# Mass, fine structure constant & annihilation

Hi,

If the mass is very high and the fine structure constant very small, is it true particles of opposite charge can't annihilate? If yes. What has mass and fine structure constant got to do with annihilation?

## Answers and Replies

fzero
Homework Helper
Gold Member
Hi,

If the mass is very high and the fine structure constant very small, is it true particles of opposite charge can't annihilate?

A particle and its antiparticle are always allowed to annihilate.

If yes. What has mass and fine structure constant got to do with annihilation?

The mass, momenta and fine structure constant all enter into the amplitude for annihilation of charged particles. So they all have an effect on the relative probability that the particle and antiparticle annihilate instead of just scattering from one another.

A particle and its antiparticle are always allowed to annihilate.

The mass, momenta and fine structure constant all enter into the amplitude for annihilation of charged particles. So they all have an effect on the relative probability that the particle and antiparticle annihilate instead of just scattering from one another.

I was scrutinizing this paper submitted in the Physical Review D (a valid mainstream journal) written by Caltech physicists:

http://authors.library.caltech.edu/13143/1/ACKprd09.pdf

It is mentioned:

"We explore the feasibility and astrophysical consequences of a new long-range U(1) gauge field (‘‘dark electromagnetism’’) that couples only to dark matter, not to the standard model. The dark matter consists of an equal number of positive and negative charges under the new force, but annihilations are suppressed if the dark-matter mass is sufficiently high and the dark fine-structure constant is sufficiently small"

So why is annihilation suppressed if the particles mass is sufficiently high and the dark fine-structure constant is sufficiently small??

fzero
Homework Helper
Gold Member
I was scrutinizing this paper submitted in the Physical Review D (a valid mainstream journal) written by Caltech physicists:

http://authors.library.caltech.edu/13143/1/ACKprd09.pdf

It is mentioned:

"We explore the feasibility and astrophysical consequences of a new long-range U(1) gauge field (‘‘dark electromagnetism’’) that couples only to dark matter, not to the standard model. The dark matter consists of an equal number of positive and negative charges under the new force, but annihilations are suppressed if the dark-matter mass is sufficiently high and the dark fine-structure constant is sufficiently small"

So why is annihilation suppressed if the particles mass is sufficiently high and the dark fine-structure constant is sufficiently small??

Fig. 2 has the leading-order diagrams for annihilation of the DM fermions discussed in the paper. The amplitude for this process contains two factors of $$\sqrt{\hat{\alpha}}$$, one for each vertex, while the presence of the fermion propagator introduces a scale factor of $$1/ m_\chi$$. To obtain the cross section for annihilation in equation (10), this amplitude gets squared, so

$$\sigma\sim \left( \frac{\hat{\alpha}}{m_\chi} \right)^2,$$

which has the claimed suppression properties.

Instead of annihilating, these particles tend to just exchange dark photons when they get near one another.

Fig. 2 has the leading-order diagrams for annihilation of the DM fermions discussed in the paper. The amplitude for this process contains two factors of $$\sqrt{\hat{\alpha}}$$, one for each vertex, while the presence of the fermion propagator introduces a scale factor of $$1/ m_\chi$$. To obtain the cross section for annihilation in equation (10), this amplitude gets squared, so

$$\sigma\sim \left( \frac{\hat{\alpha}}{m_\chi} \right)^2,$$

which has the claimed suppression properties.

Instead of annihilating, these particles tend to just exchange dark photons when they get near one another.

Conceptually speaking. So if let's say the electron and positron were to have sufficiently higher mass and sufficiently smaller fine structure constant. They couldn't annihilate too but just exchange photons when they get near one another??

fzero
Homework Helper
Gold Member
Conceptually speaking. So if let's say the electron and positron were to have sufficiently higher mass and sufficiently smaller fine structure constant. They couldn't annihilate too but just exchange photons when they get near one another??

The probability for annihilation just gets smaller as the mass increases and fine structure constant decreases. It only goes to zero in the singular limits where the fine structure constant is literally zero or the mass is infinite. This isn't really the whole story, because if we were actually talking about the electron, there are other couplings that would allow the electron and positron to annihilate.

If a particle has no couplings to anything else, annihilation is forbidden by energy conservation. There would be no channel for the energy of the particle-antiparticle pair to go anywhere. However there are no completely noninteracting particles known to exist.

The probability for annihilation just gets smaller as the mass increases and fine structure constant decreases. It only goes to zero in the singular limits where the fine structure constant is literally zero or the mass is infinite. This isn't really the whole story, because if we were actually talking about the electron, there are other couplings that would allow the electron and positron to annihilate.

If a particle has no couplings to anything else, annihilation is forbidden by energy conservation. There would be no channel for the energy of the particle-antiparticle pair to go anywhere. However there are no completely noninteracting particles known to exist.

Thanks. I'd like to inquire about plasma. It says "If mx is sufficiently large and alpha is sufficiently small, annihilations of DM particles through the new force freeze out in the early universe and are negligible today, despite there being equal numbers of positively- and negatively-charged particles. The dark matter in our model is therefore a plasma, which could conceivably lead to interesting collective effects in the DM dynamics." and "Although there are new light degrees of freedom, their temperature is naturally lower than that of the SM plasma, thereby avoiding constraints from Big-Bang Nucleosynthesis (BBN)."

So lower temperature plasma they are proposing dark matter to be. We know plasma is only if temperature is high. You think it's possible for dark matter to be lower temperature plasma? Any experimental predictions you can give that can refute or confirm it?

fzero
Homework Helper
Gold Member
So lower temperature plasma they are proposing dark matter to be. We know plasma is only if temperature is high. You think it's possible for dark matter to be lower temperature plasma? Any experimental predictions you can give that can refute or confirm it?

SM matter only forms a plasma at high energies. The fermion considered in the paper is a hidden sector and behaves differently. As for comparison with experiment, I'd suggest reading the rest of the paper. I'm sure they give references to experimental results that would constrain their model.