Evidence for the semileptonic decays $Λ_c^{+} \to Σ^{\pm} π^{\mp} e^+ ν_e$

Using 4.5 fb⁻¹ of $e^+e^-$ collision data collected by the BESIII detector, researchers report the first evidence for the semileptonic decays $\Lambda_c^{+} \to \Sigma^{\pm} \pi^{\mp} e^+ \nu_e$ with a significance of 3.6$\sigma$ and measure a branching fraction of $(7.7^{+2.5}_{-2.3}\pm1.3)\times 10^{-4}$, which aligns with quark model predictions.

The Gist

The Big Picture: Catching a Ghost in a Cosmic Factory

Imagine the BESIII detector as a massive, high-tech camera inside a giant ring-shaped racetrack (the BEPCII collider). Scientists smash electrons and positrons (matter and antimatter) together at incredible speeds. When they collide, they create a shower of new particles, much like two cars crashing and sending debris flying everywhere.

Among this debris, the scientists are looking for a very specific, rare event: the decay of a particle called the $\Lambda_c^+$ (Lambda-c-plus).

Think of the $\Lambda_c^+$ as a heavy, unstable "parent" particle. It doesn't last long. It wants to break apart. Usually, it breaks apart in predictable ways. But this paper is about a "ghostly" breakup where one of the pieces is a neutrino—a particle so shy and light that it passes through the entire Earth without hitting anything. We can't see it, but we know it's there because something is missing.

The Mystery: The "Missing" Neutrino

The specific decay the scientists are hunting is:
$\Lambda_c^+$ $\rightarrow$ $\Sigma$ + $\pi$ + $e^+$ + $\nu_e$

In plain English:

1. The heavy parent ($\Lambda_c^+$) splits.
2. It creates a new baryon ($\Sigma$), a pion ($\pi$), and a positron ($e^+$, which is like a positive electron).
3. Crucially, it also creates a neutrino ($\nu_e$).

The Problem: Since the neutrino is invisible, the detector sees the other three particles, but the total energy and momentum don't add up. It's like watching a magician pull a rabbit out of a hat, but the hat is lighter than it should be. The "missing weight" tells you the rabbit (the neutrino) is there.

The Strategy: The "Double-Tag" Trick

How do you find a needle in a haystack when the needle is invisible? The BESIII team uses a clever trick called Double-Tagging.

Imagine you have a pair of identical twins (the $\Lambda_c^+$ and its antiparticle, the $\Lambda_c^-$) born from the collision.

1. The Single Tag (The Anchor): The scientists look at one twin ($\Lambda_c^-$) and reconstruct its entire breakup perfectly. They know exactly what it turned into. Because they know exactly what the twin turned into, they know exactly how much energy and momentum the other twin ($\Lambda_c^+$) started with.
2. The Signal (The Hunt): Now, they look at the other twin. They see the visible pieces ($\Sigma$, $\pi$, $e^+$). They calculate: "If the visible pieces weigh X, and the twin started with Y, then the missing piece must weigh Y minus X."

If that missing piece matches the profile of a neutrino, they have a candidate!

The Challenge: The "Noise"

The racetrack is chaotic. There are millions of other particle crashes happening that look almost like the signal but aren't.

• The "Fake" Neutrinos: Sometimes, a particle gets lost or a detector glitch makes it look like something is missing when it isn't.
• The "Lookalikes": Other decays produce similar particles ($\Sigma$, $\pi$, $e^+$) but without the neutrino.

The scientists had to build a very strict filter (like a bouncer at a club) to let only the real signal through. They checked:

• Did the particles come from the right spot?
• Did the angles make sense?
• Did the "missing energy" line up perfectly with the theory of a neutrino?

The Results: A "Maybe" but a Strong One

After analyzing 4.5 inverse femtobarns of data (which is a fancy way of saying "a huge amount of collision data"), here is what they found:

1. The Discovery: They found evidence for this decay happening. It wasn't a "slam dunk" discovery (which usually requires a 5-sigma confidence level, or a 1 in 3.5 million chance of being a fluke). Instead, they found 3.6 sigma evidence.

   • Analogy: If you flip a coin 100 times and get 60 heads, it's suspicious. If you get 90 heads, you know the coin is rigged. This result is like getting 85 heads. It's very likely the coin is rigged, but you'd want to flip it a few more times to be 100% sure.

