Cross section for two identical particles in the final state

In summary, the conversation discusses a calculation of cross section for a particular decay and the discrepancy of a factor of half from the known value. It is mentioned that the decay involves two identical particles in the final state, and there is a rule of not summing over diagrams that differ only by vertex permutation. The speaker also mentions a reference for this statement and clarifies that there is only one vertex involved in the decay of Higgs into two Z bosons. The factor of two discrepancy is explained by the integration over the momenta of the two Z particles, where counting the points separately leads to the same point in phase space due to the identical particles.
  • #1
krishna mohan
117
0
I was calculating the cross section for a particular decay and saw that I was off by a factor of half from the known value..


Now, the decay has two identical particles in the final state and I seem to remember having read somewhere that this requires a factor of half...but I am not able to find the statement in standard books like Peskin(P93-symmetry factors)...maybe it is given somewhere else in Peskin...

Could anyone give me a reference for the above statement?
 
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  • #2
The rule is that you don't sum over diagrams that differ only by vertex permutation. In your case, two vertices corresponding to final state particles are identical.
 
  • #3
No...in this case there is only one vertex...I was considering the decay of the Higgs into two Z bosons...

But I know now why there is a factor of two...

In calculating the Cross section, we integrate over all the momenta of the two Z particles, say Z_1 and Z_2, with momenta denoted by p_1 and p_2...

But in doing so we count the points

( p_1 = x , p_2 = y ) and (p_1 = y, p_2 = x )

separately...although they are infact one and the same point in phase space since Z_1 and Z_2 are identical particles...
 

FAQ: Cross section for two identical particles in the final state

What is the meaning of "cross section" in particle physics?

The cross section in particle physics is a measure of the probability of a specific interaction occurring between two particles when they collide. It is represented by the symbol σ and is typically measured in units of area.

What does it mean for two particles to be "identical" in the final state?

In particle physics, identical particles refer to particles that are indistinguishable in terms of their properties, such as mass, charge, and spin. This means that they behave in the same way during interactions, leading to the same final state after a collision.

Why is the cross section for two identical particles in the final state important?

The cross section for two identical particles in the final state is important because it can provide information about the underlying physics processes that are occurring during collisions. It can also help determine the fundamental properties of particles, such as their mass and interactions.

How is the cross section for two identical particles in the final state calculated?

The cross section for two identical particles in the final state is calculated using mathematical models and experimental data. It takes into account factors such as the energy of the particles, the angle at which they collide, and the interaction strength between them.

What are some applications of studying the cross section for two identical particles in the final state?

Studying the cross section for two identical particles in the final state can provide insights into the fundamental laws of nature and help us understand the behavior of matter at a subatomic level. It also has practical applications, such as in the development of new technologies and medical treatments.

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