Search for the decays $B_{(s)}^0\to J/\psi\gamma$ at LHCb

Using proton-proton collision data from the LHCb experiment, this study sets new 90% confidence level upper limits on the branching fractions of the rare decays $B_{s}^0\to J/\psi\gamma$ and $B^0\to J/\psi\gamma$, improving the previous limit for the $B_{s}^0$ mode by a factor of 2.5.

The Gist

Imagine the universe as a giant, high-speed racetrack where tiny particles zoom around at nearly the speed of light. At CERN, the LHCb experiment is like a super-advanced camera crew stationed on the sidelines, trying to catch a glimpse of a very specific, incredibly rare "accident" that happens when these particles crash.

Here is the story of their latest hunt, explained simply:

The Mystery: A Disappearing Act

The scientists were looking for a specific particle called a $B^0_s$ meson (think of it as a heavy, unstable "cosmic balloon"). Usually, when this balloon pops, it breaks apart in predictable ways. But the scientists wanted to see if it ever popped in a very strange, rare way: turning into a $J/\psi$ particle (a heavy, stable "marble") and a photon (a single particle of light).

In the language of physics, this is written as: $B^0_s \to J/\psi \gamma$.

Why is this exciting?

• It's a Ghost: In the standard rules of physics (the Standard Model), this event is supposed to be incredibly rare—like finding a specific grain of sand on a beach the size of the Earth.
• The Treasure Hunt: If they find it more often than the rules predict, it means there are "new physics" at play—maybe invisible particles or forces we don't know about yet are helping the balloon pop.

The Challenge: Finding a Needle in a Haystack

The problem is that the "haystack" is massive. Every time the particles collide, they create billions of other things. The signal the scientists are looking for is buried under a mountain of "noise" (other particles that look similar but aren't the target).

To solve this, the LHCb team used a few clever tricks:

1. The Time Machine: They looked at data collected over several years (from 2010 to 2018), giving them a huge pile of "footage" to review.
2. The Detective Work: They didn't just look for the final products. They looked for clues. For example, they tracked how the particles moved and used powerful computer algorithms (called Boosted Decision Trees) to act like a super-smart filter, sorting the "real" suspects from the "lookalikes."
3. The Two Categories: They split their search into two groups based on how the light particle (photon) was detected:
   • "Long" category: The photon converted into an electron and positron early in the detector, leaving a long, clear trail.
   • "Downstream" category: The conversion happened later, leaving a shorter, fuzzier trail.

The Result: The "Almost" Moment

After sifting through 9 billion collision events (a massive dataset), the scientists looked at their results.

• Did they find the ghost? No. They didn't see a clear "bump" in the data that would prove the rare decay happened.
• Did they find nothing? Not exactly. They found that the number of events they saw was consistent with what they expected from background noise. It was like searching a dark room for a specific firefly and finding only the usual dust motes dancing in the light.

The Verdict: Setting the Boundaries

Since they didn't find the particle, they couldn't say how often it happens. Instead, they set a speed limit (an upper limit).

They announced: "If this rare decay happens, it must happen less than 2.9 times out of every million attempts."

Think of it like this: If you flip a coin a million times, and you never see it land on its edge, you can't say it's impossible, but you can confidently say, "It happens less than 3 times in a million flips."

Why This Matters

Even though they didn't find the "new physics" they were hoping for, this is a huge victory for science:

1. Shrinking the Search Area: They improved their previous limit by a factor of 2.5. They have narrowed the search area significantly. If this rare event does exist, it's hiding in an even smaller box now.
2. Ruling Out Theories: They were able to rule out a specific theory that predicted the event would happen 5 times out of a million. That theory is now in trouble!
3. Better Tools: The techniques they developed to filter out the noise are now ready for the next generation of experiments.

The Bottom Line

The LHCb team acted like master detectives in a cosmic crime scene. They didn't catch the criminal (the rare decay), but they proved that the criminal is much more elusive than some theories suggested. They have tightened the noose, and future experiments with even more powerful data will have to work even harder to find this ghost.

In short: They looked hard, they looked smart, they didn't find the ghost, but they proved the ghost is very, very shy.

Technical Summary

1. Problem Statement and Physics Motivation

The paper addresses the search for the rare, pure annihilation-type radiative decays $B^0_s \to J/\psi\gamma$ and $B^0 \to J/\psi\gamma$.

• Standard Model (SM) Context: In the SM, these decays proceed via $W$-boson exchange between the $b$-quark and a light-flavor quark. Theoretical predictions for the branching fraction of $B^0_s \to J/\psi\gamma$ range from $1.5 \times 10^{-7}$ to $5 \times 10^{-6}$, depending on the factorization scheme used. The $B^0 \to J/\psi\gamma$ decay is Cabibbo-suppressed and predicted to be at least an order of magnitude lower.
• New Physics Potential: These decays are sensitive probes for physics beyond the SM (BSM). They could be significantly enhanced by:
  • Intrinsic charm components in $B$ mesons.
  • Right-handed currents.
  • Other BSM contributions.
• Current Status: Prior to this analysis, only upper limits existed (from BaBar and previous LHCb Run 1 data). The most stringent previous limit for $B^0_s \to J/\psi\gamma$ was $7.3 \times 10^{-6}$ at 90% confidence level (CL), which was already close to the upper bound of SM predictions.

2. Methodology and Experimental Setup

Dataset and Detector:

• Data: The analysis utilizes proton-proton collision data collected by the LHCb experiment during Run 1 (7 and 8 TeV) and Run 2 (13 TeV), corresponding to a total integrated luminosity of 9 fb$^{-1}$ (3 fb$^{-1}$ at 7/8 TeV and 6 fb$^{-1}$ at 13 TeV).
• Detector: LHCb is a single-arm forward spectrometer ($2 < \eta < 5$). The analysis relies on the tracking system, particle identification (RICH, calorimeters, muon chambers), and the trigger system.

