Breit-Wigner Cross section

[secret2]

Is anyone familiar with Breit-Wigner Cross section? Say, for a reaction with 2 particles in the initial state, 1 intermediate and 2 final:

$$\sigma = \frac{g \pi \lambda^2 \Gamma_i \Gamma_f}{(E-E_0)^2 + \frac{\Gamma^2}{4}}$$

I can't see why for the wavelength we should use the momentum of EITHER one particle in the initial state. Sure, I can choose either one because in the COM frame it doesn't matter which momentua of the initial particles I choose. But in the derivation of the above equation it is not obvious why the momentum cannot be, say, the TOTAL momentum in the lab frame. Afterall, isn't it true that working in the COM frame is simply a convention?

 

[dextercioby]

Okay.Here's my advice:do the computation if the lab frame.From the very beginning till the end.No reference to COM,whatsoever.And then compare the results...

Yes,it is true.Most (if not all) scattering processes are analyzed using the COM reference frame for ease of calculations and for the fact that the COM is ALWAYS an IRS (elementary,relativistic level)...


Daniel.

 

[sir-pinski]

Breit-Wigner cross section is a widely used formula in particle physics to describe the probability of a certain reaction occurring between particles. It is commonly used in the study of resonance phenomena, where an intermediate particle is produced and then quickly decays into final state particles. The formula you have provided is the general form for a reaction with two particles in the initial state, one intermediate particle, and two final state particles.

In regards to your question about the use of momentum in the derivation of the formula, it is important to note that the Breit-Wigner cross section is derived from quantum field theory and takes into account the properties of the particles involved in the reaction. The momentum used in the formula is related to the properties of the intermediate particle, such as its mass and decay width. This momentum is chosen to be that of one of the initial particles because in the COM frame, the momenta of the initial particles are equal and opposite, making it easier to calculate the properties of the intermediate particle.

While it is true that working in the COM frame is a convention, it is a useful one in the context of particle physics as it simplifies calculations and allows for a more intuitive understanding of the interactions between particles. Ultimately, the choice of momentum in the formula is based on the properties of the particles involved and the specific reaction being studied.