Measurement of $B \to K{}^{*}(892)γ$ decays at Belle II

Using 365 fb⁻¹ of data collected by the Belle II experiment, this paper presents measurements of branching fractions and CP asymmetries for $B \to K^*(892)\gamma$ decays, yielding results that are consistent with world-average values and theoretical predictions.

The Gist

Imagine the universe as a giant, high-speed racetrack where tiny particles zoom around at nearly the speed of light. The Belle II experiment is like a massive, ultra-sensitive camera team stationed at a specific spot on this track (the SuperKEKB collider in Japan) to take "photos" of these particles when they crash into each other.

This specific paper is about the team taking a very close-up look at a rare and tricky event: a heavy particle called a B-meson breaking apart to create a specific pair of lighter particles (a K-star meson and a photon, which is a particle of light).

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

1. The Goal: Catching a Rare "Ghost"

In the world of particle physics, some events happen all the time, while others are like finding a specific grain of sand on a beach. The decay of a B-meson into a K-star and a photon is one of those rare events.

Why do they care? Because the "Standard Model" (the rulebook of how the universe works) predicts exactly how often this should happen and how the particles should behave. If the real-world numbers don't match the rulebook, it could mean there are "ghosts" in the machine—new, undiscovered particles or forces influencing the crash.

2. The Setup: A Blinded Detective

The team collected data from 2019 to 2022, which amounts to about 387 million collisions of a specific type (called $\Upsilon(4S)$ events).

To avoid cheating or accidentally "seeing" what they wanted to see, the scientists worked "blind." Imagine a detective solving a crime who isn't allowed to look at the evidence until they have written down their entire theory and method. They finalized all their rules for spotting the signal before they ever looked at the actual data in the "crime scene" (the signal region).

3. The Hunt: Filtering the Noise

The problem is that the "photos" they take are incredibly messy. For every one rare event they want, there are millions of "background" events—like trying to hear a whisper in a stadium full of cheering fans.

• The Noise: Most of the background comes from other particles (like pions) that accidentally look like the photon they are hunting.
• The Filter: The team used a sophisticated digital sieve (called a BDT, or Boosted Decision Tree). Think of this as a highly trained bouncer at a club. It checks the shape of the energy, the timing, and the path of the particles. If a particle doesn't look exactly like the rare signal, the bouncer kicks it out.
• The Result: They managed to filter out about 70–80% of the background noise while keeping most of the rare signals.

4. The Measurement: Weighing the Evidence

Once they had their filtered list of candidates, they had to count them. They used a statistical method (a "fit") to separate the true signals from the remaining background noise.

They measured two main things:

1. Branching Fraction: This is simply the "frequency" of the event. Out of every million B-mesons, how many do this specific decay?
2. CP Asymmetry: This is a measure of "left-right" bias. Does the particle decay slightly more often into a "left-handed" version of itself than a "right-handed" one? In the Standard Model, this bias should be almost zero.

5. The Results: The Rulebook Holds Up

After crunching the numbers, the Belle II team found:

• The Frequency: They measured how often this happens with high precision. The numbers are roughly 4.1 out of 100,000 for neutral B-mesons and 4.0 out of 100,000 for charged ones.
• The Bias (CP Asymmetry): They found a tiny, negative bias for the neutral version and a near-zero bias for the charged version. Crucially, these numbers are consistent with zero within their margin of error.
• The Comparison: They compared the neutral and charged versions (Isospin Asymmetry) and found a small difference, but again, it aligns with what the Standard Model predicts.

The Bottom Line

The paper concludes that the "rulebook" (the Standard Model) is still holding up. The rare decay they observed behaves exactly as predicted.

• Did they find new physics? No.
• Did they break the universe? No.
• Did they do something important? Yes. They proved that their new, high-tech camera (Belle II) works perfectly. They have set a new, very precise baseline. Now, if future experiments find a deviation from these numbers, scientists will know for sure that it's a sign of new physics, not just a measurement error.

In short: They looked for a needle in a haystack, found the needle, measured its size and shape, and confirmed it looks exactly like the needle described in the instruction manual. For now, the universe is behaving as expected.

Technical Summary

Technical Summary: Measurement of $B \to K^*(892)\gamma$ Decays at Belle II

Problem and Motivation
Radiative decays of the $B$ meson to a $K^*(892)$ meson and a photon ($B \to K^*\gamma$) are suppressed in the Standard Model (SM), proceeding primarily via a one-loop $b \to s\gamma$ transition. Because these processes involve loop diagrams, they are sensitive probes for physics beyond the SM (BSM), where new particles could contribute to the internal loop and alter branching fractions or asymmetries. Key observables for testing the SM include the CP-violating asymmetry ($A_{CP}$) and the isospin asymmetry ($\Delta_{0+}$). While the SM predicts small values for these observables (with $\Delta_{0+}$ estimated between 3% and 8% and $A_{CP} < 1\%$), BSM scenarios, such as the aligned two-Higgs-doublet model, can predict significant deviations, including negative values for $\Delta_{0+}$. Previous measurements by the Belle and BABAR experiments reported a positive $\Delta_{0+}$ with a significance of roughly 3.1 standard deviations, while $A_{CP}$ measurements remained consistent with zero. This paper presents updated measurements using the larger dataset from the Belle II experiment to refine these constraints.

