Doubt about Bhabha scattering.

[arroy_0205]

I have one doubt about Bhabha scattering which is scattering between one electron and one positron, two oppositely charged particles. Why should they scatter each other away rather than attract and eventually annihilate themselves, giving rise to the pair annihilation process? (This process is dealth with in for example, Peskin-Scroeder's book on QFT). But I do not understand when they would annihilate and when they would scatter each other. Both are described in QED, by exchange of photon. But in one case there is attraction in the other, there is repulsion. How is that possible?

 

[mjsd]

I have one doubt about Bhabha scattering which is scattering between one electron and one positron, two oppositely charged particles. Why should they scatter each other away rather than attract and eventually annihilate themselves, giving rise to the pair annihilation process? (This process is dealth with in for example, Peskin-Scroeder's book on QFT). But I do not understand when they would annihilate and when they would scatter each other. Both are described in QED, by exchange of photon. But in one case there is attraction in the other, there is repulsion. How is that possible?

Firstly, let's make one thing clear: e- and e+ always "attract" each other for they carry opposite charge. A system with an e- and e+ is basically the positronium. "scattering" is just a term to say there is an interaction. Now from QED, there are two possible diagrams that contribute to this (ie. two diagrams with the same initial and final states): one is what you call the annihilation diagram and the other one is the "direct"/"standard" one (strictly speaking you can call it what you want). So when you wish to work out the amplitude/cross-section for this interaction, QED is telling you that there are two ways via which this can happen so you need to consider them both to get the total rate. Namely, e- and e+ go close to each other an interact via a virtual photon or they annihilate each other first then reappear again. NB: you final states e- and e+ will still be attracted to each other via the electromagnetic force. So interpreting that there is a repulsion may be a bit misleading for the "direct" case.

 

[sir-pinski]

This is a valid question and one that may require a deeper understanding of quantum field theory (QFT) to fully grasp. In Bhabha scattering, the electron and positron do indeed have opposite charges and could potentially attract each other. However, the fundamental laws of QFT, specifically the conservation of energy and momentum, dictate that the particles must follow certain rules in their interactions.

In the case of Bhabha scattering, the particles are not simply colliding head-on, but rather they are exchanging virtual photons. These virtual photons carry energy and momentum between the particles, causing them to scatter away from each other. The exchange of virtual photons can also result in the creation of additional particles, such as a photon or a Z boson.

On the other hand, in pair annihilation, the particles are directly interacting and can annihilate each other, resulting in the production of photons or other particles. This process also follows the laws of QFT, where the conservation of energy and momentum must be upheld.

So, in summary, the difference between Bhabha scattering and pair annihilation lies in the specific interactions and exchanges of energy and momentum between the particles. Both processes are described by QFT and are consistent with the fundamental laws of physics. I hope this helps to clarify your doubt about Bhabha scattering.