When are temperature effects included in collisions?

In summary, when two particles collide, their momenta determine the physics of the interaction and ambient temperature is irrelevant. In lead-lead collisions, the environment is also irrelevant. At high temperatures, the symmetry of a scalar field can be restored, potentially making the particles in heavy ion collisions massless. However, the LHC operates at energies far from this scenario. In thermal equilibrium, the rate of a process like \nu n \rightarrow p e is determined by an equation that takes into account the Fermi-Dirac distribution function, but in non-equilibrium conditions like particle collisions in accelerators, we are more interested in the cross-section.
  • #1
geoduck
258
2
When a proton collides with a proton say at the LHC, is vacuum field theory used? It seems like you shouldn't have to include temperature effects since there are only two particles. But then again, all experiments take place at finite temperature, the ambient temperature of the room?

When a heavy ion collides with a heavy ion, I assume you have to use thermal field theory. But what if you collide them really slowly? Also, at high temperatures, symmetry of a scalar field can be restored, i.e., the Higgs vacuum expectation value can be zero again. Does this mean the particles in heavy ion collisions can be massless?

I guess I'm confused about ambient temperature versus collision temperature, how many particles are required to define a thermal system versus a vacuum system, and also about the Higgs field: if the temperature of one part of the universe is really really high, do particles in the vicinity lose mass?
 
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  • #2
When two particles collide their momenta determine the physics of the interaction. Ambient temperature is irrelevant.
 
  • #3
It seems like you shouldn't have to include temperature effects since there are only two particles.
Right.

In lead-lead collisions, the collision partners can produce a small, hot volume (with temperatures of the order of 100 MeV), but the environment is always irrelevant.

Also, at high temperatures, symmetry of a scalar field can be restored, i.e., the Higgs vacuum expectation value can be zero again. Does this mean the particles in heavy ion collisions can be massless?
The LHC is far away from those energies.
 
  • #4
I am also having this kind of question, for example if someone wants to study the Big Bang Nucleosynthesis, he can find there that the width for the interaction:

[itex] \nu n \rightarrow p e [/itex]
is given by:

[itex] \Gamma = \int d \Pi \bar{\delta} |M_{\nu n \rightarrow p e}|^{2} f_{n} f_{\nu} (1-f_{p})(1-f_{e})[/itex]
where by [itex] d \Pi[/itex] I mean the product of each momentum phase space, [itex]M[/itex] is the interaction invariant matrix element, [itex]\bar{\delta}[/itex] the appropriate delta function to conserve 4momentum and [itex]f_{i}[/itex] the Fermi-Dirac distribution function.
Why in general don't we take the last into account in other interactions such as the pp collision?
If it's already been answered by someone above, I am sorry but I didn't "get" the answer.
 
  • #5
Your equation here considers the rate of this process in thermal equilibrium, with many neutrinos and neutrons flying around.
Collisions in particle accelerators are far away from this equilibrium, and we are interested in the cross-section instead of the rate (the rate then just follows from geometry).
 

1. When do temperature effects need to be included in collisions?

Temperature effects need to be included in collisions when the particles involved have a significant amount of thermal energy, typically at higher temperatures. This is because temperature affects the speed and motion of particles, which can impact the outcome of a collision.

2. How are temperature effects included in collisions?

Temperature effects are included in collisions by considering the kinetic energy of the particles involved. This can be done by using equations such as the Maxwell-Boltzmann distribution, which describes the distribution of speeds of particles in a gas at a given temperature.

3. What is the role of temperature in the collision theory?

In the collision theory, temperature is a key factor that influences the rate and likelihood of successful collisions between particles. Higher temperatures result in faster moving particles, increasing the frequency of collisions and the chances of particles overcoming activation energy barriers.

4. Can temperature effects be neglected in collisions?

In some cases, temperature effects can be neglected in collisions, such as when the temperature difference between the reactants and products is small. However, at higher temperatures, neglecting temperature effects can lead to inaccurate results and should be considered in collision calculations.

5. How does temperature affect the energy of collisions?

Temperature affects the energy of collisions by increasing the kinetic energy of particles. This results in higher collision energies, which can lead to more frequent and successful collisions between particles. Additionally, temperature can also affect the activation energy required for a reaction to occur, which can impact the energy of collisions.

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