Testing the hypothesis of vector X17 boson by D meson, Charmonium, and $\phi$ meson decays

This paper tests the X17 boson hypothesis by fitting coupling parameters to various meson decay data, finding that the resulting large charm quark coupling and the required up quark coupling are in serious tension with existing ATOMKI experimental results.

The Gist

Imagine the Standard Model of physics as a massive, incredibly detailed instruction manual for how the universe works. For decades, this manual has been perfect, explaining almost everything we see. But recently, a group of scientists (the ATOMKI team) found a few pages that seem to have a typo. They saw tiny atomic nuclei (like Beryllium and Helium) behaving strangely when they released energy. Instead of just shooting out a flash of light (a photon), they seemed to be spitting out a mysterious, invisible particle that immediately turned into a pair of electrons.

They called this ghost particle X17. It's named "17" because it weighs about 17 times more than an electron (roughly 17 MeV). If X17 is real, it's not just a typo; it's a whole new chapter in the manual, proving there is "New Physics" beyond what we currently know.

The Detective Story: The "Heavy" Test

This paper is like a group of detectives trying to verify if X17 is real by looking at a different crime scene. Instead of looking at tiny atomic nuclei, they decided to look at heavy mesons (particles made of heavy quarks, like Charm and Strange quarks).

Think of the universe's particles like a family.

• Light family: Up and Down quarks (found in the atoms of your body). The ATOMKI experiments saw X17 interacting with this family.
• Heavy family: Charm and Strange quarks. The question is: Does X17 hang out with them too?

If X17 is a universal "social butterfly" (a particle that treats all generations of quarks the same), it should show up in the heavy family's decays just as it did in the light family's.

The Investigation Process

The authors of this paper acted as forensic accountants. They looked at the "receipts" (experimental data) from four different heavy particle decay events:

1. D-mesons (Charm quarks).
2. Charmonium (Charm-anticharm pairs).
3. Phi-mesons (Strange-antistrange pairs).

They asked: "If X17 exists and interacts with these heavy particles, would the math match the data we already have?"

The Plot Twist: The "Family Secret"

Here is where it gets interesting. The detectives found a major contradiction.

1. The "Light" Clue: Previous experiments on light nuclei suggested X17 interacts with Up quarks with a specific, tiny strength (let's call it a "handshake strength" of about 0.0005).
2. The "Heavy" Clue: When they tried to apply that same tiny handshake strength to the heavy D-mesons, the math didn't add up. The heavy particles were decaying way too fast into electron pairs. To make the math work for the heavy particles, the "handshake strength" for the Charm quark had to be much, much stronger (about 10 to 15 times stronger) than what the light nuclei suggested.

The Analogy: The Universal Remote

Imagine X17 is a universal remote control for the universe.

• The ATOMKI experiment told us: "This remote works on the TV (Up quarks) with a very weak signal."
• The D-meson experiment told us: "Wait, this same remote is blasting the Stereo (Charm quarks) at maximum volume!"

If the remote is truly "universal" (meaning it treats all quarks the same), it shouldn't be whispering to the TV and screaming at the stereo simultaneously. The authors found that to make the data fit, the remote must have different volume settings for different rooms.

The Conclusion: A Tension in the Theory

The paper concludes with a big "Tension."

• If X17 exists, it seems to treat the Charm quark (heavy) very differently than the Up quark (light).
• The authors calculated that the "strength" of the interaction for the Charm quark needs to be huge to explain the heavy particle data, but this huge strength clashes with the tiny strength seen in the light particle data.

What's Next?

The paper suggests two possibilities:

1. X17 doesn't exist: The strange signals we saw in the light nuclei might be a fluke or a misunderstanding of the data.
2. X17 exists, but it's weird: It might not be a "universal" particle. It might have a specific preference for heavy quarks, breaking the rule that nature treats all generations of particles equally.