2. The Frequency: They measured how often this happens. It's rare. Out of every 10,000 times a $\Lambda_c^+$ decays, this specific "ghostly" breakup happens about 0.77 times.

3. The Theory Check: Theoretical physicists have been arguing about the nature of a particle called $\Lambda(1405)$. Is it a simple cluster of three quarks, or is it a "molecule" made of two other particles stuck together?

   • The scientists checked if their results matched the predictions of the "Quark Model" (the three-quark theory).
   • Verdict: The results match the Quark Model predictions within two standard deviations. This suggests the "three-quark" theory is likely correct, though the "molecule" theory isn't completely ruled out yet.

Why Does This Matter?

This is like finding a new piece of a puzzle that explains how the universe is built.

• Understanding the Strong Force: This decay involves the "Strong Force" (which holds atoms together) and the "Weak Force" (which causes radioactive decay). Studying how they play together in these heavy particles helps us understand the rules of the universe.
• The $\Lambda(1405)$ Mystery: By seeing how the $\Lambda_c^+$ turns into $\Sigma$ and $\pi$, we get clues about the hidden structure of excited particles. It's like listening to the sound of a breaking glass to figure out what the glass was made of.

The Bottom Line

The BESIII collaboration used a massive particle collider and a clever "twin" tracking method to catch a rare, ghostly decay where a heavy particle splits into visible pieces and an invisible neutrino. While they haven't reached the "gold standard" of discovery yet, they have found strong evidence (3.6 sigma) that this happens, and the rate at which it happens fits our current best theories about how quarks behave.

It's a solid step forward in mapping the strange, subatomic world.

Technical Summary

1. Problem Statement and Motivation

The paper addresses the search for the semileptonic (SL) decays of the charmed baryon $\Lambda_c^+$ into a $\Sigma \pi$ final state accompanied by an electron and a neutrino ($\Lambda_c^+ \to \Sigma^\pm \pi^\mp e^+ \nu_e$).

• Physics Context: While dominant SL decays like $\Lambda_c^+ \to \Lambda e^+ \nu_e$ are well-studied, decays involving excited $\Lambda^*$ states (which decay to $\Sigma \pi$) remain less explored.
• Theoretical Puzzle: The nature of the $\Lambda(1405)$ resonance is a long-standing mystery in QCD. It is debated whether it is a three-quark bound state or a molecular state.
  • Quark models predict a relatively large branching fraction (BF) for $\Lambda_c^+ \to \Lambda(1405) e^+ \nu_e$ (leading to $\Sigma \pi e^+ \nu_e$).
  • Chiral unitary approaches (assuming a molecular state) predict a BF nearly two orders of magnitude smaller.
• Goal: To search for $\Lambda_c^+ \to \Sigma^\pm \pi^\mp e^+ \nu_e$ to provide experimental evidence for these decays, constrain theoretical models, and potentially shed light on the nature of the $\Lambda(1405)$.

2. Methodology

The analysis utilizes data collected by the BESIII detector at the BEPCII $e^+e^-$ collider.

