Charm Rare Decays at BESIII

• Charm rare decays are highly suppressed processes in the Standard Model that provide sensitive probes for new physics through FCNC, LFV, and LNV transitions.
• BESIII utilizes advanced detector capabilities, large clean data samples, and methods like double-tagging to rigorously suppress background and achieve world-leading sensitivity.
• Recent measurements have set stringent upper limits on branching fractions, constraining both SM predictions and various new physics scenarios in the up-quark sector.

Charm rare decays at BESIII encompass studies of processes in which charm hadrons—primarily $D^0$, $D^+$, $D_s^+$ mesons and charm baryons—undergo transitions forbidden or highly suppressed in the Standard Model (SM), such as flavor-changing neutral currents (FCNC), lepton-number-violating (LNV), lepton-flavor-violating (LFV), baryon-number-violating (BNV), and weak annihilation processes. These decays offer sensitive probes for physics beyond the SM (BSM), as enhancements of their branching fractions by several orders of magnitude are predicted in numerous New Physics (NP) scenarios. The large datasets accumulated by the BESIII experiment at BEPCII, alongside low-background threshold running and precise detector capabilities, have enabled world-leading sensitivity for a wide range of rare and forbidden charm decay searches.

1. Theoretical Framework and Motivation

Rare charm decays are governed in the SM by GIM-suppressed loop diagrams and, in some cases, further suppressed by CKM factors and helicity. The effective Hamiltonian for $|\Delta C|=1$ FCNC transitions is: $$\mathcal{H}_{\rm eff} = -\frac{4 G_F}{\sqrt{2}} \sum_i C_i(\mu) O_i(\mu)$$ where the Wilson coefficients $C_i$ encode short-distance (SD) dynamics, which are highly suppressed (e.g., $D^0 \rightarrow \gamma\gamma$ SD: $\mathcal{B}_{\rm SD} \sim 3\times10^{-11}$). Long-distance (LD) effects involving intermediate resonances (e.g., $D^0 \rightarrow V V' \rightarrow \gamma\gamma$) can raise the expected branching fractions to $\mathcal{B}_{\rm LD} \sim (1-3)\times10^{-8}$ (Li, 2012). New physics—supersymmetry (SUSY), extra $D^+$0, leptoquarks, two-Higgs doublet, RPV SUSY models, and others—can enhance FCNC $D^+$1 transitions by up to two orders of magnitude, such that $D^+$2 (Li, 2012). Observation of branching fractions above the SM LD regime is unambiguous evidence for NP in the up-quark sector (Zhan, 11 Nov 2025, Wang, 2018).

2. BESIII Data Samples and Experimental Environment

BESIII operates at BEPCII ($D^+$3 collider, $D^+$4), optimized for $D^+$5-charm physics within $D^+$6 GeV (Li et al., 2024, Li, 2011). Its principal datasets for rare charm decays include:

Dataset	Luminosity/Events	Typical Use Cases
$D^+$7	$D^+$8	$D^+$9, LFV
$D_s^+$0	$D_s^+$1	Charmonium rare decays
$D_s^+$2	$D_s^+$3 at 3.773 GeV; $D_s^+$4 accumulated	Open-charm threshold, double-tag studies
$D_s^+$5	$D_s^+$6 at 4.128–4.226 GeV	$D_s^+$7 rare decays

The detector features a helium-based multilayer drift chamber, plastic-scintillator TOF, CsI(Tl) electromagnetic calorimeter (EMC, energy resolution $D_s^+$8 at 1 GeV), a 1 T solenoid, and muon system, providing high reconstruction and particle-ID efficiency crucial for rare-decay searches (Zhan, 11 Nov 2025, Li et al., 2024).

3. Analysis Methodologies: Tagging, Signal Extraction, and Background Control

At threshold energies (e.g., $D_s^+$9), BESIII extensively uses the double-tag technique: reconstructing one $|\Delta C|=1$0 meson in a hadronic mode ("tag") guarantees the presence of its partner in the recoil, allowing absolute branching fraction determination and powerful suppression of combinatorial and continuum backgrounds (Li, 2011). For inclusive $|\Delta C|=1$1 and $|\Delta C|=1$2 analyses, missing-mass squared ($|\Delta C|=1$3) is used to infer undetected (neutrino) final states. For photon and multi-lepton channels, event selection relies on tight PID (MDC $|\Delta C|=1$4, TOF, EMC), stringent shower-isolation cuts, and kinematic constraints ($|\Delta C|=1$5, $|\Delta C|=1$6).

