Probe charmonium-nucleon interactions in high energy proton-proton collisions

This paper utilizes the EPOS4+CATS framework to dynamically generate non-Gaussian emission sources for charmonium-proton pairs in high-energy pp collisions, enabling the first femtoscopic extraction of charmonium-nucleon interactions while revealing that feed-down from excited states introduces significant uncertainties in prompt $J/\psi$-proton correlation measurements.

The Gist

Imagine you are trying to understand how two very different people interact in a crowded room. One person is a tiny, heavy, and incredibly compact "VIP" (the charmonium, specifically a particle called $J/\psi$), and the other is a regular-sized person (the proton, or nucleon).

In the world of high-energy physics, scientists want to know: How strongly do these two "people" pull on each other or push each other away?

This paper is like a new, high-tech detective story that uses a unique method to figure out this relationship without ever having to stop the party and ask them directly.

The Big Picture: The "Femtoscopy" Detective Tool

Usually, to see how particles interact, scientists smash them together at near-light speed (like at the Large Hadron Collider) and watch what happens. But for these specific particles, it's hard to see the interaction directly.

Instead, the authors use a technique called Femtoscopy. Think of this like sound localization.

• If you hear two people shouting at the same time, the sound waves interfere with each other.
• If they are standing close together, the sound waves mix in a specific way. If they are far apart, they mix differently.
• By listening to the "echo" (the correlation) of the particles as they fly apart, scientists can figure out how close they were when they were born and how they influenced each other.

The New Twist: A Better Map of the "Birthplace"

In previous studies, scientists tried to guess where these particles were born (their "emission source"). They usually assumed the birthplace was a perfect, smooth ball (a Gaussian shape), like a fluffy cloud of smoke.

The breakthrough in this paper:
The authors used a super-complex computer simulation called EPOS4 to actually watch the particles being born. They found that the "birthplace" isn't a perfect fluffy cloud at all. It's lumpy, irregular, and non-Gaussian.

• Analogy: Imagine trying to guess the shape of a crowd of people leaving a concert.
  • Old way: You assume they all leave in a perfect, round circle.
  • New way: You use a drone to film the exit. You see that they are actually spilling out in a weird, jagged shape because of the doors and the crowd's movement.
  • Why it matters: If you use the wrong map (the perfect circle), your calculation of how the particles interact will be wrong. Using the real, lumpy map makes the measurement much more accurate.

The "Ghost" Problem: The Excited States

Here is the tricky part. The "VIP" particle ($J/\psi$) isn't always born directly. Sometimes, it's born as a "heavier, excited cousin" (called $\chi_c$ or $\psi(2S)$) that quickly decays (dies) into the $J/\psi$ we see.

• The Metaphor: Imagine you are trying to measure how a specific type of car (a sedan) interacts with a pedestrian. But, 40% of the time, you are actually seeing a sports car that instantly transforms into a sedan right in front of you.
• The sports car (the excited state) interacts with the pedestrian much more strongly than the sedan does.
• Because the sports car is so "loud" in its interaction, it messes up the data for the sedan. The paper shows that if you ignore these "ghost" sports cars, your measurement of the sedan's interaction will be completely off. In fact, the interaction can even look "negative" (repulsive) because of these stronger, hidden interactions.

What Did They Find?

1. The Interaction is Attractive: The VIP particle and the proton do pull on each other, but it's a weak pull, like a gentle magnet.
2. The Map Matters: By using the realistic, lumpy "birth map" from their computer simulation, they can now extract the true strength of this pull directly from experimental data.
3. The Hidden Danger: The "excited cousins" (the sports cars) create a huge amount of confusion. Even though they don't last long, their strong interaction leaves a big mark on the data, making it hard to see the true behavior of the main particle.

Why Should We Care?

Understanding how these heavy particles interact with normal matter (protons) is like finding a key to a locked room in the universe. It helps us understand:

• The Glue of the Universe: How the "glue" (gluons) holds matter together.
• Exotic Matter: It might help explain strange, heavy particles called "pentaquarks" that scientists have recently discovered.
• The Early Universe: It helps us understand what happened in the first split second after the Big Bang, when the universe was a hot soup of these particles (the Quark-Gluon Plasma).

In short: This paper gives us a sharper pair of glasses (a better simulation of the birthplace) and warns us to watch out for "imposters" (the excited states) so we can finally get a clear picture of how the universe's heavy particles dance with ordinary matter.

Technical Summary

1. Problem Statement

The interaction between charmonium (specifically $J/\psi$) and nucleons ($N$) is a critical topic in nuclear and hadronic physics. It serves as a probe for:

• The gluonic structure of the nucleon and non-perturbative QCD (specifically the trace anomaly contribution to nucleon mass).
• The nature of hidden-charm pentaquarks ($P_c$ states).
• In-medium modifications of charmonium in the Quark-Gluon Plasma (QGP).

While theoretical models (Effective Field Theory, Lattice QCD) suggest an attractive but weak interaction, experimental constraints remain weak. Traditional femtoscopic analyses often rely on the Lednický-Lyuboshits (LL) model, which assumes a Gaussian emission source. However, for rare probes like $J/\psi$ produced in the early stages of collisions, a Gaussian approximation may be invalid, leading to uncertainties in extracting interaction potentials from correlation functions. Furthermore, the contribution of excited charmonium states ($\chi_c$, $\psi(2S)$) via feed-down to the observed prompt $J/\psi$ signal has not been fully quantified in this context.

