# A Why do we know that an elementary particle is a point particle?

#### DarMM

Gold Member
Hi, @DarMM

This is way beyond my knowledge, but it sounds very interesting, and if you could explain this further I would be very interested. Particularly what "sharp mass" means.
I am currently gathering all the information required to write this up. It will be a very long set of posts. It was the last thing I promised before going inactive, so I'm working on it.

#### vanhees71

Gold Member
Since when does an electron decay? Within the Standard Model the electron as the lightest charged lepton cannot decay and thus has a sharp mass. It's a stable particle and its Green's function thus has a pole on the real axis of $s=p_{\mu} p^{\mu}$, which defines its mass.

#### A. Neumaier

Since when does an electron decay? Within the Standard Model the electron as the lightest charged lepton cannot decay and thus has a sharp mass. It's a stable particle and its Green's function thus has a pole on the real axis of $s=p_{\mu} p^{\mu}$, which defines its mass.
In QED, the electron mass is a branch point, not a pole, becaiuse of Imfrared effects coming from the zero mass of photons. Thus the electron mass spectrum is continuous.

#### vanhees71

Gold Member
True, but does this imply that the free electron is in fact unstable? If so what's the (theoretical) decay mode, and why isn't this observed?

#### A. Neumaier

True, but does this imply that the free electron is in fact unstable? If so what's the (theoretical) decay mode, and why isn't this observed?
It is a stable infraparticle, which means that it has an additional mass degree of freedom, which formally behaves like an additional momentum dof - the latter generates the continuous spectrum of the energy. In the QM treatment of multielectronic systems, this dof is generally suppressed. Indeed, infrared problems are not much addressed in the literature.

Last edited:

#### A. Neumaier

It is a stable infraparticle, which means that it has an additional mass degree of freedom, which behaves like an additional momentum dof.
Here is more on infraparticles. For more on the branch point of the electron propagator, see, e.g., section II of Thomas Appelquist and J. Carazzone, Infrared singularities and massive fields, Phys. Rev. D 11, 2856–2861 (1975).

"Why do we know that an elementary particle is a point particle?"

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving