Mini-review of charmonium weak decays at BESIII

This mini-review highlights the BESIII experiment's critical role in probing non-perturbative QCD dynamics and searching for new physics by presenting the latest stringent upper limits on rare charmonium weak decays, including flavor-changing neutral currents, derived from its unprecedented dataset of over $10^{10}$ $J/\psi$ and $2.7\times10^{9}$ $\psi(2S)$ events.

The Gist

Imagine the universe as a giant, bustling city. Most of the time, the citizens (particles) follow the strict traffic laws of the "Standard Model." But sometimes, physicists suspect there are secret underground tunnels or hidden shortcuts that these laws don't account for. These are called "New Physics."

To find these secrets, scientists need to look at the most obedient, rule-following citizens and see if they ever break the rules. Enter Charmonium.

The Characters: The "Perfectly Obedient" Couple

Think of Charmonium (specifically the particles $J/\psi$ and $\psi(2S)$) as a very wealthy, perfectly matched couple made of a "charm" quark and an "anti-charm" quark holding hands.

• The Usual Routine: Usually, this couple is so stable that they only break up in very specific, predictable ways (strong or electromagnetic forces). They are like a couple that only ever breaks up because of a scheduled appointment.
• The Rare Event: However, physics says there is a tiny, almost impossible chance that one of them could suddenly change into a different person (a "weak decay") by swapping a ticket with a messenger particle called a $W$ boson.
• The Problem: This "weak breakup" is so incredibly rare that it's like trying to find a single specific grain of sand on all the beaches on Earth. If you look at a normal amount of sand, you'll never find it.

The Detective: BESIII

This is where the BESIII experiment comes in. Imagine BESIII as a massive, high-tech sand-sifting machine built by the Sun Yat-sen University team and their collaborators.

• The Dataset: Instead of looking at a handful of sand, BESIII has sifted through 10 billion grains of sand (specifically, 10 billion $J/\psi$ events and 2.7 billion $\psi(2S)$ events).
• The Goal: They are looking for that one grain of sand that shouldn't be there—a "weak decay" that breaks the standard rules.

The Three Types of "Breakups" They Are Hunting

The paper reviews three specific ways this couple might break up, which the scientists are hunting for:

1. The "Semi-Leptonic" Breakup (The Partial Exit):
   Imagine the couple breaks up, and one partner leaves with a new partner (a lepton like an electron or muon) and a ghost (a neutrino).

   • The Hunt: BESIII looked for these specific exits. They didn't find any.
   • The Result: They set a new "world record" for how rare this event must be. They essentially said, "If this happens, it happens less than 1 time in 10 million tries." This is the tightest leash we've ever put on this possibility.

2. The "Hadronic" Breakup (The Full Party):
   Here, the couple breaks up and turns into a whole new group of particles (like a $D$ meson and a pion).

   • The Challenge: This is like trying to find a specific conversation in a crowded, noisy stadium. The "noise" (background particles from normal decays) is overwhelming.
   • The Hunt: BESIII used clever tricks (like tagging a specific "ticket" from the decay) to filter out the noise. Again, no signal found, but they set the strictest limits yet on how often this could happen.

3. The "Forbidden" Breakup (FCNC - Flavor Changing Neutral Current):
   This is the "Holy Grail." In the Standard Model, this specific type of breakup is forbidden at the basic level. It's like a law that says "You cannot change your color."

   • The Significance: If BESIII finds even one of these, it's not just a rare event; it's proof that the "Standard Model" traffic laws are wrong and there is a secret tunnel (New Physics) like Supersymmetry or extra dimensions.
   • The Result: They looked for these forbidden breaks (like $J/\psi$ turning into a $D$ meson and two muons). They found nothing. This is great news for "New Physics" hunters because it means the secret tunnels are either non-existent or much smaller than we thought.

The Verdict: "Not Found, But We Know Where to Look"

So, what did this paper conclude?

