Observation of the Electromagnetic Dalitz Transition $h_c \rightarrow e^+e^-η_c$

Using a large dataset collected by the BESIII detector, researchers report the first observation of the electromagnetic Dalitz transition $h_c \to e^+e^-\eta_c$ with a statistical significance of $5.4\sigma$ and measure the ratio of its branching fraction to the radiative decay $h_c \to \gamma\eta_c$ to be $(0.59\pm0.14)\%$.

The Gist

Imagine the subatomic world as a bustling, chaotic city where tiny particles are constantly colliding, breaking apart, and reassembling. In this city, there is a special neighborhood called "Charmonium," home to a pair of twins: a charm quark and an anti-charm quark. These twins usually stick together in very specific, stable arrangements.

For a long time, scientists knew about most of these arrangements, but one specific "house" in this neighborhood, called the $h_c$, was a bit of a mystery. We knew it existed, but we didn't know much about how it behaved or how it liked to "move" (decay) into other particles.

The Big Discovery: Catching a Ghostly Transformation

This paper reports the first time scientists have successfully "caught" the $h_c$ doing something very specific and rare: an electromagnetic Dalitz transition.

To understand this, imagine the $h_c$ is a magician. Usually, when this magician performs a trick, it turns into a different particle (the $\eta_c$) and shoots out a single, invisible flash of light (a photon). This is the "standard trick" everyone expected.

However, in this new discovery, the magician decided to do a more complex, "ghostly" version of the trick. Instead of shooting out a single flash of light, the magician shot out a virtual flash of light that immediately split into two new particles: an electron and a positron (a pair of oppositely charged twins).

This is like watching a magician throw a single coin into the air, and instead of catching one coin, you see it transform mid-air into a pair of coins before landing. This specific transformation ($h_c \rightarrow e^+e^-\eta_c$) had never been seen before.

How They Did It: The Great Detective Hunt

The scientists used a massive particle detector called BESIII, which acts like a giant, ultra-fast camera capable of taking billions of pictures of particle collisions. They had two main ways to find their "magician" ($h_c$):

1. The "Broken Toy" Method (Mode I): They took a known particle called $\psi(3686)$ and watched it break apart. Usually, it breaks into pieces that are easy to spot. But sometimes, very rarely, it breaks into a neutral pion ($\pi^0$) and our mystery magician ($h_c$). It's like finding a rare, specific toy in a pile of broken plastic.
2. The "High-Speed Crash" Method (Mode II): They smashed electrons and positrons together at very high speeds. Sometimes, this crash creates a pair of pions and our mystery magician.

They collected data from 27 billion of the "Broken Toy" events and a massive amount of "High-Speed Crash" data.

The Evidence: Finding the Needle in the Haystack

The challenge was that the "ghostly transformation" (the electron-positron pair) is very hard to spot because it looks a lot like background noise—like trying to hear a whisper in a rock concert.

The team used a clever strategy:

• They looked for the "missing" partner. Since the $h_c$ turns into an $\eta_c$ plus the electron-positron pair, they measured the "recoil mass" (the weight of everything left over after the electron and positron are removed).
• If the $h_c$ was really there, the leftover weight would form a distinct peak, like a mountain rising out of a flat plain.

The Result:
They found a clear mountain peak!

• The "Broken Toy" method showed a peak with a statistical significance of 5.4 sigma. In the world of particle physics, this is the gold standard for a "discovery." It means there is less than a one-in-a-million chance that this peak is just a random fluke.
• They also measured how often this rare "ghostly" trick happens compared to the standard "single flash" trick. They found that for every 100 times the magician does the standard trick, it does the rare ghostly trick about 0.59 times (roughly 6 times out of 1,000).

Why This Matters

Think of the $h_c$ as a character in a story. Before this paper, we only knew a few lines of its dialogue. Now, we have heard it speak a new, complex sentence.

This discovery is important because:

1. It confirms a prediction: It proves that these particles can indeed undergo this specific electromagnetic transformation.
2. It helps us understand the rules: By measuring exactly how often this happens, scientists can test their theories about how the strong force (the glue holding quarks together) and electromagnetism interact.
3. It fills a gap: It adds a crucial piece to the puzzle of the "charmonium" family, helping us understand the fundamental building blocks of our universe.

In short, the BESIII team didn't just find a new particle; they found a new way an old, mysterious particle behaves, proving that even in the tiny world of atoms, there are still surprises waiting to be discovered.

Technical Summary

1. Problem and Motivation

• Scientific Context: The charmonium system ($c\bar{c}$) is a crucial testing ground for Quantum Chromodynamics (QCD). While most charmonium states below the open-charm threshold are well-understood, the properties of the $P$-wave singlet state, $h_c(1^1P_1)$, remain poorly constrained.
• The Gap: The best-measured decay of the $h_c$ is the radiative transition $h_c \to \gamma\eta_c$. All other known decay modes sum to less than 3% of the total width. There is a lack of experimental data on Electromagnetic (EM) Dalitz decays (e.g., $h_c \to e^+e^-\eta_c$), where a virtual photon internally converts into an electron-positron pair.
• Objective: To search for the first observation of the EM Dalitz decay $h_c \to e^+e^-\eta_c$ and measure the ratio of its branching fraction to the radiative decay, $R = \mathcal{B}(h_c \to e^+e^-\eta_c) / \mathcal{B}(h_c \to \gamma\eta_c)$. This measurement helps constrain theoretical models regarding hadron structure and photon interactions.

