Search for the Lepton Flavour Violating decays $\Upsilon(2S)\rightarrow e^{\pm}\mu^{\mp}$ and $\Upsilon(3S)\rightarrow e^{\pm}\mu^{\mp}$

Using data samples of 99 million $\Upsilon(2S)$ and 122 million $\Upsilon(3S)$ mesons collected by the BABAR detector, this paper presents a search for the lepton flavour violating decays $\Upsilon(2S)\rightarrow e^{\pm}\mu^{\mp}$ and $\Upsilon(3S)\rightarrow e^{\pm}\mu^{\mp}$, which are forbidden in the Standard Model but predicted by various new physics extensions.

The Gist

Imagine the universe as a massive, high-speed dance floor where particles are the dancers. In the "Standard Model" (the rulebook of physics), there's a strict dress code: Lepton Flavor.

• Electrons are one type of dancer.
• Muons are another type.
• Taus are a third.

According to the old rulebook, an Electron dancer can never suddenly swap costumes to become a Muon dancer mid-dance. They are distinct species. However, we know that in the "neutral" sector (neutrinos), these dancers do swap identities. This suggests that somewhere in the universe, there might be a secret "New Physics" club where these swaps happen more often than the rulebook allows.

This paper is a report from the BABAR collaboration, a team of scientists who acted like detectives at a giant particle collider (the PEP-II accelerator) to catch these dancers in the act of breaking the rules.

The Mission: Catching the "Imposter"

The scientists were looking for a very specific, forbidden move:

• They watched the Upsilon mesons (heavy, unstable particles made of bottom quarks, like a heavy ballroom couple).
• Specifically, they looked at the Upsilon(2S) and Upsilon(3S) versions.
• They wanted to see if these heavy couples would decay (break apart) into an Electron and a Muon simultaneously.

If they found this, it would be like seeing a ballroom dancer suddenly turn into a completely different species. It would be the smoking gun for "New Physics" beyond our current understanding.

The Setup: A Massive Search Party

To find this needle in a haystack, the team needed a huge amount of data:

• They collected 99 million Upsilon(2S) particles and 122 million Upsilon(3S) particles.
• They used the BABAR detector, which is like a giant, 360-degree security camera system surrounding the dance floor. It has layers of sensors to track where particles go, how fast they are, and what kind of particle they are (electron vs. muon).

The "Blind" Strategy:
To ensure they didn't accidentally "cheat" by tweaking their rules to find a fake signal, they used a blind analysis. Imagine they locked the "answer key" in a safe. They spent months designing their search criteria and testing their equipment without ever looking at the final results. Only when everything was perfect did they "unblind" the data to see what they found.

The Hunt: Filtering the Noise

The real challenge was that the "forbidden dance" is incredibly rare. The background noise was deafening:

• The "Fake Outs": Sometimes, a muon might decay into an electron, or an electron might get misidentified as a muon by the sensors. It's like someone wearing a fake mask.
• The "Double Trouble": Sometimes two particles are created that look like the target but aren't.

The scientists built a sophisticated filter (a digital bouncer) to let only the perfect candidates through:

1. Two tracks: Exactly two particles coming out.
2. Opposite charges: One positive, one negative.
3. Perfect energy: They must have exactly the right amount of energy to match the Upsilon mass.
4. Identity check: One must be definitely an electron, the other definitely a muon.

The Results: The Great Silence

After all the filtering and after finally opening the safe (unblinding the data):

• They found 5 candidate events.
• But... they expected about 4.2 events just from random background noise (false alarms).

The Verdict: The 5 events they saw were statistically consistent with random noise. There was no "signal" of new physics. It was like searching a stadium for a specific person and finding 5 people who looked like them, but upon closer inspection, they were just regular fans.

What Does This Mean?

Even though they didn't find the "imposter," the search was a huge success for science.

1. Setting the Limit: They calculated that if this forbidden decay does happen, it happens less than 3.4 times in every 100 billion attempts. This is a new, stricter limit than ever before for the Upsilon(2S).
2. Ruling Out Theories: Because they didn't find it, they can tell theorists: "Your theories that predict this happens often are probably wrong." They pushed the "New Physics" scale up to 75 TeV (a massive energy scale), meaning if this new physics exists, it's hiding in a realm we can't quite reach yet.

The Takeaway

Think of this paper as a detective saying: "We searched the entire city, checked every alley, and used the best technology available. We didn't find the criminal. This doesn't mean the criminal doesn't exist, but it means they are much harder to catch than we thought, and they certainly aren't hanging out in the places we looked."

This result tightens the noose around "New Physics" theories, forcing scientists to come up with even more creative ideas to explain the universe.

Technical Summary

Here is a detailed technical summary of the paper presented by the BABAR collaboration regarding the search for Lepton Flavour Violating (LFV) decays.

1. Problem Statement and Motivation

• The Physics Gap: While neutrino oscillations have confirmed Lepton Flavour Violation (LFV) in the neutral lepton sector, the Standard Model (SM) predicts that Charged Lepton Flavour Violation (CLFV) in the charged lepton sector is unobservable due to the extreme suppression caused by tiny neutrino masses (branching fractions $\mathcal{B} \lesssim 10^{-50}$).
• New Physics Signal: The observation of any CLFV process (e.g., $\Upsilon \to e^\pm \mu^\mp$) would be a definitive signature of physics beyond the Standard Model (NP).
• Context: Previous searches have set limits on $\Upsilon(1S)$ and $\Upsilon(3S)$ decays to $e^\pm \mu^\mp$, and limits on $\tau$-lepton decays. However, this paper reports the first experimental search for the LFV decay $\Upsilon(2S) \to e^\pm \mu^\mp$.
• Theoretical Framework: The results are used to constrain effective field theory parameters ($g_{NP}/\Lambda_{NP}^2$) for new physics models involving LFV couplings.