• The Search: The BESIII team used their massive dataset to look for these incredibly rare events.
• The Outcome: They didn't find any "weak decays" yet. The universe is still being very obedient.
• The Achievement: However, they didn't just fail; they succeeded in ruling out a huge range of possibilities. They tightened the net so much that any "New Physics" trying to hide in these decays has nowhere left to hide.
• The Future: The paper ends with a promise. They are currently analyzing even more data (using the full 10 billion events). In the future, with even bigger machines (like the proposed Super Tau-Charm Facility), they might finally catch a glimpse of these rare events.

In a nutshell: This paper is a report card from the world's best particle detectives. They haven't caught the criminal yet, but they have narrowed down the suspect's location to a tiny, tiny room, and they are about to start searching that room with a microscope.

Technical Summary

1. Problem Statement

Charmonium states (specifically $J/\psi$ and $\psi(2S)$) are bound states of a charm quark and its anti-quark ($c\bar{c}$). Due to their masses lying below the open-charm threshold, they predominantly decay via Okubo-Zweig-Iizuka (OZI) suppressed strong or electromagnetic processes.

• The Challenge: Weak decays of charmonium are theoretically allowed but extremely rare (Branching Fractions, BFs, predicted to be $\sim 10^{-9}$ to $10^{-13}$).
• Scientific Motivation:
  • Standard Model (SM) Tests: These decays probe non-perturbative Quantum Chromodynamics (QCD) dynamics, specifically transition form factors and wave functions of the $c\bar{c}$ bound state.
  • New Physics (NP) Search: The extreme suppression of these decays in the SM makes them highly sensitive probes for Beyond Standard Model (BSM) physics, particularly in Flavor-Changing Neutral Current (FCNC) channels where tree-level contributions are forbidden by the GIM mechanism.
  • Experimental Gap: Prior to the BESIII dataset, the statistical power required to observe or set meaningful limits on these rare processes was lacking.

2. Methodology

The paper reviews theoretical frameworks and experimental results from the BESIII experiment at the BEPCII collider.

• Experimental Setup:

  • Dataset: BESIII utilizes the world's largest on-threshold datasets: $(10087 \pm 44) \times 10^6$ $J/\psi$ events and $(2712.4 \pm 14.3) \times 10^6$ $\psi(2S)$ events.
  • Strategy: Searches are conducted for semi-leptonic, non-leptonic, and FCNC decay modes. For non-leptonic hadronic decays (which suffer from overwhelming QCD backgrounds), the analysis often employs "tagging" via semi-leptonic decays of the light meson in the final state to reduce background.
  • Statistical Standard: All reported upper limits are set at the 90% Confidence Level (C.L.).

• Theoretical Frameworks:

  • The review aggregates predictions from various QCD models, including:
    • Heavy Quark Spin Symmetry (HQSS)
    • QCD Sum Rules (QCDSR)
    • Covariant Light-Front Quark Model (CLFQM)
    • Covariant Constituent Quark Model (CCQM)
    • Bethe-Salpeter (BS) method
    • Lattice QCD (LQCD)
  • Key Mechanisms:
    • Semi-leptonic: Tree-level $c \to s/d + W^+$ transitions.
    • Non-leptonic: $c \to s/d + u + \bar{d}/\bar{s}$ transitions involving light meson formation.
    • FCNC: Loop-level processes (e.g., $J/\psi \to \bar{D}^0 \ell^+ \ell^-$) forbidden at tree level.

3. Key Contributions

The paper synthesizes the current state of the field by:

1. Cataloging Theoretical Predictions: Providing a comprehensive table of predicted Branching Fractions across different models for semi-leptonic, non-leptonic, and FCNC channels.
2. Summarizing Experimental Limits: Compiling the most stringent upper limits established by BESIII to date, comparing them directly against SM predictions.
3. Highlighting SU(3) Symmetry Breaking: Discussing how the ratio of Cabibbo-favored to Cabibbo-suppressed decays can serve as a clean probe of SU(3) flavor symmetry breaking, as many theoretical uncertainties cancel in the ratio.
4. Assessing Lepton Flavor Universality (LFU): Reviewing the ratios of decays involving muons vs. electrons as potential probes for LFU violation.

