Leptonic and semileptonic charm decays at BESIII

This paper presents recent BESIII collaboration results on charmed purely leptonic and semileptonic decays, including measurements of branching fractions, CKM matrix elements, decay constants, form factors, and tests of lepton flavor universality derived from data collected at various center-of-mass energies.

The Gist

Imagine the universe as a giant, bustling city. Inside this city, there are tiny, short-lived citizens called charm mesons (or "D mesons"). These particles are like delivery trucks that carry heavy cargo (quarks) but are destined to break down very quickly. When they break down, they don't just vanish; they transform into other particles, sometimes shooting out tiny, ghostly messengers called neutrinos and charged particles like electrons or muons.

The BESIII experiment is like a high-tech surveillance camera set up in a massive particle collider in Beijing. Its job is to watch billions of these "delivery trucks" crash and transform, recording every detail of their final moments.

Here is what this paper is about, explained through simple analogies:

1. The Mission: Catching the "Ghost" Deliveries

The scientists are studying two specific ways these charm mesons decay:

• Leptonic Decays (The "Ghost" Exit): The meson disappears entirely, leaving behind only a charged particle (like a muon) and a neutrino. Since neutrinos are like ghosts that pass through walls without being seen, catching this event is like trying to deduce a thief's identity by only seeing the empty space they left behind.
• Semileptonic Decays (The "Partial" Exit): The meson breaks apart into a new, lighter meson (like a K-meson) plus the charged particle and the neutrino. This is like a delivery truck dropping off a package and a ghost before vanishing.

2. Why Do They Care? (The "Rulebook" Check)

The Standard Model is the universe's "Rulebook" of physics. It predicts exactly how often these trucks should break down and what the resulting particles should weigh.

• The Goal: BESIII is checking if the universe is following the Rulebook perfectly. If the numbers don't match, it might mean there are "secret rules" (new physics) we haven't discovered yet.
• The Tools: They are measuring three main things:
  1. Branching Fractions: How often does a specific type of breakdown happen? (e.g., "Out of 10,000 trucks, how many drop off a muon?")
  2. Decay Constants & Form Factors: These are like the "strength" or "shape" of the meson. Think of it as measuring the structural integrity of the delivery truck before it breaks.
  3. CKM Matrix Elements ($|V_{cs}|$ and $|V_{cd}|$): These are numbers that tell us how likely a charm quark is to change into a strange or down quark. It's like a probability dial on the truck's engine.

3. The Big Discoveries (The "News")

A. The "Double-Tag" Trick

To catch these rare events, BESIII uses a clever trick called Double-Tagging.

• Analogy: Imagine you are at a party where couples always arrive together. If you see one half of a couple (a "tag") enter the room, you know the other half is there too, even if you can't see them immediately.
• In the experiment, they create pairs of charm mesons. If they catch one meson decaying in a known way, they know exactly what the other meson was doing. This allows them to measure the "ghostly" decays with extreme precision.

B. Testing "Flavor Universality" (The "Fairness" Test)

The Standard Model says that nature treats all "flavors" of leptons (electrons, muons, and taus) fairly. They should behave the same way, just with different weights.

• The Result: BESIII checked if a charm meson is equally likely to produce an electron as it is a muon. The answer? Yes! The universe is being fair. The ratios matched the predictions perfectly, confirming the "Fairness Rule" holds up in the charm sector.

C. Measuring the "Strength" (Decay Constants)

By measuring how often these decays happen, the team calculated the "decay constants" (the structural strength of the mesons).

• The Result: Their measurements are the most precise ever made. When they compared their numbers to predictions from supercomputer simulations (Lattice QCD), they matched almost perfectly. This gives physicists great confidence that our understanding of the strong force (which holds particles together) is correct.

D. Finding New "Shapes" (Axial-Vector and Scalar Mesons)

In the semileptonic section, the team looked at the debris left behind. They found that sometimes the debris forms specific shapes (like $K_1$ or $b_1$ particles).

• The Discovery: They observed some of these shapes for the first time in these specific decays. It's like finding a new type of car model in a junkyard that no one knew existed. They also measured how these shapes spin and rotate, confirming they behave exactly as the Rulebook predicts.

4. The "Secret" Search (New Physics?)

The scientists also looked for a "scalar current"—a hypothetical force that isn't in the standard Rulebook.

• The Result: They found a tiny, tiny hint of something strange in the muon channels (a 1.9 sigma deviation), but it's not strong enough to say "We found new physics!" yet. It's more like a whisper that needs to be heard louder in future experiments.

