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I have a question about understanding the physical interpretation of the thermal mass and width of a particle.

If we consider a particle in a plasma (which lets say is in the early universe and so does not have a "mass" from spontaneous symmetry breaking). The thermal mass of the particle comes from the loop correction to its propagator when it interacts with the plasma.

Essentially the particle cannot travel at the speed of light due to this correction and it has some mass from its interaction with the plasma.

But now how do I understand the thermal width? This is related to the imaginary part of the self-energy. I would like a physical interpretation if possible.

thanks

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  • $\begingroup$ Do you have a concrete example in mind? I have only found references related to quarkonia decays; the physics is nicely explained in arxiv.org/pdf/0706.2183.pdf for instance. $\endgroup$ – xi45 May 16 '16 at 10:36
  • $\begingroup$ I had no particular example in mind. Simply a particle in thermal bath (high temperature and pressure). Thank you for putting this example up, I will have a read and if I get a good explanation I will post it back here so people can see. Thank you again! $\endgroup$ – SAMCRO May 16 '16 at 10:58
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Collisions of a state with other particles, present at finite density, influence the life-time of the state as energy can be transferred to those other particles during inelastic collisions (i.e. they can change state). This change in life-time is related to a change in the width via the uncertainty relation and gives the thermal width.

There is a physical effect known as "collisional broadening" that affects the emission spectrum of gasses at finite density. It occurs because the atoms, during collisions with other atoms of the gas, undergo small temporary changes of the energy levels of their atomic shell. Elastic collisions cause a shift of the spectral lines (thermal mass) and inelastic ones their spectral broadening (thermal width). It can be discussed quantitatively in simple terms and might be the best way to understand these effects. See e.g. Demtroeder - Laser Spectroscopy.

If you are looking at your problem in terms of QFT the analogy is that the states in the medium are not the free quantum states but deformed effective ones that have a different mass and lifetime due to the cumulative interaction with other states in the medium. Colissions with other particles can make a state decay and therfore alter its natural vacuum width. Technically, the real and imaginary parts of a thermal self-energy correspond to the effective mass and in-medium width as you write.

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  • $\begingroup$ Thank you, that was useful. For my purposes, I am thinking of the thermal width as the mean free path of a particle in the plasma. However, I will look up that reference. $\endgroup$ – SAMCRO Jul 27 '16 at 9:37
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    $\begingroup$ See my updates. $\endgroup$ – highsciguy Jul 27 '16 at 11:27

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