4. Key Results

The BESIII collaboration has established world-leading upper limits for various channels, though no significant signals have been observed yet.

A. Semi-Leptonic Decays ($J/\psi \to D^{(*)-}_{(s)} \ell^+ \nu_\ell$)

• Cabibbo-Suppressed ($|V_{cd}|$):
  • $B(J/\psi \to D^- e^+ \nu_e) < 7.1 \times 10^{-8}$
  • $B(J/\psi \to D^- \mu^+ \nu_\mu) < 5.6 \times 10^{-7}$
• Cabibbo-Favored ($|V_{cs}|$):
  • $B(J/\psi \to D^-_s e^+ \nu_e) < 1.0 \times 10^{-7}$
  • $B(J/\psi \to D^{*-}_s e^+ \nu_e) < 1.8 \times 10^{-6}$ (based on partial dataset)
• Note: Current limits are still roughly 1–2 orders of magnitude above the highest theoretical predictions ($\sim 10^{-10}$).

B. Non-Leptonic Hadronic Decays ($J/\psi \to D^{(*)} M$)

• Cabibbo-Favored:
  • $B(J/\psi \to D^-_s \rho^+) < 8.0 \times 10^{-7}$
  • $B(J/\psi \to D^-_s \pi^+) < 4.1 \times 10^{-7}$
• Cabibbo-Suppressed:
  • $B(J/\psi \to D^- \pi^+) < 7.0 \times 10^{-8}$
  • Limits set for channels involving $\bar{D}^0, \eta, \rho^0, K^{*0}$ range from $10^{-7}$ to $10^{-8}$.

C. FCNC Decays ($J/\psi \to \bar{D}^0 \ell^+ \ell^-$)

• These are the most sensitive to New Physics.
  • $B(J/\psi \to \bar{D}^0 \mu^+ \mu^-) < 1.1 \times 10^{-7}$
  • $B(J/\psi \to \bar{D}^0 e^+ e^-) < 8.5 \times 10^{-8}$ (based on $1.3 \times 10^9$ events; full dataset analysis ongoing)
  • $B(J/\psi \to \gamma D^0) < 9.1 \times 10^{-8}$
• Significance: These limits are orders of magnitude above SM predictions ($\sim 10^{-13}$), but they severely constrain BSM parameter spaces (e.g., TopColor, SUSY).

D. $\psi(2S)$ Weak Decays

• $B(\psi(2S) \to D^0 e^+ e^-) < 1.4 \times 10^{-7}$
• $B(\psi(2S) \to \Lambda^+_c \bar{\Sigma}^-) < 1.4 \times 10^{-5}$ (Weak baryonic decay)

5. Significance and Outlook

• Current Status: While BESIII has set the most stringent limits globally, the current experimental upper limits are still generally above the theoretical predictions for SM weak decays. No SM signal has been observed yet.
• Impact on Theory: The results constrain non-perturbative QCD models (form factors) and rule out specific regions of parameter space for BSM theories that predict enhanced FCNCs.
• Future Prospects:
  • Full Dataset Analysis: Updates using the full $10^{10}$ $J/\psi$ and $2.7 \times 10^9$ $\psi(2S)$ datasets are in progress, which will improve sensitivity.
  • Next Generation: The paper highlights the potential of the proposed Super Tau-Charm Facility (STCF). With higher luminosity, future experiments could push sensitivity down to $10^{-9}$ or lower, potentially reaching the level where the first observation of charmonium weak decays becomes feasible.
  • Synergy: The field relies on the continued development of Lattice QCD and other non-perturbative methods to provide precise theoretical predictions for direct comparison with upcoming experimental data.