First search for $B \rightarrow X_{s} \nu \bar{\nu}$ decays

Using 365 fb⁻¹ of data from the Belle II detector, the first search for the flavor-changing neutral-current decay $B \rightarrow X_{s} \nu \bar{\nu}$ was conducted via a sum-of-exclusives approach, yielding no significant signal and establishing an upper limit on the branching fraction of $3.3 \times 10^{-4}$.

The Gist

Imagine the universe is a giant, high-speed particle factory. In this factory, heavy particles called B mesons are constantly being created and then immediately breaking apart into smaller pieces. Usually, these breakups follow strict rules set by the Standard Model (the rulebook of physics).

However, sometimes, a B meson might break apart in a very rare, "forbidden" way: it turns into a strange particle (called Xs) and two invisible ghosts called neutrinos (which we can't see or catch). This specific breakup is called $B \to X_s \nu\bar{\nu}$.

Here is what the Belle II collaboration did to hunt for these rare events, explained simply:

1. The Setup: A Cosmic Speed Trap

The scientists used a massive machine called the SuperKEKB collider. Think of this as a racetrack where they smash electrons and positrons (anti-electrons) together at nearly the speed of light.

• The Goal: Create millions of B mesons.
• The Problem: These B mesons decay almost instantly. To study them, you need to catch them in the act.
• The Tool: The Belle II detector is like a giant, 360-degree camera surrounding the crash site. It takes billions of "photos" (data points) of these collisions.

2. The Strategy: The "Missing Money" Trick

Detecting these specific decays is tricky because the neutrinos are invisible. It's like trying to find a thief who stole a bag of money, but the thief vanished without a trace. You can't see the thief, but you know the money is gone.

The scientists used a clever two-step detective method:

• Step 1: Tagging the Partner. When a B meson is created, it's usually born with a "twin" partner. The scientists fully reconstructed (identified) this partner B meson first. This is like finding the twin and knowing exactly what the original twin should have looked like.
• Step 2: The Sum of Exclusives. Instead of trying to guess what the invisible neutrinos did, they looked at the other pieces left over (the Xs system). They didn't just look for one specific shape; they looked for 30 different combinations of particles (like different arrangements of Lego bricks) that could make up the "strange" particle. By adding up all these specific possibilities, they could estimate the total amount of "missing money" (the neutrinos) with high precision.

3. The Filter: Sorting the Noise

The detector sees everything, including background noise (like static on a radio). Most of the time, the particles seen are just ordinary debris from the collision, not the rare decay they are looking for.

• To clean up the signal, they used a Boosted Decision Tree (BDT). Think of this as a super-smart AI filter. It looks at 32 different clues (like how fast particles are moving, their angles, and how much energy is missing) to decide: "Is this a rare signal, or just background noise?"
• They set a very strict threshold: only events that the AI was 86% sure were "signal-like" were kept for analysis.

4. The Results: The Hunt for Ghosts

After analyzing data equivalent to 365 "inverse femtobarns" (a unit of collision data that represents a massive amount of information), the team looked for the "missing energy" signature in three different mass ranges of the strange particle (light, medium, and heavy).

• The Outcome: They found no significant signal. In other words, they didn't find the "thief" stealing the money more often than the rulebook predicts.
• The Conclusion: Because they didn't see the event, they couldn't measure exactly how often it happens. Instead, they set an upper limit.
  • They can say with 90% confidence that this rare decay happens less than 3.3 times out of every 10,000 B mesons.
  • They also set stricter limits for the different mass ranges (e.g., for the lightest particles, it happens less than 2.2 times out of 100,000).

5. Why This Matters

Even though they didn't find a "new" discovery, this is a huge deal because:

• It's the First Time: This is the first-ever search for this specific type of inclusive decay (looking at all possible strange particle combinations together).
• Testing the Rules: The Standard Model predicts exactly how often this should happen. If the real world had more of these decays than the model predicts, it would mean there are "new physics" at play—perhaps invisible particles like dark matter or new forces we haven't discovered yet.
• The Verdict: Since their results match the Standard Model's predictions (within the margin of error), the current rulebook still holds up. The "thief" is still hiding, or perhaps doesn't exist in the way we suspected.