Summary

Think of this paper as a high-precision quality control report for the universe's particle factory.

• BESIII checked millions of "delivery trucks."
• They confirmed the Rulebook is mostly correct.
• They measured the strength and shape of the particles with record-breaking accuracy.
• They found no major violations of the rules, but they are keeping a sharp eye out for the tiniest cracks that might lead to a whole new understanding of the universe.

The team is now ready with even more data (a bigger dataset) to make these measurements even sharper, hoping to catch that elusive "ghost" of new physics if it's hiding in the shadows.

Technical Summary

1. Problem and Motivation

The Standard Model (SM) of particle physics relies on the Cabibbo-Kobayashi-Maskawa (CKM) matrix to describe quark mixing. Precise measurements of charm meson ($D$ and $D_s$) decays are critical for:

• Determining CKM matrix elements ($|V_{cs}|$ and $|V_{cd}|$) to test the unitarity of the CKM matrix.
• Extracting hadronic parameters such as decay constants ($f_{D^{(*)}}$) and form factors ($f_+$, etc.), which are essential inputs for Lattice Quantum Chromodynamics (LQCD) calculations.
• Testing Lepton Flavor Universality (LFU), a fundamental SM prediction that interaction strengths are identical for electrons, muons, and taus.
• Searching for physics beyond the Standard Model (BSM) by looking for deviations in decay rates, asymmetries, or the presence of non-SM currents (e.g., scalar currents).

2. Methodology

The BESIII experiment utilizes data collected at the Beijing Electron Positron Collider II (BEPCII) via symmetric $e^+e^-$ collisions. The analysis employs the double-tag method, a technique where one charm meson is fully reconstructed (the tag), allowing the properties of the other charm meson in the event to be inferred with high precision and minimal background.

Data Samples:

• $\sqrt{s} = 3.773$ GeV: 20.3 fb$^{-1}$ of data collected near the $\psi(3770)$ resonance, producing $D\bar{D}$ pairs. Used primarily for $D$ meson decays.
• $\sqrt{s} = 4.128–4.226$ GeV: Data samples for $e^+e^- \to D_s^\pm D^{*\mp}_s$.
• $\sqrt{s} = 4.237–4.669$ GeV: Data samples for $e^+e^- \to D_s^+ D_s^{*-}$ and $D_s^{*+} D_s^{*-}$. Used for $D_s$ meson decays.

Analysis Techniques:

• Branching Fraction Measurements: Counting signal events normalized to the total number of $D\bar{D}$ events.
• Radiative Corrections: Incorporation of structure-dependent bremsstrahlung and electroweak corrections (short- and long-distance) for leptonic decays.
• Amplitude Analysis: Helicity amplitude analyses using kinematic variables ($M^2$, $q^2$, angles) to disentangle partial waves (S, P, D-waves) and determine form factors.
• Simultaneous Fits: Fitting multiple decay channels simultaneously to constrain parameters like decay constants and CKM elements while accounting for correlations.

3. Key Contributions and Results

A. Purely Leptonic Decays ($D_{(s)} \to \ell^+\nu_\ell$)

• $D^+ \to \mu^+\nu_\mu$:
  • Measured branching fraction: $(4.034 \pm 0.080_{stat} \pm 0.040_{syst}) \times 10^{-4}$.
  • Extracted $f_{D^+}|V_{cd}| = (48.02 \pm 0.48_{stat} \pm 0.24_{syst} \pm 0.12_{ext})$ MeV.
  • Derived $|V_{cd}| = 0.2265 \pm 0.0023_{stat} \pm 0.0011_{syst} \pm 0.0009_{ext}$ (using LQCD $f_{D^+}$).
  • Derived $f_{D^+} = (213.5 \pm 2.1_{stat} \pm 1.1_{syst} \pm 0.8_{ext})$ MeV (using SM global fit $|V_{cd}|$).
• $D_s^+ \to \ell^+\nu_\ell$ ($\ell = \mu, \tau$):
  • Simultaneous fit to 10.64 fb$^{-1}$ of data at higher energies.
  • Branching fractions: $B(D_s^+ \to \tau^+\nu_\tau) = (5.60 \pm 0.16 \pm 0.20)\%$ and $B(D_s^+ \to \mu^+\nu_\mu) = (0.547 \pm 0.026 \pm 0.016)\%$.
  • Extracted $f_{D_s^+} = (252.1 \pm 1.3 \pm 1.7)$ MeV and $|V_{cs}| = 0.982 \pm 0.005 \pm 0.007$.
  • These results provide the most precise single determinations of these parameters to date.

