Study of the thermodynamic properties of hot QCD matter with the CMS experiment

This paper presents recent CMS measurements at the LHC that extract the squared speed of sound of hot QCD matter from ultra-central PbPb collisions, yielding a value of $c_s^2 = 0.241 \pm 0.002\, (\mathrm{stat}) \pm 0.016\, (\mathrm{syst})$ at $T_{\mathrm{eff}} \approx 219\,\mathrm{MeV}$ which aligns well with lattice-QCD predictions, alongside complementary studies in pPb collisions to probe quark-gluon plasma signatures in smaller systems.

The Gist

Imagine you are trying to understand how a giant, invisible balloon behaves when you squeeze it. In the world of particle physics, scientists at the Large Hadron Collider (LHC) smash heavy lead atoms together at nearly the speed of light. When they do this, they create a tiny, super-hot drop of "soup" made of the smallest building blocks of the universe (quarks and gluons). This soup is called the Quark-Gluon Plasma (QGP).

The paper you are reading is a report from the CMS experiment, a massive detector at the LHC, describing how they measured the "stiffness" of this cosmic soup.

Here is the breakdown of their work in simple terms:

1. The Goal: Measuring the "Stiffness" of the Universe's Soup

In everyday life, if you push on a sponge, it squishes easily. If you push on a steel block, it barely moves. In physics, this resistance to being squeezed is related to the speed of sound.

• In a soft, squishy material, sound travels slowly.
• In a stiff, rigid material, sound travels fast.

The scientists wanted to find out: How stiff is this super-hot quark-gluon soup? Specifically, they wanted to measure the "squared speed of sound" (a fancy way of saying how the pressure changes as you add more energy).

2. The Method: The "Crowded Party" Analogy

To measure this, the scientists didn't just look at one collision. They looked at thousands of lead-lead collisions and grouped them by how "crowded" the party was.

• The Setup: They focused on the most extreme collisions, called "ultra-central" collisions. Imagine two billiard balls hitting each other dead-center. In these crashes, the size of the "room" (the volume) is fixed by the size of the lead atoms.
• The Variable: Even though the room size is fixed, the number of people in the room (the number of particles created) varies slightly from crash to crash.
• The Logic: The scientists reasoned that if you pack more people (particles) into the same-sized room, the room gets hotter and more pressurized. By measuring how much the "temperature" (represented by the average speed of the particles) went up when they added more "people" (particles), they could calculate the stiffness of the soup.

They used a clever formula: If you know how much the crowd size changed, and you know how much the temperature changed, you can figure out how stiff the soup is.

3. The Results: It's a "Perfect Liquid"

The team found a specific number for the stiffness: 0.241.

• What does this mean? This number matches almost perfectly with predictions made by super-computers using "Lattice QCD" (a complex mathematical way of simulating the strong force).
• The Conclusion: This confirms that the matter created in these collisions behaves like a "perfect liquid." It flows with almost no friction (viscosity), much like a magical fluid that is incredibly smooth and efficient. This proves that at these extreme temperatures, the universe behaves exactly as our best theories predict.

4. The Side Quest: Smaller Systems (pPb)

The scientists also tried this experiment with proton-lead (pPb) collisions.

• The Analogy: If lead-lead collisions are like two huge trucks crashing, proton-lead collisions are like a small motorcycle crashing into a truck.
• The Question: Can you make this "perfect liquid" soup in such a small crash?
• The Finding: In the biggest motorcycle crashes (high-multiplicity events), they saw hints that the soup might be forming there too. The results were consistent with the big truck crashes, suggesting that even in these tiny systems, the matter might act like a fluid. However, the signal is much fainter, and the math is trickier because the "room" isn't as symmetrical.

5. What They Did Not Do

It is important to note what this paper is not about:

• It does not discuss how this helps build new engines or medical devices.
• It does not claim to solve the mysteries of the entire universe's history right now.
• It is purely a measurement of the fundamental properties of matter under extreme heat.

Summary

In short, the CMS team acted like cosmic chefs. They smashed atoms together to cook up a tiny drop of the universe's hottest soup. By counting how many ingredients they used and measuring how hot the soup got, they calculated exactly how "stiff" the soup is. The result? The soup is a "perfect liquid," and its behavior matches our best computer simulations of the universe's fundamental rules.

Technical Summary

Technical Summary: Study of the Thermodynamic Properties of Hot QCD Matter with the CMS Experiment

Problem and Motivation
The primary objective of this work is to extract the squared speed of sound ($c_s^2$) of strongly interacting matter at extreme temperatures. This parameter is a fundamental component of the equation of state (EoS) for the quark-gluon plasma (QGP), a deconfined state of quarks and gluons created in ultrarelativistic heavy-ion collisions. While the QGP is well-described by relativistic hydrodynamics as an almost "perfect liquid," precise experimental constraints on its EoS, particularly the relationship between pressure and energy density, remain critical. The paper addresses the challenge of measuring $c_s^2$ in ultra-central lead-lead (PbPb) collisions and explores whether similar thermodynamic properties can be extracted in smaller proton-lead (pPb) systems, where the formation of a QGP is still under active investigation.

