Observation of the doubly charmed baryon $\it{\Xi}_{cc}^+$ with the LHCb Run 3 detector

Using 2024 proton-proton collision data from the LHCb Run 3 detector, this paper reports the first observation of the doubly charmed baryon $\it{\Xi}_{cc}^+$ decaying into $\it{\Lambda}_c^+ K^-\pi^+$ with a statistical significance exceeding seven standard deviations and provides a precise measurement of its mass and mass difference relative to the $\it{\Xi}_{cc}^{++}$.

The Gist

The Big Picture: Finding the "Missing Twin"

Imagine the universe is a giant Lego set. Most of the heavy things we see (like protons and neutrons) are built from three smaller Lego bricks called quarks. Usually, these bricks come in different flavors: "up," "down," "strange," "charm," "bottom," and "top."

For a long time, physicists knew about a very special, heavy Lego structure called the $\Xi^{++}_{cc}$ (pronounced "Xi-double-plus"). It was built with two "charm" bricks and one "up" brick. It was like a rare, heavy truck.

But theory said there had to be a twin brother to this truck. This twin, called the $\Xi^{+}_{cc}$ (pronounced "Xi-plus"), should be built with two "charm" bricks and one "down" brick. It's the same heavy truck, just with a slightly different color of the third brick.

The Problem: We had seen the "up" version ($\Xi^{++}_{cc}$) clearly, but the "down" version ($\Xi^{+}_{cc}$) had been hiding. In fact, a different experiment years ago (called SELEX) claimed to have found it, but they said it was much lighter than it should be. Everyone else looked for it and couldn't find it, leading to a scientific mystery: Does this twin exist, or was the first sighting a mistake?

The Detective Work: The LHCb "Super-Camera"

To solve this, the LHCb collaboration at CERN used their upgraded detector, the LHCb Run 3. Think of this detector as a super-speed, high-definition camera sitting in a tunnel where two beams of protons (tiny particles) crash into each other at nearly the speed of light.

• The Crash: They smashed protons together in 2024 at a record-breaking energy level.
• The Goal: They were looking for a specific "debris" pattern. When the heavy $\Xi^{+}_{cc}$ twin is created, it doesn't last long. It instantly falls apart (decays) into three other particles: a Lambda-c baryon, a kaon, and a pion.
• The Filter: The detector sees millions of collisions every second. It's like trying to find a specific needle in a haystack the size of a mountain. The team used a smart computer program (a "multivariate classifier") to filter out the junk and keep only the events that looked like the needle.

The Breakthrough: "We Found It!"

After analyzing data equivalent to 6.9 "inverse femtobarns" (a fancy unit meaning they collected a massive amount of collision data), they found a clear signal.

• The Evidence: They saw a distinct "bump" in their data graph at a mass of 3619.97 MeV/c².
• The Confidence: In the world of particle physics, you need to be 99.9999% sure before you claim a discovery. This result had a statistical significance of over 7 standard deviations.
  • Analogy: If you flipped a coin 10 times and got heads every time, that's lucky. If you flipped it 1,000 times and got heads every time, that's suspicious. Getting a 7-sigma result is like flipping a coin 10 million times and getting heads every single time. It is statistically impossible to be a fluke.

Why This Matters: Solving the Mystery

1. The Twin Exists: They confirmed that the $\Xi^{+}_{cc}$ baryon is real.
2. The Weight Check: They measured its weight (mass) and found it is slightly lighter than its twin brother ($\Xi^{++}_{cc}$).
   • Analogy: Imagine two identical twins. One eats a slightly heavier breakfast (the "up" quark), and the other eats a slightly lighter one (the "down" quark). The "down" twin is a tiny bit lighter. This matches the predictions of the Standard Model of physics perfectly.
3. The SELEX Mystery Solved: The earlier experiment (SELEX) that claimed to find this particle years ago said it weighed about 3518. They were off by about 100 units. This new paper proves that the SELEX team likely saw something else entirely, or made a measurement error. The "twin" is heavier than they thought.

The "Why It Took So Long" Factor

You might wonder, "If it's so common, why did it take so long to find?"

The answer is time. The $\Xi^{+}_{cc}$ twin is a very impatient particle. It decays (falls apart) incredibly fast—much faster than its brother.

