Recent results on (semi)-leptonic $D$ decays and charm baryons at BESIII

This paper presents recent BESIII results on pure leptonic and semileptonic decays of $D$ mesons and charm baryons, as well as baryon pair polarization, leveraging the world's largest datasets collected at open-charm production thresholds.

The Gist

Imagine the BESIII experiment as a massive, ultra-precise camera sitting inside a particle accelerator called BEPCII. This camera doesn't take pictures of landscapes or people; it snaps photos of subatomic particles crashing into each other at incredibly high speeds. Specifically, it focuses on "charm" particles, which are like heavy, short-lived cousins of the protons and neutrons that make up our everyday world.

The paper is essentially a report card on what this camera has captured recently. The team has gathered the largest collection of these charm particles ever assembled, allowing them to study how these particles break apart (decay) with unprecedented clarity.

Here is a breakdown of their latest discoveries using simple analogies:

1. The "Double-Tag" Detective Method

One of the biggest challenges in particle physics is that some particles, like neutrinos, are ghosts—they pass right through detectors without leaving a trace. To catch them, the BESIII team uses a clever trick called the "Double-Tag" method.

Imagine you are at a party where guests always arrive in pairs holding hands. If you see one guest (the "tag") walk into a room, you know for a fact their partner is in the room too, even if you can't see them.

• How it works: The experiment creates pairs of charm particles. The team reconstructs one partner perfectly (the tag). Because they know exactly how much energy and momentum the pair started with, they can calculate exactly what the other partner must have done, even if that partner vanished into a neutrino. This allows them to measure rare decays that were previously impossible to see clearly.

2. Testing the Rules of the Universe (CKM Matrix & Universality)

The Standard Model is the rulebook of physics. The team used their new data to check if the rules are being followed strictly.

• The "Flavor" Check: They looked at how charm particles decay into electrons versus muons (which are like heavy, unstable electrons). The rulebook says nature should treat them almost exactly the same. BESIII found that they do! The rates were nearly identical, confirming that the universe plays fair with these different types of particles.
• The "Handshake" Strength: They measured how strongly charm particles "shake hands" with other particles (specifically a value called $|V_{cs}|$). Their measurement is the most precise one ever made, acting like a new, ultra-accurate ruler for physicists. However, when they compared this ruler to predictions made by supercomputers (Lattice QCD), they found a tiny mismatch—a "tension" of about 2 standard deviations. It's like measuring a table with a laser ruler and getting a result that is slightly different from the architect's blueprint. It might just be a measurement quirk, or it might hint at new physics we don't understand yet.

3. Catching the "Ghost" Neutrinos in Baryons

The team also studied "charm baryons" (particles made of three quarks, like a proton). They achieved a historic first: observing a charm baryon turning into a neutron and an electron.

• The Challenge: This is like trying to spot a specific type of bird in a forest where a very similar-looking bird is hiding in the bushes. The "hiding" bird was a background noise that looked almost exactly like the signal.
• The Solution: They used a "Graph Neural Network" (a type of advanced AI) trained to spot the subtle differences between the real signal and the background noise. This AI acted like a super-smart birdwatcher, successfully separating the two. This allowed them to measure a specific transition ($c \to d$) that had never been seen in baryons before.

4. Spinning Top Polarization

Finally, they looked at how these charm baryons spin when they are created in pairs.

• The Analogy: Imagine spinning two tops in opposite directions. If the tops are perfectly balanced, they spin straight up. But if there is a slight imbalance, they might wobble or tilt sideways.
• The Discovery: BESIII found evidence that these charm baryons do wobble sideways (transverse polarization) when created. This wobble tells them about the internal structure of the particles. While the size of the wobble matched some predictions, the direction of the wobble (the phase) was surprisingly different from what theorists expected.

Summary

In short, the BESIII collaboration has used the world's largest dataset of charm particles to:

1. Refine the rules: Confirm that electrons and muons are treated equally in these decays.
2. Find a crack in the blueprint: Notice a small discrepancy between their measurements and computer predictions regarding particle interaction strengths.
3. Spot the invisible: Use AI and clever math to catch particles that usually hide (neutrinos) and distinguish them from background noise.
4. Watch them spin: Observe a new type of "wobble" in charm baryons that challenges current theories.