The authors also predict what we should see in a specific, unmeasured experiment (the decay of a $D^+$ meson). If future experiments find that the $D^+$ decay rate is high, it confirms that X17 is real but "picky" about which particles it talks to. If the rate is low, it might mean X17 is just a ghost story.

In a Nutshell:
The paper is a reality check. It says, "Hey, if this new particle X17 is real, it's acting very strangely with heavy particles compared to light ones. We need to check our math, check our assumptions, and maybe wait for new data to see if this particle is a universal traveler or a heavy-quark specialist."

Technical Summary

1. Problem Statement

The paper addresses the hypothesis of a new vector boson, X17 (mass $\approx$ 17 MeV), proposed to explain anomalous internal pair creation in nuclear transitions of excited $^8$Be, $^4$He, and $^{12}$C states observed by the ATOMKI collaboration.

• The Conflict: Previous studies assumed generation universality for the X17 couplings to quarks (i.e., $\epsilon_u = \epsilon_c$ and $\epsilon_s = \epsilon_d$). Under these assumptions, using updated ATOMKI data which suggests smaller coupling strengths ($|\epsilon_u| \sim 10^{-4}$), theoretical predictions for heavy meson decays (specifically $D^*_s \to D_s e^+e^-$) were inconsistent with experimental data.
• The Specific Anomaly: Recent BESIII measurements of the ratio $R_{D^*_0} \equiv \Gamma(D^*_0 \to D^0 e^+e^-)/\Gamma(D^*_0 \to D^0 \gamma)$ show a significant excess over Standard Model (SM) predictions. If attributed to X17, this requires a large coupling to the up-quark ($\epsilon_u$), which contradicts the small values derived from nuclear anomalies.
• Goal: To rigorously test the X17 hypothesis in heavy-flavor meson decays ($D^*$, $D^*_s$, $\psi(2S)$, $\phi$) by relaxing the assumption of generation universality and treating couplings $\epsilon_u, \epsilon_c, \epsilon_s$ as independent parameters.

2. Methodology

The authors employ a phenomenological approach combining effective field theory and the Vector Meson Dominance (VMD) model.

• Theoretical Framework:

  • The interaction Lagrangian is defined as $\mathcal{L}_{X(Q,q)} = e\epsilon_Q X_\mu (\bar{Q}\gamma^\mu Q) + e\epsilon_q X_\mu (\bar{q}\gamma^\mu q)$, where $Q$ represents heavy quarks ($c$) and $q$ represents light quarks ($u, d, s$).
  • The decay rates for $H^* \to H e^+e^-$ are calculated as the sum of SM photon-mediated contributions ($R^\gamma_{H^*}$) and X17-mediated contributions ($R^X_{H^*}$).
  • Form Factors: The transition form factors are calculated using the VMD model. The authors explicitly correct a calculation error in a previous study (Ref. [30]) regarding the effective light-quark mass parameter $m_q(q^2)$, which significantly alters the predicted branching ratios.
  • Narrow Width Approximation: Used for the X17 propagator to simplify the integration over the dilepton invariant mass squared ($q^2$).

• Data Sets Used for Fitting:

  • $R_{D^*_s} = \Gamma(D^*_s \to D_s e^+e^-)/\Gamma(D^*_s \to D_s \gamma)$ (CLEO data).
  • $R_{D^*_0} = \Gamma(D^*_0 \to D^0 e^+e^-)/\Gamma(D^*_0 \to D^0 \gamma)$ (BESIII data).
  • $R_{\psi(2S)} = \Gamma(\psi(2S) \to \eta_c e^+e^-)/\Gamma(\psi(2S) \to \eta_c \gamma)$ (BESIII data).
  • $R_{\phi} = \Gamma(\phi \to \eta e^+e^-)/\Gamma(\phi \to \eta \gamma)$ (SND, CMD-2, KLOE-2 data).