In short: The scientists built a massive camera, caught millions of particle collisions, used a smart AI to filter out the noise, and looked for a specific, invisible breakup. They didn't find it, but they proved that if it does happen, it's incredibly rare, keeping our current understanding of the universe intact.

Technical Summary

Technical Summary: First Search for $B \to X_s \nu \bar{\nu}$ Decays

Problem and Motivation
Flavor-changing neutral current (FCNC) decays of the form $b \to s \nu \bar{\nu}$ are highly suppressed in the Standard Model (SM) due to the Glashow-Iliopoulos-Maiani (GIM) mechanism, occurring only via loop diagrams (penguin and box). Unlike $b \to s \ell^+ \ell^-$ decays, which suffer from long-distance contributions involving photon exchange and charm loops, $b \to s \nu \bar{\nu}$ decays allow for precise theoretical predictions. These decays are sensitive to physics beyond the SM (BSM), such as virtual contributions from leptoquarks or $Z'$ bosons, and can probe invisible particles like light scalars or fermionic dark matter.

While the Belle II collaboration previously reported evidence for the exclusive decay $B^+ \to K^+ \nu \bar{\nu}$ with a branching fraction of $(2.3 \pm 0.7) \times 10^{-5}$ (2.7$\sigma$ above the SM prediction), the inclusive decay $B \to X_s \nu \bar{\nu}$ (where $X_s$ is a hadronic system with strangeness $S=1$) had not been studied. The inclusive branching fraction is predicted to be $(2.9 \pm 0.3) \times 10^{-5}$ in the SM. Theoretical sum rules relate the inclusive and exclusive rates, providing strong motivation for an inclusive search to constrain BSM parameters. Previous limits from the ALEPH collaboration at the $Z$-pole were less stringent and lacked a reliable theoretical framework for inclusive $b$-hadron decays.

Methodology
This analysis utilizes data collected by the Belle II detector at the SuperKEKB asymmetric-energy $e^+e^-$ collider. The dataset comprises an integrated luminosity of $365.4 \pm 1.7 \text{ fb}^{-1}$ collected at the $\Upsilon(4S)$ resonance and $42.7 \pm 0.2 \text{ fb}^{-1}$ collected 60 MeV below resonance to estimate continuum backgrounds.

The analysis employs a "tag-and-probe" strategy:

1. Tagging: One $B$ meson ($B_{\text{tag}}$) from the $\Upsilon(4S) \to B\bar{B}$ decay is fully reconstructed in hadronic modes using the Full Event Interpretation (FEI) algorithm. Candidates are selected based on beam-energy-constrained mass ($M_{\text{bc}} > 5.27 \text{ GeV}/c^2$) and energy difference ($|\Delta E| < 0.2 \text{ GeV}$).
2. Signal Reconstruction ($X_s$): The remaining particles in the event are used to reconstruct the $X_s$ system. A sum-of-exclusives approach is used, reconstructing 30 specific decay modes ($K n\pi$, $K n\pi K_S^0$, etc., with $0 \le n \le 4$). This method covers approximately 83% of non-resonant $X_s$ decays and 93% of the total $B \to X_s \nu \bar{\nu}$ branching fraction in simulation.
3. Background Suppression:
   • Kinematic Cuts: The reconstructed $X_s$ mass ($M_{\text{reco}}^{X_s}$) is required to be $< 2.0 \text{ GeV}/c^2$, and its momentum in the center-of-mass frame is constrained to $0.5 < p^*_{X_s} < 2.96 \text{ GeV}/c$.
   • Missing Momentum: The polar angle of the missing momentum vector is restricted to the detector acceptance ($17^\circ < \theta_{\text{miss}} < 150^\circ$) to reject particles escaping undetected.
   • Rest-of-Event (ROE): The ROE is required to have zero tracks from the interaction point, zero $\pi^0$, and zero $K_S^0$. Extra energy ($E_{\text{extra}}$) in the electromagnetic calorimeter is limited to $< 1.3 \text{ GeV}$.
   • Multivariate Analysis: A Boosted Decision Tree (BDT) utilizing 32 input variables (kinematics, event shape, ROE, and $D$-meson suppression variables) is used to separate signal from continuum ($e^+e^- \to q\bar{q}$) and non-signal $B\bar{B}$ backgrounds. The BDT output ($O_{\text{BDT}}$) is required to be $> 0.86$.