• Analogy: Imagine the brother ($\Xi^{++}_{cc}$) is a slow-moving snail that leaves a long, clear trail. The twin ($\Xi^{+}_{cc}$) is a firecracker that explodes almost instantly. Because it explodes so fast, it travels a very short distance before vanishing.
• The new LHCb detector is so fast and precise that it can catch these "firecrackers" before they disappear. The old detectors were like trying to photograph a firecracker with a slow shutter speed; the image was just a blur. The new detector is a high-speed camera that froze the action.

The Bottom Line

This paper is a victory for the Standard Model (the rulebook of how the universe works). It confirms that:

1. The "missing twin" baryon exists.
2. It has the exact mass difference predicted by theory.
3. The upgraded LHCb detector is a powerhouse, capable of finding particles that were previously invisible.

It's like finding the final piece of a cosmic puzzle that has been missing for decades, proving that our understanding of how matter is built is correct.

Technical Summary

1. Problem and Motivation

The paper addresses the long-standing search for the doubly charmed baryon $\Xi_{cc}^+$ (quark content $ccd$), the isospin partner of the previously observed $\Xi_{cc}^{++}$ ($ccu$).

• Theoretical Context: In the constituent quark model, the $\Xi_{cc}^+$ is expected to have a mass slightly lower than the $\Xi_{cc}^{++}$ (by a few MeV/$c^2$) due to the competition between electromagnetic and isospin-breaking effects. Its lifetime is predicted to be significantly shorter (3–6 times) than that of the $\Xi_{cc}^{++}$ due to $W$-exchange contributions and destructive Pauli interference.
• Historical Conflict: The SELEX collaboration previously claimed an observation of the $\Xi_{cc}^+$ with a mass of $\approx 3519$ MeV/$c^2$. However, this mass was $\approx 100$ MeV/$c^2$ lower than the established $\Xi_{cc}^{++}$ mass ($\approx 3621$ MeV/$c^2$), contradicting theoretical expectations. Subsequent searches by FOCUS, BaBar, Belle, and LHCb (Run 1 & 2) failed to confirm the SELEX result, leaving the existence and properties of the $\Xi_{cc}^+$ unresolved.
• Objective: To definitively observe the $\Xi_{cc}^+$ using the upgraded LHCb Run 3 detector, measure its mass, and determine the mass difference relative to the $\Xi_{cc}^{++}$ to test theoretical predictions and resolve the SELEX discrepancy.

2. Methodology

The analysis utilizes proton-proton ($pp$) collision data collected in 2024 at a center-of-mass energy of $\sqrt{s} = 13.6$ TeV, corresponding to an integrated luminosity of 6.9 fb$^{-1}$.

• Decay Channel: The search focuses on the decay chain:
  $$\Xi_{cc}^+ \to \Lambda_c^+ K^- \pi^+$$
  where the $\Lambda_c^+$ is reconstructed via $\Lambda_c^+ \to p K^- \pi^+$.
• Control Mode: The decay $\Xi_{cc}^{++} \to \Lambda_c^+ K^- \pi^+ \pi^+$ is used as a control mode to calibrate the mass scale, optimize selection criteria, and validate the simulation.
• Detector and Trigger: The analysis leverages the LHCb Run 3 detector, which features a fully software-based trigger. This allows for a 2–4 times improvement in trigger efficiency for hadronic decays compared to Run 2, crucial for capturing the short-lived $\Xi_{cc}^+$.
• Event Selection:
  • Reconstruction: Candidates are formed by combining a reconstructed $\Lambda_c^+$ with additional charged tracks ($K^-$ and $\pi^+$).
  • Vertexing: Strict requirements are applied to vertex quality, ensuring the $\Xi_{cc}^+$ decay vertex is displaced from the primary vertex (PV) and upstream of the $\Lambda_c^+$ decay vertex.
  • Kinematics: Candidates must have transverse momentum $p_T > 3$ GeV/$c$.
  • Multivariate Analysis (MVA): Two Boosted Decision Tree (BDT) classifiers are employed:
    1. To select $\Lambda_c^+$ candidates (trained on data with sPlot background subtraction).
    2. To select $\Xi_{cc}^+$ candidates (trained on simulated signal and wrong-sign data combinations).
• Mass Calibration: The invariant mass is calculated using a "constrained" method to improve resolution:
  $$m_{cand}(\Xi_{cc}^+) = m(\Lambda_c^+ K^- \pi^+) - m([pK^-\pi^+]_{\Lambda_c^+}) + M_{PDG}(\Lambda_c^+)$$
  This technique reduces the impact of momentum scale uncertainties by referencing the well-known $\Lambda_c^+$ mass.
• Systematic Corrections: Corrections are applied for biases induced by multiple scattering and final-state radiation (FSR). The momentum scale is calibrated using $J/\psi \to \mu^+\mu^-$ and $B^+ \to J/\psi K^+$ decays.

