Wednesday, March 13, 2019

nuclear physics - Does the Breit Wigner formula apply to intermediate virtual particles?


Breit Wigner Formula describes the cross section for interactions that proceed dominantly via a intermediate particle (O*) A+B → O* → C + D:


$$σ = \frac{2\Pi}{k^{2}}\frac{Γ_{i}Γ_{f}}{(E-E_{o})^{2} + (Γ/2)^{2}}$$


A short question: Does the formula apply to situations when the intermediate particle is actually virtual?


For example, in positron electron annihilation, they form a photon which might eventually decay into another two particles. Can we calculate the resonant cross section for this process with the Breit Wigner Formula as well? If it is possible, what should we put in for $E_0$, which is supposed to be the rest mass of the intermediate particle?




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