Pair production in boson-boson collision

In summary, the interaction Lagrangian involves an electron, a neutral scalar field, and a coupling constant. The task is to calculate the amplitude for a process involving two electrons and two neutral bosons, with two Feynman diagrams contributing to the matrix element. There is no relative minus sign due to the outgoing fermions being non-identical. The propagator remains the same in both cases.
  • #1
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Homework Statement



I'm given this interaction Lagrangian:

[tex]L_I (x) = -g \overline{\psi}(x) \psi (x) \phi (x)[/tex]

where [tex]g[/tex] is the coupling constant, [tex]\psi[/tex] is an electron and [tex]\phi[/tex] is a neutral scalar field. I have to calculate the amplitude for process
[tex] \psi + \psi \rightarrow e^- + e^+[/tex] that is to say that I have to calculate the matrix element

[tex] \langle e^+ (\vec{p}_3) e^- (\vec{p}_4) |S| \phi (\vec{p}_1 ) \phi (\vec{p}_2)\rangle [/tex]


Homework Equations



I'm stuck determining the relative sign of the contributions. I know that there are two Feynman diagrams contributing to the matrix element and that the final fermions are swapped in the two diagrams, so there's a - (minus) sign in the relative contributions.

On the other side, I find that in the first graph the propagator is given by

[tex] \langle 0 | T [\overline{\psi}(x) \psi(y)] |0 \rangle [/tex]

while in the second graph the propagator is given by

[tex] \langle 0 | T [\psi (x) \overline{\psi}(y)] |0 \rangle [/tex]

I just need to know if this change in the propagator adds a new - (minus) sign, so that the relative contributions end up having the same sign or if they ends up having opposite sign.

The Attempt at a Solution



I know thath this is a second order process in g and I know also that the final state is produced by a fermionic propagator between the neutral bosons. I've calculated many similar processes but this question on relative signs of the two contributions is really blocking me.

Sorry for my English, I'm not a native speaker. Thank you in advance for you help.
 
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  • #2
There is no relative minus sign. Physically, this is because the two outgoing fermions are not identical. Or, you can see the two diagrams as related by swapping the two incoming particles, which are identical; but these are bosons, so there is no relative sign.
 
  • #3
Oh well. I've to think about it. I just tought that "swapping" two fermions always lead to a minus sign...
But, about the propagator, it stays the same in both cases?

Thank you for your help
 

Related to Pair production in boson-boson collision

1. What is pair production in boson-boson collision?

Pair production in boson-boson collision is a phenomenon that occurs when two high-energy boson particles collide and produce a pair of particles with opposite charges, such as an electron and a positron. This process is governed by the laws of quantum mechanics and can only occur in the presence of strong electromagnetic fields.

2. What are boson particles?

Boson particles are a type of subatomic particle that have integer spin, in contrast to fermions which have half-integer spin. Examples of bosons include photons, which are the particles of light, and W and Z bosons, which are responsible for the weak nuclear force.

3. How does pair production in boson-boson collision relate to the Standard Model of particle physics?

In the Standard Model of particle physics, boson-boson collisions are one of the ways in which particles interact with each other. The production of new particles through these collisions is a key component of the Standard Model and helps to explain the behavior and interactions of subatomic particles.

4. What is the significance of studying pair production in boson-boson collision?

Studying pair production in boson-boson collision allows scientists to better understand the fundamental forces and particles that make up the universe. It also has practical applications in fields such as particle accelerators and medical imaging technology.

5. Can pair production in boson-boson collision be observed in experiments?

Yes, pair production in boson-boson collision has been observed in various experiments, including those conducted at the Large Hadron Collider (LHC) in Switzerland. These experiments provide valuable data and insights into the behavior of particles and the laws of physics.

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