The paper concludes that while they have learned a tremendous amount, the data is so rich that there is still much more to uncover, especially as they plan to upgrade their equipment to see even heavier and more exotic particles in the future.

Technical Summary

Technical Summary: Recent Results on (Semi)-leptonic $D$ Decays and Charm Baryons at BESIII

Problem and Context
The BESIII collaboration operates at the Beijing Electron Positron Collider (BEPCII), collecting data in the center-of-mass energy range of 2–5 GeV. This energy regime is optimal for producing open-charm hadrons near their production thresholds. The primary physics goals addressed in these proceedings are the precision measurement of CKM matrix elements ($|V_{cd}|$ and $|V_{cs}|$), tests of lepton flavor universality (LFU), the determination of non-perturbative QCD parameters (decay constants and form factors), and the study of light hadron structure and baryon polarization. To achieve these goals, the collaboration leverages the world's largest datasets for open-charm production, specifically a 20.3 fb$^{-1}$ sample collected at the $\psi(3770)$ resonance (completed in 2024) and a 6.4 fb$^{-1}$ sample collected between 4.60 and 4.95 GeV.

Methodology
The core experimental technique employed is the double-tag method. In $e^+e^-$ collisions near the open-charm threshold, charmed hadrons are produced in pairs. One hadron (the "tag") is reconstructed in a clean hadronic decay mode. The presence of this tag guarantees the existence of the partner hadron (the "signal") in the event. This allows for the inclusive study of the signal decay, including modes with neutrinos, by analyzing the remainder of the event.

Key kinematic variables used to identify signal events and extract yields include:

• Beam-constrained mass ($M_{BC}$): Used to determine tag yields.
• Missing mass squared ($M^2_{miss}$) and Missing energy-momentum ($U_{miss}$): Used to identify signal decays involving neutrinos by calculating the difference between the initial $e^+e^-$ four-momentum and the sum of visible particles.
• Graph Neural Networks (GNN): Specifically utilized in the $\Lambda_c^+ \to n e^+ \nu_e$ analysis to discriminate between neutrons and $\Lambda$ baryons decaying to $n\pi^0$ (where the $\pi^0$ is unreconstructed), a major background source.
• Multi-dimensional fits: Used for differential decay rate measurements, incorporating variables such as invariant mass ($m_{K\pi}$), $q^2$, and helicity angles.

Key Contributions and Results

1. Pure Leptonic $D^+$ Decays:
   Using the full 20.3 fb$^{-1}$ dataset, the branching fraction for $D^+ \to \mu^+ \nu_\mu$ was measured with eight different tag modes. The result, $\mathcal{B}(D^+ \to \mu^+ \nu_\mu) = (3.98 \pm 0.08 \pm 0.04) \times 10^{-4}$, represents a 2.3-fold improvement in precision over previous measurements. Combined with the $D^+$ lifetime, this yields $f_{D^+}|V_{cd}| = (47.53 \pm 0.48 \pm 0.24 \pm 0.12_{\text{ext}})$ MeV. A complementary measurement of $D^+ \to \tau^+ \nu$ was also performed using a subset of the data.

2. Semileptonic $D \to K \ell \nu$ Decays and LFU:
   Analysis of $D^0 \to K^- (e^+/\mu^+) \nu$ and $D^+ \to K_S^0 (e^+/\mu^+) \nu$ using a 7.9 fb$^{-1}$ sample achieved relative precisions of 0.5%–1.1%. The ratio of decay rates to muons versus electrons was measured as $R_{D^+}^{\mu/e} = 0.978(7)_{\text{stat}}(13)_{\text{syst}}$ and $R_{D^0}^{\mu/e} = 0.971(4)_{\text{stat}}(6)_{\text{syst}}$, consistent with Standard Model expectations.
   A simultaneous fit to $D^0$ and $D^+$ modes determined $f_+^{K}(0)|V_{cs}| = 0.7171(11)_{\text{stat}}(13)_{\text{syst}}$. Using the PDG2022 value for $|V_{cs}|$, the form factor $f_+^{K}(0) = 0.7366 \pm 0.0011 \pm 0.0013$ was extracted. The paper notes a $\sim 2\sigma$ tension between this result and recent lattice QCD calculations.

