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Study of $\chi_{\mathrm{c}}$ production in pPb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 8.16 TeV

This paper presents a study of prompt $\chi_{\mathrm{c1}}$ and $\chi_{\mathrm{c2}}$ production in pPb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 8.16 TeV using CMS data, finding that their production ratio is independent of event multiplicity and kinematic variables, and shows no strong relative modification compared to proton-proton collisions, unlike the behavior observed for $\psi$ (2S) states.

Original authors: CMS Collaboration

Published 2026-07-21

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: CMS Collaboration

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Cosmic Dance of Tiny Particles

Imagine the universe as a giant, chaotic dance floor where the smallest building blocks of matter are constantly bumping into each other. Sometimes, these particles crash so hard that they create new, exotic forms of matter that exist for only a fleeting instant before vanishing. This is the world of high-energy physics, a field dedicated to smashing particles together at near-light speeds to see what happens. One of the most interesting "dancers" in this arena is the quarkonium, a tiny, heavy atom made of a charm quark and its anti-particle. Think of it like a microscopic solar system where two heavy planets orbit each other so tightly they form a single, compact unit.

Scientists are particularly interested in how these tiny atoms behave when the dance floor gets crowded. In the real world, we know that if you squeeze a balloon, it changes shape. In the subatomic world, when particles collide inside a dense environment (like the core of a heavy nucleus), these quarkonium atoms might get squished, broken apart, or slowed down by the surrounding "crowd" of other particles. This is called the "nuclear medium effect." By studying how these atoms change when they travel through a heavy nucleus (like lead) compared to when they travel through empty space (like in a proton-only collision), physicists hope to understand the rules of this dense environment. This is crucial because it helps us figure out what happened in the very first moments of the universe, right after the Big Bang, when everything was incredibly hot and dense.

The Paper's Story: A Tale of Two Cousins

In this paper, the CMS Collaboration at CERN's Large Hadron Collider (LHC) decided to play detective with a specific pair of these tiny atoms: the $\chi_{c1}$ and $\chi_{c2}$ . You can think of these two as cousins in the quarkonium family. They are both "P-wave" states, which is a fancy way of saying they have a specific type of spin and orbit that makes them slightly larger and less tightly bound than the most famous member of the family, the $J/\psi$ . Because they are cousins, they have very similar sizes and shapes, but they have slightly different masses and internal structures.

The big question the scientists wanted to answer was: If we smash protons into lead nuclei, do these two cousins get treated differently?

To find out, the team used data from 175 nanobarns of collisions (a tiny amount of data, but enough to see these rare events) collected in 2016. They looked for these particles by watching how they decay. The $\chi_{c}$ particles are unstable and quickly break apart into a $J/\psi$ particle and a photon (a particle of light). The $J/\psi$ then breaks into two muons (heavy electrons), and the photon converts into an electron-positron pair. By tracking these specific decay products, the scientists could count how many $\chi_{c1}$ and $\chi_{c2}$ particles were produced.

What they found:
The researchers measured the ratio of how often $\chi_{c2}$ is produced compared to $\chi_{c1}$ . They checked this ratio under three different conditions:

Crowd Size: Did the ratio change if the collision produced a lot of other particles (high multiplicity) or just a few?
Speed: Did the ratio change depending on how fast the particles were moving (transverse momentum)?
Direction: Did the ratio change depending on which way the particles were flying (rapidity)?

The answer was surprisingly simple: No change. The ratio of $\chi_{c2}$ to $\chi_{c1}$ remained constant, regardless of how crowded the collision was, how fast the particles were moving, or where they were heading.

Why this matters:
This result is a bit of a twist compared to what scientists have seen with other particles. For example, when they look at the $J/\psi$ and its excited cousin, the $\psi(2S)$ , they see that the $\psi(2S)$ gets suppressed (broken apart) much more easily in crowded collisions. This is because the $\psi(2S)$ is larger and looser, making it easier for the "crowd" to knock it apart.

However, the $\chi_{c1}$ and $\chi_{c2}$ are so similar in size (both about 0.39 femtometers across) that the nuclear medium treats them exactly the same. The dense environment created in the proton-lead collisions is powerful enough to tell the difference between a small, tight atom and a large, loose one, but it isn't sensitive enough to tell the difference between these two very similar cousins.

How sure are they?
The scientists are quite confident in this finding, though they note that their measurements have some uncertainty (around 16–17%), mostly due to the difficulty of detecting the photons involved. Despite this margin of error, the data consistently shows a flat line. The ratio doesn't wiggle or shift. This suggests that, within the limits of their current tools, the proton-lead environment does not differentiate between these two specific P-wave states. It's as if the "crowd" at the dance floor is too busy to notice the tiny difference in the dance moves of these two specific cousins, even though it can easily spot the difference between a solo dancer and a large group.

In short, this paper tells us that while the nuclear medium is a powerful force capable of breaking apart larger, looser atoms, it leaves the relative production of these two similar-sized P-wave charmonium states completely untouched.