Signal extraction typically employs unbinned maximum-likelihood fits to invariant-mass, $|\Delta C|=1$7, or energy-difference $|\Delta C|=1$8 distributions, with signal PDF shapes derived from full Monte Carlo and backgrounds coupled from empirical models or MC. Upper limits at 90% confidence are determined by Bayesian procedures (uniform prior, systematic uncertainties incorporated via parameter scaling or marginalization) or the Feldman–Cousins approach (Li, 2012, Zhan, 11 Nov 2025, Li et al., 2024).

Dominant systematic uncertainties are assigned for tracking, PID, photon/$|\Delta C|=1$9 reconstruction, signal Monte Carlo modeling, fitting, and normalization, with quadratic sum typically $$\mathcal{H}_{\rm eff} = -\frac{4 G_F}{\sqrt{2}} \sum_i C_i(\mu) O_i(\mu)$$0–$$\mathcal{H}_{\rm eff} = -\frac{4 G_F}{\sqrt{2}} \sum_i C_i(\mu) O_i(\mu)$$1 (Zhan, 11 Nov 2025, Li et al., 2024).

4. Key Measurements and Limits on Rare and Forbidden Modes

Recent BESIII results have covered a comprehensive landscape of rare and forbidden charm processes:

Flavor-Changing Neutral Currents:

• $$\mathcal{H}_{\rm eff} = -\frac{4 G_F}{\sqrt{2}} \sum_i C_i(\mu) O_i(\mu)$$2: $$\mathcal{H}_{\rm eff} = -\frac{4 G_F}{\sqrt{2}} \sum_i C_i(\mu) O_i(\mu)$$3 (90% CL), improving CLEO-c and approaching BaBar's sensitivity (Li, 2012).
• $$\mathcal{H}_{\rm eff} = -\frac{4 G_F}{\sqrt{2}} \sum_i C_i(\mu) O_i(\mu)$$4: $$\mathcal{H}_{\rm eff} = -\frac{4 G_F}{\sqrt{2}} \sum_i C_i(\mu) O_i(\mu)$$5
• $$\mathcal{H}_{\rm eff} = -\frac{4 G_F}{\sqrt{2}} \sum_i C_i(\mu) O_i(\mu)$$6: $$\mathcal{H}_{\rm eff} = -\frac{4 G_F}{\sqrt{2}} \sum_i C_i(\mu) O_i(\mu)$$7
• $$\mathcal{H}_{\rm eff} = -\frac{4 G_F}{\sqrt{2}} \sum_i C_i(\mu) O_i(\mu)$$8: $$\mathcal{H}_{\rm eff} = -\frac{4 G_F}{\sqrt{2}} \sum_i C_i(\mu) O_i(\mu)$$9

Lepton-Number and Lepton-Flavor Violation, and Baryon/Other Exotic Channels:

• $C_i$0: $C_i$1 (Li et al., 2024)
• $C_i$2 (LNV via Majorana $C_i$3): $C_i$4
• $C_i$5 (massless dark photon): $C_i$6

Selected Summary Table

Channel	Dataset	Branching Fraction UL (90% CL)
$C_i$7	$C_i$8 $C_i$9	$D^0 \rightarrow \gamma\gamma$0
$D^0 \rightarrow \gamma\gamma$1	$D^0 \rightarrow \gamma\gamma$2GeV	$D^0 \rightarrow \gamma\gamma$3
$D^0 \rightarrow \gamma\gamma$4	$D^0 \rightarrow \gamma\gamma$5	$D^0 \rightarrow \gamma\gamma$6
$D^0 \rightarrow \gamma\gamma$7	$D^0 \rightarrow \gamma\gamma$8 $D^0 \rightarrow \gamma\gamma$9	$\mathcal{B}_{\rm SD} \sim 3\times10^{-11}$0

No statistically significant excesses above background expectations have been found in any forbidden or FCNC charm channel (Zhan, 11 Nov 2025, Li et al., 2024, Wang, 2018).

5. Comparison with Standard-Model and BSM Predictions

SM SD branching fractions for $\mathcal{B}_{\rm SD} \sim 3\times10^{-11}$1 FCNC processes such as $\mathcal{B}_{\rm SD} \sim 3\times10^{-11}$2, $\mathcal{B}_{\rm SD} \sim 3\times10^{-11}$3, and $\mathcal{B}_{\rm SD} \sim 3\times10^{-11}$4 are in the $\mathcal{B}_{\rm SD} \sim 3\times10^{-11}$5–$\mathcal{B}_{\rm SD} \sim 3\times10^{-11}$6 regime (Li, 2012, Zhan, 11 Nov 2025). Long-distance resonance effects can raise some modes to $\mathcal{B}_{\rm SD} \sim 3\times10^{-11}$7. Existing BESIII upper limits are $\mathcal{B}_{\rm SD} \sim 3\times10^{-11}$81–2 orders of magnitude above LD theory expectations for key modes, leaving room for NP enhancements but with rapidly shrinking parameter space (Zhan, 11 Nov 2025, Wang, 2018, Li et al., 2012).