2. Methodology and Experimental Setup

• Data Source: The analysis utilizes data collected by the BABAR detector at the PEP-II $e^+e^-$ collider at SLAC.
  • Signal Sample: 99 million $\Upsilon(2S)$ mesons collected at a center-of-mass (CM) energy of 10.02 GeV (Run 7, 2008), corresponding to an integrated luminosity of $12.61 \pm 0.03 \text{ fb}^{-1}$ (after excluding a blind sample).
  • Control Samples: Data from $\Upsilon(4S)$ (Run 6), and off-resonance data (40 MeV below $\Upsilon(4S)$ and $\Upsilon(2S)$) were used to estimate non-resonant backgrounds and study systematic effects.
• Blind Analysis Strategy: To prevent bias, a "blind" approach was employed. A small subset of the data ($0.995 \text{ fb}^{-1}$) was used to optimize selection criteria and evaluate systematics. The final signal region remained hidden until the analysis strategy was finalized.
• Event Selection Criteria:
  • Topology: Events must contain exactly two oppositely charged tracks (one electron candidate, one muon candidate).
  • Kinematics:
    • Tracks must have energies close to half the beam energy ($E \approx E_{beam}$).
    • The invariant mass of the $e\mu$ pair must peak at the $\Upsilon$ mass.
    • A specific kinematic cut was applied in the $(p/E_{beam})$ plane: $(p_e/E_{beam} - 1)^2 + (p_\mu/E_{beam} - 1)^2 < 0.01$.
    • The angle between the two tracks in the CM frame must be $> 179^\circ$.
  • Particle Identification (PID):
    • Electron: Identified via energy deposition in the Electromagnetic Calorimeter (EMC) and momentum ($E/p > 0.8$).
    • Muon: Identified via penetration through the Instrumented Flux Return (IFR) and minimal energy in the EMC ($E/p < 0.8$).
    • Specific Muon Cut: The muon candidate must deposit at least 50 MeV in the EMC to suppress Bhabha events where an electron is misidentified as a muon due to passing between crystals.
  • Background Suppression: Kinematic requirements efficiently remove $\tau^+\tau^- \to e^\pm \mu^\mp \nu\nu$ backgrounds, as well as two-photon processes and beam-gas interactions.

3. Key Contributions

• First Search: This work constitutes the first experimental search for the LFV decay $\Upsilon(2S) \to e^\pm \mu^\mp$.
• Systematic Evaluation: The collaboration developed a robust method to evaluate systematic uncertainties using a control sample of $\tau^+\tau^- \to e^\pm \mu^\mp \nu\nu$ events (reversing major kinematic cuts to create a sideband).
• Efficiency Optimization: The analysis achieved a total signal efficiency of 18.37% ± 0.47% after applying optimized PID and kinematic cuts.
• Constraint on New Physics: The results provide a direct constraint on the energy scale of New Physics ($\Lambda_{NP}$) for models predicting LFV in $b\bar{b}$ bound states.

4. Results

• Observation: After unblinding the data, 5 candidate events were observed.
• Background Estimation: The expected background from continuum processes and misidentification was calculated to be 4.19 ± 0.83 events.
• Statistical Conclusion: The observed number of events is consistent with the background expectation (no significant signal excess).
• Branching Fraction Calculation:
  • Central value: $\mathcal{B}(\Upsilon(2S) \to e^\pm \mu^\mp) = (0.5 \pm 1.3_{stat} \pm 0.5_{syst}) \times 10^{-6}$.
  • Upper Limit: Using the $CL_s$ method (modified frequentist approach) to account for systematic uncertainties and potential background fluctuations, a 90% Confidence Level (CL) upper limit was set:
    $$\mathcal{B}(\Upsilon(2S) \to e^\pm \mu^\mp) < 3.4 \times 10^{-6}$$
• New Physics Constraint: Using the relationship between the LFV branching fraction and the dilepton branching fraction ($\mathcal{B}(\Upsilon(2S) \to \mu^+\mu^-)$), the result translates to a lower limit on the New Physics energy scale:
  $$\Lambda_{NP} / \sqrt{g_{NP}} > 75 \text{ TeV}$$

5. Significance

• Experimental Milestone: This result fills a gap in the experimental landscape of LFV searches within the bottomonium family, providing the first limit for the $\Upsilon(2S)$ state.
• Theoretical Impact: The derived limit of $75 \text{ TeV}$on the New Physics scale is a stringent constraint on models that predict enhanced LFV in vector meson decays. It complements existing limits from$\Upsilon(1S)$and$\Upsilon(3S)$ searches, helping to map the parameter space for potential new physics couplings.
• Methodological Validation: The successful application of the blind analysis strategy and the use of $\tau$-pair control samples demonstrate the robustness of the BABAR analysis techniques in handling low-statistics, high-background searches.