2. Methodology

The authors employ a novel, fully dynamical framework combining EPOS4 (a Monte Carlo event generator) and CATS (Correlation Analysis Tool using the Schrödinger equation).

• EPOS4 Framework:

  • Used to simulate high-energy $pp$ collisions at $\sqrt{s} = 13$ TeV.
  • Charmonium Production: Utilizes a quantum density matrix formalism based on the projection of $c\bar{c}$ pairs. The $c\bar{c}$ relative distance is modeled as a Gaussian distribution with an effective width $\sigma_{c\bar{c}} \approx 0.3\text{--}0.35$ fm.
  • Source Generation: Unlike previous studies that assumed a static Gaussian source, EPOS4 dynamically generates the emission source of charmonium-proton pairs based on string fragmentation and fluid decay mechanisms.
  • Validation: The model successfully reproduces experimental $J/\psi$ transverse momentum ($p_T$) and rapidity distributions from ALICE and LHCb.

• Interaction Potentials:

  • QCD Multipole Expansion (QCDME): The potential is derived from the chromoelectric dipole coupling, parameterized by the chromoelectric polarizability ($\alpha_\psi$). Two scenarios are tested: perturbative ($\alpha_{J/\psi} = 0.2 \text{ GeV}^{-3}$) and non-perturbative ($\alpha_{J/\psi} = 1.6 \text{ GeV}^{-3}$).
  • HAL QCD: A three-range Gaussian potential derived from Lattice QCD simulations (with physical pion masses) is also used for comparison.
  • Excited States: Since Lattice data for excited states is unavailable, the authors estimate the polarizabilities for $\chi_c$ and $\psi(2S)$ using scaling relations based on the root-mean-square radius and binding energy, finding significantly larger values ($\alpha_{\chi_c} \approx 10.4 \text{ GeV}^{-3}$, $\alpha_{\psi(2S)} \approx 47.7 \text{ GeV}^{-3}$).

• Femtoscopic Calculation:

  • The correlation function $C(k)$ is calculated by convolving the dynamically generated source function $S(r)$ with the scattering wave function $\psi_k(r)$, obtained by solving the radial Schrödinger equation (including partial waves up to $l_{max}=3$).
  • Feed-down: The observed "prompt" correlation is constructed by weighting the direct $J/\psi$ correlation with contributions from $\chi_c$ and $\psi(2S)$ decays (branching ratios $\approx 30\%$ and $61\%$, respectively).

3. Key Contributions

1. Dynamic Source Generation: This is the first study to dynamically generate the charmonium-nucleon emission source using EPOS4 rather than assuming a Gaussian shape.
2. Non-Gaussian Source Discovery: The study reveals that the realistic emission source for charmonium-proton pairs is non-Gaussian, deviating significantly from the standard approximation used in femtoscopy.
3. Feed-down Quantification: The paper provides a rigorous calculation of how excited charmonium states ($\chi_c, \psi(2S)$) affect the observed prompt $J/\psi$ correlation, a factor often neglected or oversimplified.
4. Unified Framework: The EPOS4+CATS approach offers a unified method to probe quarkonium-hadron interactions and simulate correlations for arbitrary hadron pairs.

4. Key Results

• Emission Source Structure: The normalized emission source $S(r)$ for $J/\psi-N$, $\chi_c-N$, and $\psi(2S)-N$ pairs is found to be essentially identical and non-Gaussian. A Gaussian fit with the same RMS radius fails to capture the true shape of the source.
• Correlation Function Sensitivity:
  • The magnitude of the correlation function directly reflects the interaction strength.
  • Using the HAL QCD potential (stronger attraction) yields a different correlation shape compared to the QCDME potentials.
• Impact of Excited States:
  • Although the production yield of excited states is lower than the ground state, their stronger interactions (due to larger polarizabilities) result in correlation functions that can be sizable and even negative.
  • When feed-down is included, the observed prompt $J/\psi-N$ correlation is significantly distorted. The negative correlation from excited states can reduce or invert the positive correlation expected from the ground state, introducing sizable uncertainties in extracting the ground-state interaction if not properly accounted for.
• Spin Dependence: The study calculates spin-averaged correlations ($1/3$ for $S=1/2$, $2/3$ for $S=3/2$), noting that the spin configuration significantly influences the scattering wave function.

5. Significance

• Methodological Advancement: By replacing the static Gaussian source assumption with a dynamically generated one, the paper significantly improves the precision of femtoscopic constraints on charmonium-nucleon interactions.
• Experimental Guidance: The results highlight that future experimental analyses (e.g., at LHC Run 3) must account for the non-Gaussian nature of the source and the substantial feed-down effects from excited states to accurately extract the $J/\psi-N$ scattering length and effective range.
• Theoretical Insight: The finding that excited states induce negative correlations suggests the possible formation of bound states under certain potentials, offering new avenues for investigating hidden-charm pentaquarks and the nature of the QCD trace anomaly.

In conclusion, this work establishes a robust, data-driven framework for probing heavy-light hadronic interactions, demonstrating that accurate extraction of interaction potentials requires a realistic treatment of both the emission source and the complex feed-down hierarchy of charmonium states.