Methodology
The analysis utilizes an integrated luminosity of $365 \text{ fb}^{-1}$ collected by the Belle II detector at the SuperKEKB asymmetric-energy $e^+e^-$ collider between 2019 and 2022. The dataset corresponds to $(387 \pm 6) \times 10^6$ $\Upsilon(4S)$ events. The analysis is performed in a "blind" manner, with all selection criteria and fitting procedures finalized before examining the signal region.

• Reconstruction: The study reconstructs $B \to K^*\gamma$ decays through four intermediate channels: $K^{*0} \to K^+\pi^-$, $K^{*0} \to K_S^0\pi^0$, $K^{*+} \to K^+\pi^0$, and $K^{*+} \to K_S^0\pi^+$. Charged tracks are identified using likelihoods from the TOP and ARICH detectors, while photons are reconstructed from energy deposits in the electromagnetic calorimeter (ECL).
• Background Suppression: Significant backgrounds arise from continuum events ($e^+e^- \to q\bar{q}$) and photons from $\pi^0$ and $\eta$ decays. The analysis employs a Boosted Decision Tree (BDT) to distinguish high-energy signal photons from $K_L^0$ clusters and to veto photons consistent with $\pi^0$ or $\eta$ origins. Continuum background is suppressed using a separate BDT (CSBDT) that utilizes event shape variables, such as modified Fox–Wolfram moments and thrust axis characteristics.
• Fit Strategy: Signal yields are extracted using a two-dimensional extended maximum-likelihood fit to the beam-constrained mass ($M_{bc}$) and energy difference ($\Delta E$) distributions. The fit model includes three components: signal (modeled by Crystal Ball functions), continuum background (ARGUS function and polynomial), and $B\bar{B}$ background (nonparametric PDF). The analysis accounts for "self-crossfeed" (misreconstructed signal events) and separates $B^0$ and $B^+$ candidates where flavor tagging is possible via the charge of the $K^*$ decay products.

Key Contributions and Results
The paper reports measurements of branching fractions ($\mathcal{B}$), CP asymmetries ($A_{CP}$), the difference in CP asymmetries ($\Delta A_{CP}$), and the isospin asymmetry ($\Delta_{0+}$). The results are:

• Branching Fractions:
  • $\mathcal{B}(B^0 \to K^{*0}\gamma) = (4.14 \pm 0.10 \text{ (stat)} \pm 0.11 \text{ (syst)}) \times 10^{-5}$
  • $\mathcal{B}(B^+ \to K^{*+}\gamma) = (4.04 \pm 0.13 \text{ (stat)} ^{+0.13}_{-0.15} \text{ (syst)}) \times 10^{-5}$
• CP Asymmetries:
  • $A_{CP}(B^0 \to K^{*0}\gamma) = (-3.3 \pm 2.3 \text{ (stat)} \pm 0.4 \text{ (syst)})\%$
  • $A_{CP}(B^+ \to K^{*+}\gamma) = (-0.7 \pm 2.9 \text{ (stat)} \pm 0.5 \text{ (syst)})\%$
• Derived Observables:
  • Difference in CP asymmetries: $\Delta A_{CP} = (+2.6 \pm 3.8 \text{ (stat)} \pm 0.6 \text{ (syst)})\%$
  • Isospin asymmetry: $\Delta_{0+} = (+4.8 \pm 2.0 \text{ (stat)} \pm 1.8 \text{ (syst)})\%$ (with an additional uncertainty of $\pm 1.5\%$ due to the $\Upsilon(4S)$ branching fraction ratio).

Systematic uncertainties were evaluated for various sources, including tracking efficiency, particle identification, photon selection, $K_S^0$ and $\pi^0$ reconstruction, and fit biases. The total systematic uncertainties are approximately 2.7% for the neutral channel and 3.5% for the charged channel.

Significance
The authors state that these results are consistent with world-average values and Standard Model predictions. Specifically, the measured $A_{CP}$ values are consistent with zero, and the measured $\Delta_{0+}$ is positive, confirming the trend observed in previous Belle and BABAR measurements. The precision of these measurements is comparable to previous experimental results, providing a robust test of the SM in the radiative $b \to s\gamma$ sector. The paper does not claim evidence for new physics but rather establishes updated constraints on the branching fractions and asymmetries that any BSM theory must satisfy.