Methodology
The analysis utilizes data collected by the CMS experiment at the LHC. The methodology relies on a novel approach proposed in Ref. [8], which exploits the thermodynamic relation between the mean transverse momentum ($\langle p_T \rangle$) and charged-particle multiplicity ($N_{ch}$) in ultra-central collisions.

• Experimental Setup:
  • PbPb Collisions: Data from 2018 at $\sqrt{s_{NN}} = 5.02$ TeV (integrated luminosity 0.607 nb$^{-1}$) were used. Ultra-central events (near-zero impact parameter) were selected using the Hadron Forward (HF) calorimeters and Zero-Degree Calorimeters (ZDCs) to reject pileup.
  • pPb Collisions: Data from 2016 at $\sqrt{s_{NN}} = 5.02$ TeV and 8.16 TeV were analyzed to investigate high-multiplicity events.
• Reconstruction and Corrections:
  • Charged-particle tracks were reconstructed within specific pseudorapidity ranges ($|\eta| < 0.5$ for PbPb, $|\eta| < 1.5$ for pPb) and transverse momentum thresholds ($p_T > 0.3$ GeV).
  • Tracking efficiency and misreconstruction rates were evaluated using HYDJET events with full GEANT4 detector simulation. Correction factors were applied as functions of $\eta$, $p_T$, and detector occupancy.
  • $p_T$ spectra were extrapolated to the full range using Hagedorn function fits to avoid bias.
• Observable Definition:
  • The core observable is the normalized mean transverse momentum ($\langle p_T \rangle_{norm}$) as a function of normalized charged-particle multiplicity ($N_{ch}^{norm}$).
  • The squared speed of sound is extracted by fitting the relation:
    $$\langle p_T \rangle_{norm} = \left( \frac{N_{ch}^{norm}}{\langle N_{ch}^{knee} | N_{ch}^{norm} \rangle} \right)^{c_s^2}$$
    where the term in the denominator accounts for the "knee" in the multiplicity distribution at zero impact parameter.
  • For pPb collisions, a two-energy method was employed, fitting $\langle p_T \rangle = C N_{ch}^{c_s^2}$ across different collision energies at fixed centrality intervals.

Key Results

• PbPb Collisions:
  • The analysis of ultra-central PbPb collisions reveals a weak decline in $\langle p_T \rangle_{norm}$ followed by a steep rise at high multiplicities, consistent with hydrodynamic expectations where system volume saturates and temperature increases with entropy density.
  • Fitting the high-multiplicity region ($N_{ch}^{norm} > 1.14$) yields:
    $$c_s^2 = 0.241 \pm 0.002 \text{ (stat)} \pm 0.016 \text{ (syst)}$$
    at an effective temperature of $T_{eff} = 219 \pm 8 \text{ (syst)}$ MeV.
  • This result shows excellent agreement with Lattice QCD calculations and the TRAJECTUM hydrodynamic simulation.
• pPb Collisions:
  • In pPb collisions, the quantity $d \ln \langle p_T \rangle / d \ln N_{ch}$ was studied as a function of $T_{eff}$.
  • Under a boost-invariant scenario ($T_{eff} \approx \langle p_T \rangle / 3$), pPb results agree well with Lattice QCD and PbPb data, extending the temperature coverage.
  • Under a three-dimensional evolution scenario ($T_{eff} \approx \langle p_T \rangle / 2.45$), the agreement with Lattice QCD worsens, with data lying 1–2 standard deviations below predictions.
  • The HIJING Monte Carlo model fails to describe the rising trend observed at the highest multiplicities in pPb collisions, suggesting that non-thermal mechanisms alone cannot explain the collectivity observed in these small systems.

Significance and Claims
The paper claims that the precise measurement of $c_s^2$ in ultra-central PbPb collisions provides strong evidence for the formation of a deconfined QCD phase at LHC energies. The agreement between the extracted $c_s^2$ and Lattice QCD calculations validates the use of hydrodynamic probes to study the thermodynamic properties of the QGP.

Regarding smaller systems, the authors state that while thermodynamic descriptions appear applicable to high-multiplicity pPb events under certain assumptions, the interpretation is highly sensitive to the dynamical evolution model (boost-invariant vs. 3D). The work highlights the need for refined theoretical modeling of system-size effects and the relationship between $\langle p_T \rangle$ and effective temperature. The paper concludes by noting that future extensions to other collision systems (e.g., O-O, Ne-Ne) and more sophisticated fluctuation analyses will further constrain the EoS of hot QCD matter.