Search for a hypothetical gauge boson and dark photons in charmonium transitions

Using a sample of 2.7 billion $\psi(3686)$ events collected by the BESIII detector, this study reports no significant evidence for a 17 MeV/$c^2$ gauge boson or dark photons in charmonium transitions, establishing new upper limits on the charm quark coupling strength and the photon-dark photon mixing parameter.

The Gist

The Big Picture: Hunting for a "Ghost" Particle

Imagine the universe is a giant, complex orchestra playing a symphony. For decades, physicists have known the sheet music for most of the instruments (the Standard Model of physics). But recently, a few musicians in a small lab (in Hungary) noticed a weird, extra note being played during a specific experiment with atoms. They called this mysterious note the "X17" particle (or a "dark photon").

This paper is like a team of detectives (the BESIII collaboration in China) saying, "We heard about this weird note. Let's check our own massive concert hall to see if we can hear it too."

The Setting: A Particle Collision Factory

The researchers used the BESIII detector, which is essentially a giant, high-tech camera sitting inside a particle accelerator.

• The Analogy: Think of the accelerator as a racetrack where tiny cars (electrons and positrons) zoom around and crash into each other at incredible speeds.
• The Crash: When these cars crash, they create a shower of debris. Sometimes, this debris forms a specific type of heavy particle called Charmonium (specifically the $\psi(3686)$).
• The Decay: This heavy particle is unstable. It immediately breaks apart, usually into a lighter particle called $J/\psi$ and a flash of light (a photon).

The Hunt: Looking for the Invisible

The team was looking for a specific, rare event in this debris. They were hoping that instead of just a normal flash of light, the heavy particle would break apart and release a new, invisible particle (the X17 or Dark Photon) that immediately turns into a pair of electrons and positrons.

• The Analogy: Imagine you are watching a magician pull a rabbit out of a hat. Usually, you see a rabbit. But the physicists are hoping that instead of a rabbit, the magician pulls out a ghost that instantly turns into two real rabbits. They are looking for those two rabbits appearing out of nowhere in a very specific spot.

They analyzed 2.7 billion of these crash events. That is a lot of data! It's like watching 2.7 billion magic tricks to see if the ghost appears even once.

The Method: Filtering the Noise

The hard part is that the "ghost" signal is very faint and looks a lot like normal background noise.

• The Background: Most of the time, the particles just behave normally. Sometimes, a photon (light) accidentally bumps into the detector wall and creates a fake electron pair. This is like a stagehand accidentally dropping a prop that looks like a rabbit.
• The Filter: The scientists built a sophisticated computer filter (a "veto") to ignore the fake rabbits. They looked at exactly where the particles came from and how much energy they had. If the "rabbit" came from the wrong angle or had the wrong energy, they threw that data out.

The Results: The Silence

After sifting through all 2.7 billion events and applying all the filters, the result was... silence.

• The Finding: They did not find the X17 particle. They did not find the Dark Photon.
• The Analogy: It's like searching a massive library for a specific book that was rumored to be hidden on a shelf. You check every single book, you check the shelves, you check the floor, and you find nothing.

What Does This Mean?

Even though they didn't find the particle, this is still a huge success for science. Here is why:

1. Ruling Out Possibilities: By not finding it, they have drawn a new, tighter boundary around where this particle could exist. It's like saying, "We know the ghost isn't in the basement, the attic, or the kitchen. It must be somewhere else, or it doesn't exist at all."
2. Setting Limits: They calculated exactly how strong the "connection" (coupling) between this new particle and normal matter would have to be for them to have seen it. Since they didn't see it, they know the connection must be weaker than a specific number.
3. The "Dark" Connection: They also put strict limits on "Dark Photons." These are hypothetical particles that might be the key to understanding Dark Matter (the invisible stuff that holds galaxies together). Their results say, "If Dark Photons exist, they are very shy and very weak."

The Takeaway

The BESIII team performed a massive, high-precision search for a new type of particle that could explain some weird anomalies in nuclear physics. They found nothing.

In simple terms: They looked for a needle in a haystack of 2.7 billion pieces of hay. They didn't find the needle. But by proving the needle isn't in this haystack, they have helped the rest of the scientific community stop looking in the wrong place and start looking elsewhere. It's a classic "null result," which is just as important as a discovery because it tells us what the universe is not.

Technical Summary

1. Problem and Motivation

The paper addresses two major anomalies in particle physics:

• The "17 MeV Anomaly" (X17): Experiments using the ATOMKI pair spectrometer observed an anomalous excess of $e^+e^-$ pairs in nuclear transitions of $^8$Be, $^4$He, and $^{12}$C. This suggests the existence of a new light gauge boson, $X$ (or $X_{17}$), with a mass of approximately $17 \text{ MeV}/c^2$. The leading theoretical explanation is a protophobic vector gauge boson that couples non-universally to Standard Model (SM) fermions.
• Dark Photons ($\gamma'$): Many Beyond Standard Model (BSM) theories propose a "dark sector" containing a dark photon ($\gamma'$) that kinetically mixes with the SM photon. This mixing is parameterized by a strength $\epsilon$.

The Gap: While previous searches have been conducted in fixed-target and beam-dump experiments, there was a lack of direct searches for these particles in charmonium transitions, specifically in the decay chain $\psi(3686) \to \gamma \chi_{cJ} \to \gamma \gamma' (X) J/\psi$. This paper aims to fill that gap using high-statistics data from the BESIII detector.

