exponential function. The dataset is split into four categories based on run period and trigger type (Run 1/2 and TIS/TOS) to account for efficiency variations.

Key Contributions and Results
The analysis yields a total signal yield of $46.4 \pm 9.7$ events for the $B^0_s \to \phi\eta'$ decay. The statistical significance of the signal, computed using Wilks' theorem, is $3.5\sigma$. This constitutes the first evidence for the $B^0_s \to \phi\eta'$ decay.

The branching ratio relative to the $B^0_s \to \phi\phi$ mode is determined to be:
$$R \equiv \frac{\mathcal{B}(B^0_s \to \phi\eta')}{\mathcal{B}(B^0_s \to \phi\phi)} = (3.56 \pm 0.79_{\text{stat}} \pm 0.18_{\text{syst}} \pm 0.06_{\text{ext}}) \times 10^{-2}$$

Using the known branching fraction $\mathcal{B}(B^0_s \to \phi\phi) = (1.84 \pm 0.14) \times 10^{-5}$, the absolute branching fraction is calculated as:
$$\mathcal{B}(B^0_s \to \phi\eta') = (0.66 \pm 0.15_{\text{stat}} \pm 0.03_{\text{syst}} \pm 0.02_{\text{ext}}) \times 10^{-6}$$

Systematic uncertainties are dominated by the hardware trigger efficiency (Run 1) and photon reconstruction efficiency. The uncertainty from external branching fractions and the $B^0_s$ lifetime assumption are also included.

Significance
The paper claims that the measured branching fraction lies within the broad range of theoretical predictions ($0.05 - 20) \times 10^{-6}$. The primary significance of this result is that it provides an experimental data point to discriminate between different QCD models for charmless $b$-hadron decays to vector-pseudoscalar ($V-P$) and pseudoscalar-vector ($P-V$) states. Specifically, the measurement helps quantify the influence of the colour-suppressed QCD penguin loop and the cancellations between amplitudes involving the spectator $s$ quark. The authors note that further improvements in the understanding of this mode will be pursued with the larger datasets expected from LHCb Run 3.