3. Key Contributions

• First Run 3 Observation: This is the first observation of a new particle made with the LHCb Run 3 detector, demonstrating the efficacy of the upgraded trigger and reconstruction systems.
• Resolution of the SELEX Anomaly: The analysis definitively rules out the low-mass state claimed by SELEX ($\approx 3519$ MeV/$c^2$) and confirms the existence of the $\Xi_{cc}^+$ at a mass consistent with the $\Xi_{cc}^{++}$.
• Precision Mass Measurement: Provides the most precise measurement of the $\Xi_{cc}^+$ mass to date, including a detailed breakdown of uncertainties related to the unknown lifetime.

4. Results

• Observation Significance: A clear signal structure is observed in the $\Lambda_c^+ K^- \pi^+$ mass spectrum with a statistical significance exceeding 7 standard deviations ($\sigma$).
• Signal Yield: The fitted signal yield is $915 \pm 120$ events.
• Mass Measurement:
  The mass of the $\Xi_{cc}^+$ is measured to be:
  $$M(\Xi_{cc}^+) = 3619.97 \pm 0.83 \text{ (stat)} \pm 0.26 \text{ (syst)} \begin{smallmatrix} +1.90 \\ -1.30 \end{smallmatrix} \text{ (lifetime)} \text{ MeV}/c^2$$
  • The "lifetime" uncertainty arises because the selection efficiency depends on the particle's flight distance, which is a function of its unknown lifetime. The baseline assumption is 45 fs, with a range of 15–160 fs.
• Mass Difference: The mass difference between the $\Xi_{cc}^+$ and $\Xi_{cc}^{++}$ is determined to be:
  $$\Delta M = M(\Xi_{cc}^+) - M(\Xi_{cc}^{++}) = -1.77 \pm 0.84 \text{ (stat)} \pm 0.15 \text{ (syst)} \begin{smallmatrix} +1.90 \\ -1.30 \end{smallmatrix} \text{ (lifetime)} \text{ MeV}/c^2$$
  This negative value (indicating $\Xi_{cc}^+$ is lighter) is consistent with theoretical predictions involving QCD and QED effects.
• Comparison with SELEX: The observed mass is $101 \pm 2$ MeV/$c^2$ higher than the SELEX claim, confirming that the SELEX state was not the $\Xi_{cc}^+$ baryon.
• Cross-Check: A re-analysis of Run 2 data (2016–2018) using improved selection criteria also reveals a $4\sigma$ signal with a consistent mass ($3620.8 \pm 2.2$ MeV/$c^2$), reinforcing the Run 3 result.

5. Significance

• Validation of QCD: The observation confirms the existence of the isospin partner to the $\Xi_{cc}^{++}$, validating the constituent quark model and theoretical predictions regarding mass splittings in doubly heavy baryons.
• Technological Milestone: The success of the Run 3 detector and its fully software-based trigger in capturing rare, short-lived heavy-flavor decays marks a significant advancement in experimental particle physics capabilities.
• Future Physics: The precise measurement of the mass difference provides a stringent test for lattice QCD and effective field theories. Furthermore, the observation opens the door for future measurements of the $\Xi_{cc}^+$ lifetime and CP violation studies in the charm sector, which are currently limited by the lack of a confirmed signal.
• Resolution of Discrepancy: The paper effectively closes the chapter on the SELEX anomaly, clarifying that the previously claimed low-mass state was likely a background fluctuation or a different physical process, and establishing the correct mass scale for the doubly charmed baryon system.