• Dataset: $4.5 \text{ fb}^{-1}$ of integrated luminosity collected at center-of-mass energies between $4.600$ and $4.699$ GeV (near the $\Lambda_c^+ \bar{\Lambda}_c$ production threshold).
• Tagging Technique: The Double-Tag (DT) method is employed to reduce background and reconstruct the unobserved neutrino kinematics.
  • Single Tag (ST): One $\bar{\Lambda}_c^-$ is fully reconstructed in 12 hadronic decay modes (e.g., $\bar{p}K_S^0$, $\bar{p}K^+\pi^-$, etc.).
  • Signal Side: The recoiling $\Lambda_c^+$ is searched for in the signal decay modes.
• Signal Reconstruction:
  • Modes: $\Lambda_c^+ \to \Sigma^+ \pi^- e^+ \nu_e$ and $\Lambda_c^+ \to \Sigma^- \pi^+ e^+ \nu_e$.
  • $\Sigma$ Decays:
    • $\Sigma^+ \to p \pi^0$ (reconstructed via photons in the EMC).
    • $\Sigma^+ \to n \pi^+$ and $\Sigma^- \to n \pi^-$ (reconstructed via neutron showers in the EMC).
  • Particle ID: Charged tracks identified via Time-of-Flight (TOF) and $dE/dx$; positrons identified using EMC shower shape and likelihood; photons via EMC energy deposits.
• Kinematic Variables:
  • Since the neutrino is undetected, the analysis relies on missing energy ($E_{miss}$) and missing momentum ($\vec{p}_{miss}$).
  • Key variables used for signal extraction:
    • $U_{miss} = E_{miss} - c|\vec{p}_{miss}|$
    • $M_{miss}^2 = E_{miss}^2/c^4 - |\vec{p}_{miss}|^2/c^2$
  • Signal events are expected to peak near zero for these variables.
• Fit Strategy:
  • A simultaneous unbinned maximum likelihood fit is performed on the $M_{miss}^2$ (for $p\pi^0$ mode) and $U_{miss}$ (for neutron modes) distributions.
  • Isospin Symmetry: The branching fractions of $\Lambda_c^+ \to \Sigma^+ \pi^- e^+ \nu_e$ and $\Lambda_c^+ \to \Sigma^- \pi^+ e^+ \nu_e$ are assumed equal to improve statistical power.
  • Backgrounds (peaking and continuum) are modeled using dedicated Monte Carlo (MC) samples and inclusive MC.

3. Key Contributions

• First Observation: This is the first experimental search for the specific semileptonic decays $\Lambda_c^+ \to \Sigma^\pm \pi^\mp e^+ \nu_e$.
• Evidence for Decay: The collaboration reports the first evidence for these decays with a statistical significance of 3.6$\sigma$ (when combining modes under isospin symmetry).
• Branching Fraction Measurement: The paper provides the first measurement of the branching fraction for this channel.
• Systematic Handling: A rigorous treatment of systematic uncertainties, particularly those related to neutron reconstruction efficiency and $\pi^0$ vetoes, which are critical for the neutron-involved decay modes.

4. Results

• Branching Fraction:
  Assuming isospin symmetry, the measured branching fraction is:
  $$\mathcal{B}(\Lambda_c^+ \to \Sigma^\pm \pi^\mp e^+ \nu_e) = (7.7^{+2.5}_{-2.3}(\text{stat}) \pm 1.3(\text{syst})) \times 10^{-4}$$
• Significance:
  • Simultaneous fit (combined modes): 3.6$\sigma$.
  • Separate fits (without symmetry assumption): $3.1\sigma$ for $\Sigma^+ \pi^-$ and $2.4\sigma$ for $\Sigma^- \pi^+$.
• Upper Limits:
  For the separate fits where significance is $<3\sigma$, 90% confidence level upper limits are set:
  • $\mathcal{B}(\Lambda_c^+ \to \Sigma^+ \pi^- e^+ \nu_e) < 1.41 \times 10^{-3}$
  • $\mathcal{B}(\Lambda_c^+ \to \Sigma^- \pi^+ e^+ \nu_e) < 1.51 \times 10^{-3}$
• Comparison with Theory:
  The measured value is consistent with predictions from non-relativistic quark models (which predict $\sim 0.36\%$ for the cascade $\Lambda_c^+ \to \Lambda^* e^+ \nu_e \to \Sigma \pi e^+ \nu_e$) within two standard deviations. It is significantly higher than predictions from chiral unitary approaches assuming a molecular $\Lambda(1405)$.
• Resonance Structure:
  The $M_{\Sigma\pi}$ invariant mass distribution shows a hint of $\Lambda^*$ resonance structures, suggesting the decay proceeds via intermediate excited $\Lambda$ states.

5. Significance

• QCD Insight: The results provide crucial data on non-perturbative QCD effects in the charmed baryon sector, specifically regarding the transition form factors of $\Lambda_c^+$ to excited $\Lambda^*$ states.
• $\Lambda(1405)$ Nature: By measuring the rate of $\Sigma \pi$ production in semileptonic decays, the paper helps constrain the nature of the $\Lambda(1405)$. The result favors the quark model interpretation over the molecular state hypothesis (though more data is needed for a definitive conclusion).
• Future Prospects: The paper highlights that with larger datasets expected at BESIII, a detailed study of the $\Lambda(1405)$ and $\Lambda(1520)$ contributions in this channel will be possible, offering a new platform for studying $\Lambda$ baryon spectroscopy.