First evidence of the $B_s^0\rightarrow K^-\pi^+\gamma$ decay

This paper reports the first search for the $B_s^0\rightarrow K^-\pi^+\gamma$ decay within the invariant mass range of $796$ to $1800\,\text{MeV/}c^2$, resulting in a measured ratio of ${\cal R} = (0.2\pm2.7\pm1.3)\times10^{-2}$ and no significant evidence of the decay.

The Gist

Imagine the Large Hadron Collider (LHC) at CERN as a massive, high-speed particle racetrack. Inside this track, scientists smash protons together at nearly the speed of light, creating a chaotic explosion of new particles. Among the debris, they are looking for a very specific, rare event: a heavy particle called a $B_s^0$ meson decaying (falling apart) into a specific trio of smaller particles: a negative kaon, a positive pion, and a photon (a particle of light).

This paper reports the first time anyone has seen evidence of this specific decay happening. Here is how they did it, explained simply:

1. The Challenge: Finding a Needle in a Haystack

The decay they are looking for is incredibly rare. It's like trying to find a specific grain of sand on a beach, but that grain of sand is also glowing. The problem is that the "beach" is full of other glowing grains (background noise) that look almost exactly the same.

To make this harder, the "light" they are looking for is a photon. In most detectors, photons are tricky to catch because they don't leave a clear trail like charged particles do. It's like trying to track a ghost that leaves no footprints.

2. The Trick: Catching the Ghost's Shadow

The LHCb team used a clever trick to catch these photons. Instead of trying to see the photon directly, they waited for it to bump into the detector's material and turn into an electron-positron pair (a particle and its anti-particle).

Think of it this way: If you are trying to track a ghost, you can't see it. But if the ghost walks through a wall and leaves a pair of footprints on the other side, you can trace the path back to where the ghost was. By looking for these "footprints" (the electron and positron), the scientists could reconstruct the path of the original photon with much higher precision. This improved their ability to distinguish the rare signal from the background noise by a factor of three.

3. The Search: Sorting the Noise

The team analyzed data from billions of collisions collected over several years (Run 1 and Run 2). They used powerful computer algorithms (called "Boosted Decision Trees") to act like a super-smart filter. These algorithms looked at the shape, speed, and path of the particles to decide: "Is this the rare decay we want, or just random junk?"

They divided their search into two groups based on the mass of the particles produced:

• The "Low Mass" group: Where the particles form a known, stable shape (like a resonance called $K^*(892)^0$).
• The "High Mass" group: Where the particles are in a more chaotic, heavier state.

4. The Result: A "3.5 Sigma" Discovery

After sifting through the data, they found a small "bump" in the numbers where they expected the signal to be.

• The Significance: They measured this bump with a statistical significance of 3.5 standard deviations (often called "sigma").
• What that means: In the world of particle physics, a "3-sigma" result is considered "evidence." It's like flipping a coin 10 times and getting heads every time; it's very unlikely to be a fluke, but not quite enough to say "we have proven it" (which usually requires 5 sigma). It's a strong hint that the decay is real.

5. The Comparison: The Ratio Test

The scientists didn't just count the events; they compared this rare decay to a more common "sibling" decay ($B^0 \to K^-\pi^+\gamma$).

• They found that the rare $B_s^0$ decay happens about 3.7% as often as the common one.
• Why this matters: This ratio is a test of the "Standard Model" (the current rulebook of physics). The result they found matches the predictions of the Standard Model perfectly. This means the rulebook is still holding up, and there is no immediate sign of "New Physics" (like mysterious new particles) interfering with this specific process.

Summary

In short, the LHCb collaboration used a clever "shadow-tracking" technique to spot a very rare particle decay for the first time. They found strong evidence (3.5 sigma) that it exists, and the rate at which it happens fits perfectly with our current understanding of how the universe works. It's a successful hunt for a ghost, confirming that the ghost is real, but it's still following the rules we already knew.

Technical Summary

1. Problem and Motivation

The paper addresses the search for the rare radiative decay $B^0_s \to K^-\pi^+\gamma$.

• Physics Context: In the Standard Model (SM), radiative decays like $b \to d\gamma$ and $b \to s\gamma$ proceed via electroweak loop diagrams. While $b \to s\gamma$ transitions have been extensively measured, $b \to d\gamma$ transitions remain less constrained.
• Goal: The primary goal is to measure the branching fraction of $B^0_s \to K^-\pi^+\gamma$ relative to the favored $B^0 \to K^-\pi^+\gamma$ decay. This ratio, $R$, allows for the extraction of the CKM matrix element ratio $|V_{td}/V_{ts}|$.
• Theoretical Advantage: The ratio $R \equiv \mathcal{B}(B^0_s \to K^{*}(892)^0\gamma) / \mathcal{B}(B^0 \to K^{*}(892)^0\gamma)$ is theoretically "cleaner" than other determinations because dominant uncertainties related to form-factor ratios largely cancel out. The SM prediction for this ratio is $R = (3.9 \pm 0.7) \times 10^{-2}$.
• Challenge: The $B^0_s \to K^-\pi^+\gamma$ decay is extremely rare and suffers from significant background, particularly from the more common $B^0 \to K^-\pi^+\gamma$ decay and misidentified hadronic decays.