B. Semileptonic Decays to Pseudoscalars ($D \to P \ell^+\nu_\ell$)

• $D \to \bar{K} \ell^+\nu_\ell$:
  • Measured branching fractions for $D^0 \to K^-\ell^+\nu_\ell$ and $D^+ \to \bar{K}^0\ell^+\nu_\ell$ with high precision.
  • LFU Test: Ratios $R^\mu/e$ are consistent with SM predictions ($0.975 \pm 0.001$), confirming LFU.
  • Extracted $f_+^{D\to\bar{K}}(0)|V_{cs}| = 0.7160 \pm 0.0007 \pm 0.0014$.
  • BSM Search: Forward-backward asymmetries measured. A $1.9\sigma$ deviation was observed in the muon channel for the scalar Wilson coefficient ($c_S^\mu$), though not yet conclusive.
• $D \to \eta \ell^+\nu_\ell$:
  • First precise measurements of absolute branching fractions for $D^+ \to \eta e^+\nu_e$ and $D^+ \to \eta \mu^+\nu_\mu$.
  • Improved precision on form factor $f_+^{D\to\eta}(0)$ by a factor of 3.4 compared to previous measurements.

C. Semileptonic Decays to Vectors ($D \to V \ell^+\nu_\ell$)

• $D \to \bar{K}^* \ell^+\nu_\ell$:
  • First observation of $D^+ \to K_S^0 \pi^0 \mu^+\nu_\mu$.
  • First complete angular analysis of $D^+ \to \bar{K}^*(892)^0 \ell^+\nu_\ell$, measuring CP-averaged and CP-asymmetric asymmetries consistent with SM.
  • D-wave Observation: First observation of the $D$-wave component ($K_2^*(1430)$) in $D^0 \to \bar{K}^0 \pi^- \ell^+\nu_\ell$ and $D^0 \to K^- \pi^+ e^+\nu_e$ with significances of $8.0\sigma$ and $7.9\sigma$.
  • LFU ratios ($R^\mu/e$) consistent with SM.

D. Semileptonic Decays to Axial-Vectors and Scalars

• $D \to \bar{K}_1 \ell^+\nu_\ell$:
  • First amplitude analysis of $D^{+(0)} \to K^- \pi^+ \pi^0 e^+\nu_e$.
  • Determined hadronic form factor parameters ($r_V, r_A$) and measured branching fractions for $D^+ \to \bar{K}_1(1270)^0 e^+\nu_e$ and $D^0 \to \bar{K}_1(1270)^- e^+\nu_e$.
  • First observation of $D^+ \to \bar{K}_1(1270)^0 \mu^+\nu_\mu$ and $D^0 \to \bar{K}_1(1270)^- \mu^+\nu_\mu$.
  • First observation of $D^0 \to b_1(1235)^- e^+\nu_e$ ($12.5\sigma$).
• $D \to a_0(980) \ell^+\nu_\ell$:
  • First measurement of $B(D^0 \to a_0(980)^- e^+\nu_e) = (0.86 \pm 0.17 \pm 0.05) \times 10^{-4}$.
  • First determination of $f_+^{D\to a_0}(0)|V_{cd}|$.

4. Significance

• Precision Physics: The paper presents the most precise single determinations of decay constants ($f_D, f_{D_s}$) and CKM elements ($|V_{cs}|, |V_{cd}|$) in the charm sector. The precision on $|V_{cs}|$ and $|V_{cd}|$ reaches 0.23% and 1.2%, respectively.
• Standard Model Validation: The results strongly support the SM, particularly confirming Lepton Flavor Universality across various decay modes and channels.
• Theoretical Input: The precise extraction of form factors and decay constants provides critical benchmarks for LQCD calculations, helping to reduce theoretical uncertainties in global CKM fits.
• New Physics Sensitivity: While no major deviations were found, the measurement of forward-backward asymmetries and scalar current contributions sets stringent constraints on BSM models. The observed $1.9\sigma$ deviation in the scalar coefficient for muon channels warrants further investigation with larger datasets.
• Discovery of New Modes: The first observations of several decay modes (e.g., $D^+ \to K_S^0 \pi^0 \mu^+\nu_\mu$, $D \to b_1(1235)$) and partial waves (D-wave) significantly expand the understanding of charm decay dynamics.

In conclusion, this work represents a major advancement in charm physics, utilizing the unique capabilities of the BESIII detector to provide high-precision tests of the Standard Model and essential inputs for theoretical QCD.