Event Reconstruction and Selection:

• Signal Topology: The decay is reconstructed via $J/\psi \to \mu^+\mu^-$ and a photon ($\gamma$) that converts into an electron-positron pair ($e^+e^-$) within the detector material.
• Photon Conversion Categories: Candidates are split into two categories based on where the photon converts:
  • Long: Conversion occurs early enough for the $e^+e^-$ tracks to be fully reconstructed in the vertex detector.
  • Downstream: Conversion occurs later; only track segments are available.
• Selection Criteria:
  • Muons must have $p_T > 500$ MeV and significant impact parameters relative to the primary vertex (PV).
  • Converted photons must form a good vertex with an invariant mass $< 60$ MeV (Long) or $< 100$ MeV (Downstream) and $p_T > 1$ GeV.
  • A kinematic fit constrains the dimuon mass to the known $J/\psi$ mass and forces the $B$ candidate to originate from its associated PV.
• Background Suppression:
  • Combinatorial Background: Rejected using a Boosted Decision Tree (BDT) trained on kinematic and geometric variables, plus isolation criteria.
  • Partially Reconstructed Backgrounds: Major backgrounds include $B^0 \to J/\psi\pi^0$, $B^0 \to J/\psi\eta$, and $B^0_s \to J/\psi\eta$ (where a photon from $\pi^0/\eta$ decay is missed). A second BDT specifically targets these.
  • Blinding: The invariant mass region around the $B^0_s$ mass (5250–5450 MeV) was not examined until the analysis procedure was finalized to avoid bias.

Statistical Analysis:

• Fitting: An unbinned maximum-likelihood fit is performed simultaneously on the $m(J/\psi\gamma)$ distributions for both Long and Downstream categories.
• Signal Shape: Modeled by a modified Crystal Ball function (DSCB) with a Gaussian core and power-law tails. The resolution is dominated by the photon energy resolution.
• Background Shapes:
  • Partially reconstructed decays ($B \to J/\psi\eta, \pi^0$) are modeled using ARGUS functions or DSCB functions convolved with resolution.
  • Combinatorial background is modeled with a third-order Bernstein polynomial.
• Normalization: Signal yields are normalized to the $B^0 \to J/\psi\pi^0$ yield in the downstream category, utilizing known branching fractions and fragmentation fractions ($f_s/f_d$).
• Systematics: Sources include mass resolution modeling, background shape modeling, selection efficiency, and external branching fraction uncertainties. These are incorporated as nuisance parameters with Gaussian constraints in the likelihood fit.

3. Key Contributions

• Improved Sensitivity: This analysis improves the limit for $B^0_s \to J/\psi\gamma$ by a factor of 2.5 compared to the previous LHCb Run 1 result.
• Dual Search: It performs independent searches for both $B^0_s \to J/\psi\gamma$ and $B^0 \to J/\psi\gamma$, setting limits for both channels simultaneously.
• Advanced Background Handling: The use of converted photons significantly improves mass resolution and reduces partially reconstructed backgrounds compared to analyses using prompt photons.
• Comprehensive Systematics: The analysis provides a detailed breakdown of systematic uncertainties, showing that statistical uncertainty remains the dominant factor, while systematic uncertainties are well-controlled (approx. 25%).

4. Results

Observation:

• No significant signal peak was observed in either the $B^0_s$ or $B^0$ mass regions.
• The measured branching fractions (statistical uncertainty only) are:
  • $\mathcal{B}(B^0_s \to J/\psi\gamma) = (1.34 \pm 0.78) \times 10^{-6}$
  • $\mathcal{B}(B^0 \to J/\psi\gamma) = (0.61 \pm 0.50) \times 10^{-6}$
• Both results are consistent with the background-only hypothesis (significance $< 2\sigma$).

Upper Limits (90% and 95% CL):
Using the $CL_s$ method:

• $B^0_s \to J/\psi\gamma$:
  • $< 2.9 \times 10^{-6}$ (90% CL)
  • $< 3.4 \times 10^{-6}$ (95% CL)
• $B^0 \to J/\psi\gamma$:
  • $< 2.6 \times 10^{-6}$ (90% CL)
  • $< 3.5 \times 10^{-6}$ (95% CL)

Exclusion of Theory:

• The perturbative QCD prediction of $\mathcal{B}(B^0_s \to J/\psi\gamma) = 5 \times 10^{-6}$ is excluded at 99.7% CL (CL value = 0.0029).
• Other theoretical models predicting lower values (e.g., $1.4 \times 10^{-6}$ or $7.2 \times 10^{-7}$) are not yet excluded but are within reach of future datasets.

5. Significance

This paper represents a major step forward in the study of rare radiative $B$ decays. By utilizing the full Run 1 and Run 2 dataset and optimizing the reconstruction of converted photons, LHCb has tightened the constraints on these annihilation modes.

• Constraint on SM: The exclusion of the $5 \times 10^{-6}$ perturbative QCD prediction suggests that either the theoretical calculations need refinement (e.g., regarding non-perturbative effects or factorization schemes) or that the true branching fraction lies lower.
• New Physics Reach: While no new physics has been discovered, the improved limits constrain models involving intrinsic charm or right-handed currents. The results demonstrate that future analyses with larger datasets (Run 3 and beyond) will have the sensitivity to probe the central values of current theoretical predictions, potentially uncovering deviations from the Standard Model.