2. Methodology

The study utilizes data collected by the BESIII detector at the BEPCII collider.

• Data Samples:
  • Mode I: $(27.12 \pm 0.14) \times 10^8$ $\psi(3686)$ decays. The $h_c$ is produced via the isospin-violating decay $\psi(3686) \to \pi^0 h_c$.
  • Mode II: $e^+e^-$ collision data at center-of-mass energies ranging from 4.130 to 4.780 GeV (total integrated luminosity of 10507.44 pb$^{-1}$). The $h_c$ is produced via $e^+e^- \to \pi^+\pi^- h_c$.
• Event Selection and Reconstruction:
  • Tracks: Charged tracks are reconstructed in the Main Drift Chamber (MDC) with strict impact parameter and polar angle cuts.
  • Particle Identification (PID): Electrons/positrons are identified using specific ionization energy loss ($dE/dx$) and Time-of-Flight (TOF) data, plus an $E/p$ cut (energy in EMC vs. momentum in MDC).
  • Photon Selection: Photons are reconstructed in the Electromagnetic Calorimeter (EMC) with energy thresholds (25 MeV barrel, 50 MeV endcap).
  • Background Suppression:
    • $\pi^0$ rejection: Events where $e^+e^-\gamma$ invariant mass matches the $\pi^0$ mass are rejected to suppress $\pi^0 \to \gamma e^+e^-$ backgrounds.
    • Photon Conversion (PC) veto: A "photon conversion finder" is used to reject pairs originating from photon conversions in the beam pipe or MDC walls (requiring conversion distance $\delta_{xy} < 2$ cm).
    • Recoil Mass: The $\eta_c$ is selected by requiring the recoil mass against the $\pi^0$ (Mode I) or $\pi^+\pi^-$ (Mode II) system to fall within the $\eta_c$ mass window $[2.92, 3.08]$ GeV/$c^2$.
• Analysis Technique:
  • A simultaneous unbinned maximum likelihood fit is performed on the recoil mass spectra of $\pi^0$ (Mode I) and $\pi^+\pi^-$ (Mode II).
  • Signal Model: A Breit-Wigner function (fixed width 0.78 MeV) convolved with a Crystal Ball function (for resolution).
  • Background Model: Fourth-order Chebyshev function for Mode I; First-order Chebyshev for Mode II.
  • Efficiency Calculation: Monte Carlo (MC) simulations (using GEANT4, EVTGEN, and a new generator for the Dalitz decay) determine detection efficiencies.

3. Key Contributions

• First Observation: This is the first experimental observation of the electromagnetic Dalitz transition $h_c \to e^+e^-\eta_c$.
• Dual-Mode Measurement: The analysis independently measures the decay ratio using two distinct production mechanisms ($\psi(3686)$ decay and direct $e^+e^-$ annihilation), providing a robust cross-check.
• Systematic Cancellation: By measuring the ratio $R$, many systematic uncertainties (tracking efficiency, PID, production cross-sections, and $\psi(3686)$ branching fractions) cancel out, leading to a more precise result.

4. Results

• Statistical Significance: The signal for $h_c \to e^+e^-\eta_c$ is observed with a statistical significance of 5.4$\sigma$.
• Mass Measurement: The fitted $h_c$ mass is $(3524.72 \pm 0.47)$ MeV/$c^2$, consistent with the world average.
• Branching Fraction Ratio ($R$):
  • Mode I ($\psi(3686)$): $R = (0.46 \pm 0.12_{\text{stat}} \pm 0.05_{\text{syst}})\%$
  • Mode II (XYZ data): $R = (0.89 \pm 0.18_{\text{stat}} \pm 0.09_{\text{syst}})\%$
  • Combined Average: The weighted average is determined to be:
    $$R = (0.59 \pm 0.10_{\text{stat}} \pm 0.04_{\text{syst}})\%$$
• Systematic Uncertainties: Major sources include fitting range, signal/background shape modeling, and tracking/PID efficiencies. The total systematic uncertainty is small (0.04%) due to the cancellation effects in the ratio.

5. Significance

• Theoretical Impact: This result provides the first experimental input on the branching ratio of the $h_c$ Dalitz decay. It serves as a critical constraint for theoretical models describing charmonium decays and the interaction of charmonium states with the electromagnetic field.
• Hadron Structure: The measurement of EM Dalitz decays offers unique insights into the internal structure of hadrons and the mechanism of virtual photon conversion.
• Future Physics: The successful observation validates the capability of the BESIII detector to study rare charmonium transitions, paving the way for further precision measurements in the charmonium and exotic hadron sectors.