2. Methodology

Data Sample and Detector

• Dataset: The analysis utilizes $(2712.4 \pm 14.3) \times 10^6$ $\psi(3686)$ events collected by the BESIII detector at the BEPCII collider.
• Process: The search focuses on the radiative transition $\psi(3686) \to \gamma \chi_{cJ}$ (where $J=0, 1, 2$), followed by the decay $\chi_{cJ} \to \gamma' (X) J/\psi$, where the hypothetical boson decays into an electron-positron pair ($e^+e^-$).
• Final State: The reconstructed final state is $\gamma e^+ e^- \ell^+ \ell^-$ (where $\ell$ is an electron or muon from the $J/\psi$ decay).

Event Selection and Background Suppression

• Track Selection: Events must contain two positive and two negative charged tracks and at least one photon.
• Particle Identification (PID): Strict likelihood requirements are applied to identify electrons/positrons and muons.
• Kinematic Constraints:
  • The invariant mass of the high-momentum lepton pair is constrained to the $J/\psi$ mass window ($|M_{\ell^+\ell^-} - M_{J/\psi}| < 0.05 \text{ GeV}/c^2$).
  • The invariant mass of the full system is constrained to the $\psi(3686)$ mass window.
  • Specific photon energy ($E_\gamma$) and total invariant mass ($M_{e^+e^-\ell^+\ell^-}$) windows are applied to distinguish between $\chi_{c0}$, $\chi_{c1}$, and $\chi_{c2}$ candidates.
• Background Rejection:
  • Photon Conversion Veto: A major background arises from $\psi(3686) \to \gamma \chi_{cJ} \to \gamma (\gamma \to e^+e^-) J/\psi$. A conversion vertex veto is applied, rejecting events where the $e^+e^-$ pair originates from the beam pipe or MDC inner wall (projected distance $R_{xy} < 2 \text{ cm}$).
  • Dalitz Decay Veto: Invariant mass cuts exclude backgrounds from $\eta/\pi^0 \to \gamma e^+e^-$.
  • Continuum Background: Estimated using data taken at off-resonance energies ($\sqrt{s} = 3.773$ and $3.650 \text{ GeV}$) and found to be negligible.

Analysis Strategy

• Signal Extraction: Unbinned extended maximum likelihood fits are performed on the invariant mass distribution of the low-momentum $e^+e^-$ pair ($M_{e^+e^-}$).
• Systematic Uncertainties: A comprehensive evaluation includes tracking efficiency, PID, photon detection, branching fractions, signal modeling, and fit procedures. Total multiplicative systematic uncertainties range from $8.1\%$ to $8.2\%$.
• Limit Setting: Since no significant signal is observed, upper limits (UL) on the branching fractions and coupling strengths are set using a Bayesian approach at the 90% confidence level (C.L.).

3. Key Contributions

• First Search in $\chi_{cJ}$ Transitions: This is the first direct search for the $X_{17}$ boson and dark photons specifically in the $\chi_{cJ} \to \gamma' (X) J/\psi$ decay channel.
• Protophobic Boson Constraints: It provides the first direct constraint on the coupling of the hypothetical $X$ boson to charm quarks ($\epsilon_c$).
• Dark Photon Constraints: It sets new, competitive limits on the kinetic mixing parameter $\epsilon$ for dark photon masses in the range of $5 \text{ MeV}/c^2$ to $300 \text{ MeV}/c^2$, improving upon previous BESIII results for masses below $0.1 \text{ GeV}/c^2$.

4. Results

• Observation: No significant signal excess was observed in the $M_{e^+e^-}$ spectra for any of the three $\chi_{cJ}$ channels ($J=0, 1, 2$). The statistical significance of any potential signal was less than $2\sigma$ in all cases.
• Branching Fraction Limits: Upper limits on the product branching fraction $\mathcal{B}(\chi_{cJ} \to \gamma' (X) J/\psi) \times \mathcal{B}(\gamma' (X) \to e^+e^-)$ were set at 90% C.L.:
  • $\chi_{c0}$: $1.3 \times 10^{-5}$
  • $\chi_{c1}$: $7.2 \times 10^{-5}$
  • $\chi_{c2}$: $4.3 \times 10^{-5}$
• Coupling Strength Limits:
  • Charm Quark Coupling ($\epsilon_c$): For the specific mass of $17 \text{ MeV}/c^2$ (assuming $\mathcal{B}(X \to e^+e^-) = 100\%$), the upper limit is $|\epsilon_c| < 1.2 \times 10^{-2}$.
  • Dark Photon Mixing ($\epsilon$): The upper limits on the mixing strength $\epsilon$ vary with mass, falling within the range $(2.5 - 17.5) \times 10^{-3}$ for masses between $5$ and $300 \text{ MeV}/c^2$.

5. Significance

• Exclusion of Parameter Space: The results significantly constrain the parameter space for the protophobic gauge boson theory, specifically ruling out large couplings to charm quarks for the $X_{17}$ hypothesis.
• Complementarity: By probing the charm quark sector, this analysis complements searches in light quark systems (proton/neutron) and lepton-only experiments, providing a more complete picture of potential new physics.
• Future Prospects: The paper notes that while sensitivity at very low masses ($\sim 5 \text{ MeV}/c^2$) is currently limited by background, future data samples from the Super $\tau$-Charm Factory are expected to provide even more stringent constraints on these couplings.

In summary, this work represents a rigorous null result that tightens the constraints on light gauge bosons and dark photons, particularly regarding their interactions with heavy quarks, and serves as a critical benchmark for future high-luminosity experiments.