The quark-gluon plasma (QGP) is a state of matter that is believed to have existed in the early universe, shortly after the Big Bang. This state is characterized by the deconfinement of quarks and gluons, the fundamental particles that make up hadrons like protons and neutrons. Understanding the properties of the QGP, including its velocity, is crucial for gaining insights into the fundamental nature of matter and the evolution of the universe.
Measuring the Speed of Sound in Quark-Gluon Plasma
One of the key methods for determining the velocity in quark-gluon plasma is by measuring the speed of sound in this medium. The speed of sound in the QGP is related to the velocity of the particles within the plasma and can be obtained in two ways:
- Pressure-Energy Density Relationship: The speed of sound can be determined from the rate at which pressure changes in response to variations in energy density. This relationship is given by the formula:
c_s^2 = (∂P/∂ε)_s
where c_s is the speed of sound, P is the pressure, ε is the energy density, and the subscript s denotes that the derivative is taken at constant entropy.
- Temperature-Entropy Relationship: Alternatively, the speed of sound can be obtained from the rate at which temperature changes in response to variations in entropy. This relationship is given by:
c_s^2 = (∂P/∂ε)_T = (∂T/∂s)_P / (∂T/∂ε)_P
where T is the temperature and s is the entropy density.
In heavy-ion collisions, the entropy can be inferred from the number of electrically charged particles emitted from the collisions, and the temperature can be deduced from the average transverse momentum of those particles.
Experimental Measurements of the Speed of Sound in Quark-Gluon Plasma
The CMS collaboration at the Large Hadron Collider (LHC) has conducted a study to measure the speed of sound in the quark-gluon plasma. In this study, the researchers used data from lead-lead collisions at an energy of 5.02 trillion electronvolts per pair of nucleons.
The measurement was obtained by determining how the temperature varies with the entropy in central heavy-ion collisions, where the ions collide head-on and overlap almost completely. From this measurement, the CMS collaboration obtained a value for the squared speed of sound in the QGP that is nearly half the speed of light and has a record precision:
c_s^2 = 0.241 ± 0.002 (stat.) ± 0.016 (syst.)
This means that the speed of sound in the quark-gluon plasma is approximately 49% of the speed of light, with a statistical uncertainty of 0.2% and a systematic uncertainty of 1.6%.
Determining the Temperature of Quark-Gluon Plasma
In addition to the speed of sound, the temperature of the quark-gluon plasma can also be determined by measuring the average transverse momentum of the charged particles emitted from the heavy-ion collisions. This is because the transverse momentum of the particles is related to the temperature of the medium they are produced in.
In the CMS study, the effective temperature of the quark-gluon plasma was determined to be:
T = 219 ± 8 MeV
where MeV stands for million electronvolts, a unit of energy commonly used in particle physics.
Relating Velocity to Speed of Sound and Temperature
The speed of sound and temperature measurements in the quark-gluon plasma can be used to determine the velocity of the particles within the plasma. This is because the speed of sound is related to the velocity of the particles through the following relationship:
c_s = sqrt(∂P/∂ρ)
where ρ is the mass density of the plasma.
Furthermore, the temperature of the plasma is related to the average kinetic energy of the particles, which is directly proportional to their velocity. By combining the measurements of the speed of sound and temperature, one can obtain a quantifiable and measurable way to determine the velocity in the quark-gluon plasma.
Numerical Examples and Data Points
To illustrate the application of these principles, let’s consider some numerical examples and data points:
- Speed of Sound Measurement:
- In the CMS study, the squared speed of sound in the quark-gluon plasma was measured to be
c_s^2 = 0.241 ± 0.002 (stat.) ± 0.016 (syst.). -
This corresponds to a speed of sound of
c_s = 0.491 ± 0.002 (stat.) ± 0.016 (syst.)in units of the speed of light. -
Temperature Measurement:
- The effective temperature of the quark-gluon plasma in the CMS study was determined to be
T = 219 ± 8 MeV. -
This temperature corresponds to an average kinetic energy of the particles in the plasma of approximately
219 MeV. -
Velocity Calculation:
- Using the measured speed of sound and temperature, we can estimate the velocity of the particles in the quark-gluon plasma.
- Assuming a typical mass density of the QGP of
ρ = 10^18 kg/m^3, the velocity of the particles can be calculated as:
v = sqrt(∂P/∂ρ) = c_s = 0.491 ± 0.002 (stat.) ± 0.016 (syst.) c - This means that the velocity of the particles in the quark-gluon plasma is approximately 49.1% of the speed of light, with a statistical uncertainty of 0.2% and a systematic uncertainty of 1.6%.
These measurements and calculations provide a quantitative and precise way to determine the velocity in the quark-gluon plasma, which is crucial for understanding the properties and dynamics of this unique state of matter.
Conclusion
Determining the velocity in quark-gluon plasma is a complex but essential task for understanding the fundamental nature of matter and the evolution of the universe. By measuring the speed of sound and temperature in the QGP, researchers can obtain a quantifiable and measurable way to determine the velocity of the particles within this medium. The CMS collaboration’s study has provided a precise measurement of these properties, demonstrating the power of experimental techniques and the importance of continued research in this field.
References
- CERN researchers measure speed of sound in the quark–gluon plasma more precisely than ever before. (2024, February 16). Retrieved June 13, 2024, from https://phys.org/news/2024-02-cern-quarkgluon-plasma-precisely.html
- JYU DISSERTATIONS 460 Quantifying the Transport Properties of Quark-Gluon Plasma through Measurement of Higher Harmonic Flow and Their Non-Linear Response. (2021, May 31). Retrieved June 13, 2024, from https://cds.cern.ch/record/2791172/files/CERN-THESIS-2021-209.pdf
- Quark-Gluon Plasma 6. (2024, February 10). Retrieved June 13, 2024, from https://arxiv.org/html/2402.10183v2
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