Technical Summary: Study of $\chi_c$ Production in pPb Collisions at $\sqrt{s_{NN}} = 8.16$ TeV

Problem and Motivation
The production of quarkonia in proton-nucleus (pA) collisions serves as a critical probe for understanding the interplay between initial-state cold nuclear matter effects and final-state interactions. While initial-state effects, such as modifications to parton kinematics, are expected to impact all quarkonium states similarly, final-state mechanisms like coherent energy loss and breakup by comoving particles can induce state-dependent modifications. Previous studies have established that excited S-wave states, such as the $\psi(2S)$ , exhibit significantly different suppression behaviors compared to their ground states ( $J/\psi$ ) in pA collisions, a trend often attributed to the larger spatial size and weaker binding energy of the excited states. However, the behavior of P-wave charmonium states, specifically the $\chi_{c1}(1P)$ and $\chi_{c2}(1P)$ , remains less explored. These states possess binding energies and radii intermediate between the $J/\psi$ and $\psi(2S)$ , offering a unique testing ground to determine if dissociation mechanisms are driven primarily by geometric size or by finer details such as spin configuration and binding energy splittings.

Methodology
This analysis utilizes data collected by the CMS experiment during proton-lead (pPb) collisions at a center-of-mass energy per nucleon pair of $\sqrt{s_{NN}} = 8.16$ TeV, corresponding to an integrated luminosity of $175 \text{ nb}^{-1}$ . The study focuses on the prompt production of $\chi_{c1}$ and $\chi_{c2}$ mesons via the radiative decay chain $\chi_c \to J/\psi \gamma$ , followed by $J/\psi \to \mu^+\mu^-$ . The photon is reconstructed through its conversion into an electron-positron pair ( $e^+e^-$ ) within the detector material, a method chosen for its superior momentum resolution for low-momentum photons compared to electromagnetic calorimetry.

The analysis employs a two-tiered trigger system, selecting events with two muon candidates at the hardware level. Offline reconstruction utilizes the particle-flow algorithm to identify muons, electrons, and photons. Signal extraction is performed by fitting the invariant mass distribution of the $\chi_c$ candidates. The signal model consists of two double-sided crystal-ball (DCB) functions representing the $\chi_{c1}$ and $\chi_{c2}$ peaks, superimposed on a threshold function describing the combinatorial background. The ratio of production cross sections times branching fractions, $R = [\sigma(\chi_{c2})\mathcal{B}(\chi_{c2} \to J/\psi \gamma)] / [\sigma(\chi_{c1})\mathcal{B}(\chi_{c1} \to J/\psi \gamma)]$ , is measured as a function of the event charged-particle multiplicity ( $N_{\text{tracks}}$ ), the $J/\psi$ transverse momentum ( $p_T$ ), and rapidity ( $y$ ).

Systematic uncertainties are evaluated through various methods, including Gaussian-constraint fitting, alternative photon conversion selections, and data-driven efficiency checks using $\pi^0 \to \gamma\gamma$ decays. The analysis accounts for potential polarization effects by assuming specific helicity configurations ( $J_z=0$ for both states) based on prior $pp$ measurements, noting that the ratio is sensitive to polarization assumptions. Non-prompt $J/\psi$ contributions from $b$ -hadron decays are suppressed using proper decay length criteria.

Key Results
The measured $\chi_{c2}$ -to- $\chi_{c1}$ ratio is found to be consistent with a constant value across the entire kinematic range studied:

Multiplicity Dependence: The ratio shows no significant dependence on the event charged-particle multiplicity ( $N_{\text{tracks}}$ ). A constant fit yields $C = 0.23 \pm 0.03$ .
Kinematic Dependence: The ratio remains stable as a function of the $J/\psi$ transverse momentum ( $6.5 < p_T < 30$ GeV) and rapidity ( $|y| < 2.4$ ).
Comparison with Baselines: The results are consistent with existing proton-proton ($pp$) measurements at $\sqrt{s} = 7$ TeV from ATLAS and CMS, as well as with LHCb measurements in the forward region. The observed ratio is approximately $0.22\text{--}0.23$ , with total systematic uncertainties ranging from 16% to 17%, dominated by photon conversion efficiency and non-prompt contamination.

Significance and Claims
The paper concludes that the relative production of the $\chi_{c1}$ and $\chi_{c2}$ states remains unmodified in pPb collisions within the current experimental uncertainties. This finding stands in contrast to the S-wave sector, where a strong multiplicity-dependent suppression of the $\psi(2S)$ relative to the $J/\psi$ has been observed.

The authors interpret this stability as evidence that the dissociation or final-state modification mechanisms in the pPb medium do not differentiate between the $\chi_{c1}$ and $\chi_{c2}$ states. Given that these two P-wave states share nearly identical radii ( $\sim 0.39$ fm) despite their mass splitting ( $\Delta M \approx 45$ MeV), the results suggest that the medium effects are primarily driven by the macroscopic geometric size of the quarkonium state rather than its specific spin configuration or fine-structure binding energy. Consequently, the pPb medium appears capable of resolving the large size disparities between S-wave states (leading to sequential suppression) but lacks the sensitivity to distinguish the subtle internal differences between the P-wave $\chi_c$ states. This provides a baseline for interpreting quarkonium modifications in nucleus-nucleus collisions, indicating that for states of comparable spatial size, relative nuclear modification is absent.

The Cosmic Dance of Tiny Particles

The Paper's Story: A Tale of Two Cousins

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