• Fitting Strategy:

  • The mass of X17 is fixed at $m_X = 16.85$ MeV (best-fit from ATOMKI).
  • Two fitting scenarios are performed:
    1. Scenario A: Fits $\epsilon_c$ and $\epsilon_s$ using $D^*_s$, $\psi(2S)$, and $\phi$ data (excluding $D^*_0$).
    2. Scenario B: Includes $D^*_0$ data to fit $\epsilon_u, \epsilon_c, \epsilon_s$ simultaneously.

3. Key Contributions

1. Correction of Previous Calculations: The authors identify and correct a factor-of-2 error in Ref. [30] regarding the light-quark mass parameter in the VMD calculation. This correction changes the theoretical prediction for $R_{D^*_s}$, showing that the older, larger coupling values ($\epsilon_u \approx 3.7 \times 10^{-3}$) are actually in tension with CLEO data, while the updated ATOMKI values are consistent.
2. Relaxation of Generation Universality: The paper demonstrates that the assumption $\epsilon_c = \epsilon_u$ and $\epsilon_s = \epsilon_d$ is incompatible with the simultaneous description of $D^*_s$ and $D^*_0$ data. They propose treating these couplings as independent.
3. Prediction for Unmeasured Decay: The authors provide a detailed prediction for the unmeasured ratio $R_{D^*_+} = \Gamma(D^*_+ \to D^+ e^+e^-)/\Gamma(D^*_+ \to D^+ \gamma)$ based on their fitted parameters.

4. Results

• Coupling Constants:
  • Without $D^*_0$ data: The best-fit values are $|\epsilon_c| \approx 7.6 \times 10^{-3}$ and $|\epsilon_s| \approx 2.4 \times 10^{-3}$. These values are significantly larger than the ATOMKI-derived $\epsilon_u$ ($\sim 10^{-4}$), suggesting non-universality.
  • With $D^*_0$ data: To explain the large excess in $R_{D^*_0}$, the fit requires a massive up-quark coupling: $|\epsilon_u| \approx (6.1 - 6.7) \times 10^{-2}$.
• Tension with ATOMKI: The fitted $|\epsilon_u|$ from heavy meson decays is two orders of magnitude larger than the value derived from nuclear anomalies ($|\epsilon_u| \sim 0.5-0.9 \times 10^{-3}$). This indicates a "serious tension" if the X17 boson is the sole explanation for both phenomena.
• Spectral Prediction: The paper predicts the differential decay rate $dR_{D^*_0}/dq^2$. If the excess is due to X17, a distinct peak should appear at $q^2 = m_X^2$ (in the second kinematic bin of the BESIII data). Current statistics are insufficient to confirm this peak.
• $D^*_+$ Prediction: The predicted $R_{D^*_+}$ ranges widely depending on the interference between $\epsilon_c$ and $\epsilon_d$. If generation universality holds, the prediction is close to the SM value; if non-universal couplings (as fitted) are used, the central value and uncertainty increase significantly.

5. Significance

• Challenge to the X17 Hypothesis: The study highlights a critical inconsistency. If the X17 boson explains the nuclear anomalies, its coupling to up-quarks ($\epsilon_u$) must be small. However, explaining the $D^*_0$ anomaly requires a huge $\epsilon_u$. This suggests either:
  1. The $D^*_0$ excess is due to a different new physics mechanism or a SM background not yet accounted for.
  2. The X17 boson has highly non-universal couplings to quark generations ($\epsilon_c \gg \epsilon_u$), which would require a specific model of flavor violation.
• Methodological Rigor: By correcting the VMD calculation errors and utilizing a comprehensive dataset including charmonium and $\phi$ decays, the paper sets a new standard for testing light vector bosons in heavy flavor physics.
• Future Directions: The paper calls for updated measurements of the $D^*_0 \to D^0 e^+e^-$ spectrum to verify the X17 peak and a measurement of $D^*_+ \to D^+ e^+e^-$ to further constrain the coupling parameters. The results suggest that if the $D^*_0$ anomaly is real, the X17 hypothesis in its current form (with generation universality) is likely ruled out.