Key Contributions and Corrections
The analysis incorporates several data-driven corrections to address mismodeling in simulation:

• Photon Multiplicity: Corrections are applied to the photon multiplicity distribution in signal simulation based on comparisons with data using $B_{\text{tag}} X_s^0$ candidates.
• Fragmentation: The $X_s$ fragmentation is corrected using measurements of $B \to X_s \gamma$ in specific mass regions.
• Peaking Backgrounds: Modeling of $B \to X_s n\bar{n}$ and $B \to X_s K_L^0 K_L^0$ backgrounds is refined using $B \to X_s p\bar{p}$ and $B \to X_s K_S^0 K_S^0$ data, respectively.
• Efficiency Validation: Data-to-simulation efficiency ratios for the BDT selection are measured using $B \to J/\psi X_s$ events ($J/\psi \to \mu^+\mu^-$) and applied as correction factors.

Systematic uncertainties are evaluated using off-resonance data, sidebands in $M_{\text{bc}}$ and $O_{\text{BDT}}$, and variations in nuisance parameters. The dominant systematic uncertainties arise from simulated sample size and background normalization.

Results
The search is performed in three mass regions of the true $X_s$ mass ($M_{\text{true}}^{X_s}$):

1. $0.0 < M_{\text{true}}^{X_s} < 0.6 \text{ GeV}/c^2$ (dominated by $K$)
2. $0.6 < M_{\text{true}}^{X_s} < 1.0 \text{ GeV}/c^2$ (dominated by $K^*(892)$)
3. $1.0 \text{ GeV}/c^2 < M_{\text{true}}^{X_s}$ (heavier states)

No significant signal is observed in any region. The observed signal yields are consistent with background expectations. Consequently, 90% confidence level (C.L.) upper limits on the partial branching fractions are set:

• $0.0 < M_{\text{true}}^{X_s} < 0.6 \text{ GeV}/c^2$: $2.2 \times 10^{-5}$
• $0.6 < M_{\text{true}}^{X_s} < 1.0 \text{ GeV}/c^2$: $9.3 \times 10^{-5}$
• $1.0 \text{ GeV}/c^2 < M_{\text{true}}^{X_s}$: $30.9 \times 10^{-5}$

Combining all regions, the upper limit on the inclusive branching fraction is:
$$\mathcal{B}(B \to X_s \nu \bar{\nu}) < 3.3 \times 10^{-4}$$
The central value for the branching fraction is calculated as $[8.8^{+8.5}_{-8.2}(\text{stat})^{+12.6}_{-10.7}(\text{syst})] \times 10^{-5}$. Note that these results exclude the long-distance contribution from $B^+ \to \tau^+(\to X_s^+ \bar{\nu})\nu$.

Significance
This paper reports the first search for inclusive $B \to X_s \nu \bar{\nu}$ decays. While the results do not currently exceed the SM prediction to establish a discovery, the established upper limits provide the first experimental constraints on the inclusive rate. These constraints are crucial for testing the relationship between inclusive and exclusive $b \to s \nu \bar{\nu}$ decays via sum rules and for limiting potential contributions from new physics models that enhance these FCNC processes.