Limits on LNV, LFV, and dark sector processes (e.g., massless dark photon, Majorana neutrinos) provide strong constraints on BSM coupling scales: e.g., $\mathcal{B}_{\rm SD} \sim 3\times10^{-11}$9 enforces $D^0 \rightarrow V V' \rightarrow \gamma\gamma$0 few TeV for $D^0 \rightarrow V V' \rightarrow \gamma\gamma$1 couplings (Li et al., 2024). For CLFV operators, $D^0 \rightarrow V V' \rightarrow \gamma\gamma$2 searches push new scale constraints to $D^0 \rightarrow V V' \rightarrow \gamma\gamma$3 TeV (Li et al., 2024).

The following regimes emerge:

• SM SD: $D^0 \rightarrow V V' \rightarrow \gamma\gamma$4 $D^0 \rightarrow V V' \rightarrow \gamma\gamma$5
• SM LD: up to $D^0 \rightarrow V V' \rightarrow \gamma\gamma$6 ($D^0 \rightarrow V V' \rightarrow \gamma\gamma$7)
• Current BESIII ULs: $D^0 \rightarrow V V' \rightarrow \gamma\gamma$8–$D^0 \rightarrow V V' \rightarrow \gamma\gamma$9 (mix of FCNC, LNV, LFV modes)
• NP scenarios reachable with imminent increases in luminosity: down to $\mathcal{B}_{\rm LD} \sim (1-3)\times10^{-8}$0 (Zhan, 11 Nov 2025, Li et al., 2024)

NP models with predicted rates $\mathcal{B}_{\rm LD} \sim (1-3)\times10^{-8}$1 are increasingly constrained; models predicting below $\mathcal{B}_{\rm LD} \sim (1-3)\times10^{-8}$2 remain viable but may be testable with BESIII upgrades.

6. Future Prospects, Technical Improvements, and Programmatic Outlook

BESIII plans to extend its rare decay program with $\mathcal{B}_{\rm LD} \sim (1-3)\times10^{-8}$3 at $\mathcal{B}_{\rm LD} \sim (1-3)\times10^{-8}$4 GeV and additional high-luminosity data near $\mathcal{B}_{\rm LD} \sim (1-3)\times10^{-8}$5 GeV (Li et al., 2024). Key avenues for improvement include

• Larger data samples: Projected sensitivities to $\mathcal{B}_{\rm LD} \sim (1-3)\times10^{-8}$6–$\mathcal{B}_{\rm LD} \sim (1-3)\times10^{-8}$7 for several rare charm decay channels, entering the SM LD regime for $\mathcal{B}_{\rm LD} \sim (1-3)\times10^{-8}$8, $\mathcal{B}_{\rm LD} \sim (1-3)\times10^{-8}$9, and related modes (Li, 2011, Roy et al., 3 Jul 2025).
• Enhanced analysis techniques: Multivariate classification, $D^+$00-binned studies, refined photon and $D^+$01 identification, and improved background suppression (e.g., better $D^+$02 veto) (Zhan, 11 Nov 2025).
• Probes of more exotic processes: Dark photon, baryon-number and lepton-flavor violation, and four-body and baryonic rare decays.
• Model discrimination: Improved form-factor determinations, precise measurement of decay constants from leptonic/semileptonic modes for Lattice QCD validation.

A plausible implication is that as sensitivities approach $D^+$03 or below, BESIII will be positioned to exclude or discover NP scenarios with enhanced up-quark FCNC couplings, heavy mediators, or nonminimal flavor violation. Complementarity with $D^+$04 and $D^+$05 rare-decay programs ensures that the up-quark sector is not a blind spot for indirect NP searches.

7. Summary and Significance

The BESIII experiment has achieved world-leading upper limits for a wide portfolio of rare and forbidden charm decays, typically reaching or improving the $D^+$06–$D^+$07 regime for various FCNC, LNV, LFV, and exotic modes. No excess above SM background expectations has been observed. These results impose stringent constraints on NP in the up-type quark sector, Majorana neutrino mixing, new gauge bosons, and related phenomena. Continued data accumulation and advancements in analysis will further tighten these constraints and begin to access the long-distance SM predictions, closing the window for models that predict substantial enhancements to charm rare decays beyond the SM framework (Zhan, 11 Nov 2025, Li et al., 2024, Li, 2012, Wang, 2018).