3. Complex Semileptonic Transitions ($D \to K \pi X \ell \nu$):
   The decay $D^+ \to K_S^0 \pi^0 \ell^+ \nu$ was studied with the full 20.3 fb$^{-1}$ dataset. The $K\pi$ system was found to be dominated by the $K^*(892)$ resonance, with a smaller $S$-wave contribution. A five-dimensional fit extracted the $K^*(892)$ mass and width, form factor ratios ($r_2, r_V$), and shape parameters. All measured CP asymmetries and angular observables were consistent with Standard Model predictions.

4. $D \to a_0(980) \ell \nu$ and Light Hadron Structure:
   A new measurement of $D^0 \to a_0(980)^- e^+ \nu_e$ provided the first experimental determination of the $D \to a_0$ form factor. The $a_0(980)$ was parametrized using the Flatté formalism. The branching fraction was measured as $(0.86 \pm 0.17 \pm 0.05) \times 10^{-4}$, and the form factor at $q^2=0$ was determined to be $f_0^{D \to a_0} = 0.550 \pm 0.056 \pm 0.013$. This result offers discriminating power between theoretical models of the $a_0(980)$ structure.

5. Charm Baryon Semileptonic Decays:
   The first observation of the semileptonic decay $\Lambda_c^+ \to n e^+ \nu_e$ was achieved using a 4.5 fb$^{-1}$ sample at 4.6–4.7 GeV. This represents the first measurement of a $c \to d$ transition in the charmed baryon sector. Using a GNN to suppress the $\Lambda_c^+ \to \Lambda(\to n\pi^0) e^+ \nu_e$ background, the branching fraction was measured as $(0.357 \pm 0.034 \pm 0.014)\%$. Combining this with lattice QCD predictions and the $\Lambda_c^+$ lifetime yields an independent determination of $|V_{cd}| = 0.208 \pm 0.011_{\text{exp}} \pm 0.007_{\text{LQCD}} \pm 0.001_{\tau_{\Lambda_c}}$.

6. Baryon Polarization and Timelike Form Factors:
   Using 6.4 fb$^{-1}$ of data between 4.60 and 4.95 GeV, the collaboration measured the transverse polarization of $\Lambda_c^+$ baryons produced in $e^+e^- \to \Lambda_c^+ \bar{\Lambda}_c^-$. This measurement provides the first evidence for transverse polarization in charm baryon pair production. The results yielded values for the magnitude ratio $|G_E|/|G_M|$ and the relative phase $\sin \Delta \Phi$. While $|G_E|/|G_M|$ agrees with recent theoretical predictions, significant deviations were observed in the experimental determination of $\sin \Delta \Phi$ compared to theory.

Significance and Claims
The paper claims that these results constitute a "wealth of precision measurements" in charm physics. Specifically, the work highlights:

• The most precise single determination of $|V_{cs}|$ from $D \to K \ell \nu$ decays to date.
• Stringent tests of lepton flavor universality in the charm sector, confirming Standard Model expectations.
• Comprehensive studies of $D \to K \pi X \ell \nu$ transitions and the first measurement of the $D \to a_0(980)$ form factor.
• The first observation of the $c \to d$ transition in charmed baryons ($\Lambda_c^+ \to n e^+ \nu_e$).
• The first measurement of transverse polarization in $e^+e^- \to \Lambda_c^+ \bar{\Lambda}_c^-$ production.

The authors note that while the current datasets have yielded these significant results, much additional physics remains to be extracted. Future plans include utilizing the full 20.3 fb$^{-1}$ dataset for updated $D^0$ and $D^+$ measurements and leveraging the upcoming BEPCII upgrade (targeting 5.6 GeV) to study $\Sigma_c$, $\Xi_c$, and $\Omega_c$ baryon pair production, aiming for further precision tests of the Standard Model and searches for new physics.