2. Methodology

Data Sample:

• Experiment: LHCb detector at CERN.
• Dataset: Proton-proton ($pp$) collision data collected at center-of-mass energies of 7, 8, and 13 TeV.
• Integrated Luminosity: $9 \text{ fb}^{-1}$ (3 $\text{fb}^{-1}$ from Run 1 at 7/8 TeV; 6 $\text{fb}^{-1}$ from Run 2 at 13 TeV).
• Blinding: The analysis was blinded in a mass window of $\pm 40 \text{ MeV}/c^2$ around the known $B^0_s$ mass to avoid experimenter bias until the procedure was finalized.

Reconstruction Strategy:

• Photon Conversion: Instead of reconstructing photons as clusters in the electromagnetic calorimeter (ECAL), the analysis exclusively uses converted photons ($\gamma \to e^+e^-$).
  • Benefit: This improves the mass resolution of the reconstructed $B$ candidate by a factor of three compared to unconverted photons.
  • Selection: Converted photons are categorized as "long tracks" (converting early, fully reconstructed in the tracker) or "downstream tracks" (converting later, no VELO hits).
  • Vertexing: The photon trajectory is matched to the $K^-\pi^+$ vertex to suppress random combinations.
• Signal Definition: The $K^-\pi^+$ system is analyzed in two mass windows:
  1. Low Mass: $796 < m(K^-\pi^+) < 996 \text{ MeV}/c^2$ (dominated by the $K^{*}(892)^0$ resonance).
  2. High Mass: $996 < m(K^-\pi^+) < 1800 \text{ MeV}/c^2$ (higher-mass states).

Background Suppression and Modeling:

• Multivariate Analysis: Separate Boosted Decision Tree (BDT) classifiers were trained for each dataset subset (Run 1/2, track type, mass window) to reject combinatorial background.
• Control Channels: To evaluate particle misidentification (e.g., $K^+K^-$ or $pK^-$ misidentified as $K^-\pi^+$), the analysis simultaneously fits $B^0_s \to K^+K^-\gamma$ and $\Lambda^0_b \to pK^-\gamma$ candidates.
• Fit Model:
  • Signal: Modeled using Johnson SU (JSU) functions with power-law tails. A modified Gaussian (Double-Sided Crystal Ball) is added to account for downstream track mismatches.
  • Backgrounds: Includes partially reconstructed decays (ARGUS functions), misidentified hadrons, and combinatorial background (first-order polynomial).

3. Key Contributions

1. First Observation: This is the first experimental evidence for the $B^0_s \to K^-\pi^+\gamma$ decay.
2. Innovative Reconstruction: The exclusive use of converted photons to achieve superior mass resolution, crucial for distinguishing the rare $B^0_s$ signal from the abundant $B^0$ background.
3. Precision Ratio Measurement: A simultaneous measurement of the branching fraction ratio $R$ in two distinct $K^-\pi^+$ mass regions, providing a direct test of SM predictions for $b \to d\gamma$ transitions.
4. Comprehensive Systematics: A rigorous evaluation of systematic uncertainties, including those from fit bias, particle identification, production cross-sections ($f_s/f_d$), and simulation modeling.

4. Results

Significance:

• A signal excess of 3.5 standard deviations ($\sigma$) was measured.
• The total yield of $B^0_s \to K^-\pi^+\gamma$ decays is $38 \pm 18$ (statistical and systematic uncertainties combined).
• The probability of the background-only hypothesis fluctuating to this level is $2.8 \times 10^{-4}$.

Branching Fraction Ratio ($R$):
The ratio $R = \mathcal{B}(B^0_s \to K^-\pi^+\gamma) / \mathcal{B}(B^0 \to K^-\pi^+\gamma)$ was measured in two regions:

• Low Mass Region ($796 < m(K^-\pi^+) < 996 \text{ MeV}/c^2$):
  $$R_{\text{low}} = (3.7 \pm 1.2 \text{ (stat)} \pm 0.4 \text{ (syst)}) \times 10^{-2}$$

  • This result is in excellent agreement with the SM prediction of $(3.9 \pm 0.7) \times 10^{-2}$.

• High Mass Region ($996 < m(K^-\pi^+) < 1800 \text{ MeV}/c^2$):
  $$R_{\text{high}} = (0.2 \pm 2.7 \text{ (stat)} \pm 1.3 \text{ (syst)}) \times 10^{-2}$$

  • This measurement has large uncertainties and is consistent with zero, as expected for the non-resonant or higher-mass region where the signal is weaker.

Systematic Uncertainties:

• The dominant systematic uncertainties on the ratio $R$ arise from fit bias (up to 8.8% in Run 1) and production cross-section ratios ($f_s/f_d$).
• The total systematic uncertainty on the ratio is approximately 4–9% depending on the dataset.

5. Significance

• Validation of the Standard Model: The measured ratio in the $K^{*}(892)^0$ region aligns perfectly with SM predictions, reinforcing the current understanding of $b \to d\gamma$ transitions and the CKM matrix.
• Constraint on New Physics: By establishing a baseline measurement for this rare decay, the result constrains potential contributions from Beyond the Standard Model (BSM) particles that could alter the $b \to d\gamma$ amplitude.
• Future Prospects: The paper notes that with the upgraded LHCb detector and larger datasets, the precision of this measurement can be significantly improved. This will allow for a more stringent test of the SM and a more precise determination of $|V_{td}/V_{ts}|$, potentially revealing subtle deviations indicative of new physics.

In conclusion, this paper represents a milestone in heavy flavor physics, successfully isolating a previously unobserved rare decay channel through advanced reconstruction techniques and providing the first experimental evidence consistent with Standard Model expectations.