How Do You Calculate Total Angular Distribution in Particle Decay?

In summary, when finding the total angular distribution of particles produced in a decay, you can sum the two terms |Y^0_0|^2+|Y^1_1|^2 if the parity is conserved, but if it is not, you will need to use the formula |Y^0_0 + Y^1_1|^2 to account for the parity violation.
  • #1
eoghan
210
7
Hi there!
I have to find the angular distribution of a decay where I suppose I don't know if the parity is conserved. I made my calculus and I found that I have two possible final states, one with total angular momentum L=0, m=0 and one with L=1, m=1. Now I have to find the total angular distribution of the particles produced: I know that in the first state the eigenstate is Y(0,0) (Y(l,m) is the spherical harmonic), while in the second one the eigenstate is Y(1,1). How do I find the total distribution? Should I sum
[tex]|Y^0_0|^2+|Y^1_1|^2[/tex]
or should I sum
[tex]|Y^0_0 + Y^1_1|^2[/tex]?
In either case I don't find a normalized distribution
Thanks
 
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  • #2
in advance!If the parity is conserved then you can sum the two terms, |Y^0_0|^2+|Y^1_1|^2. This will give you the normalized angular distribution. However, if the parity is not conserved then you will have to use the formula |Y^0_0 + Y^1_1|^2. This will give you the normalized angular distribution, but it will also take into account the parity violation.
 

FAQ: How Do You Calculate Total Angular Distribution in Particle Decay?

What is the purpose of summing distributions?

The purpose of summing distributions is to combine multiple probability distributions into a single distribution. This can help to simplify complex models and make predictions about combined variables.

How do you sum distributions?

To sum distributions, you can add the corresponding probabilities of each value in the distributions. This can be done by hand or with the use of software such as Excel or R.

Can you sum distributions with different sample sizes?

Yes, you can sum distributions with different sample sizes. However, it is important to note that the resulting distribution may not accurately represent the underlying populations if the sample sizes are significantly different.

What is the difference between summing distributions and finding the mean of a distribution?

Summing distributions involves combining multiple distributions into a single distribution, while finding the mean of a distribution involves calculating the average value of a single distribution. Additionally, summing distributions takes into account the probabilities of each value, while finding the mean only considers the values themselves.

What types of distributions can be summed?

Any type of probability distribution can be summed, including normal distributions, binomial distributions, and Poisson distributions. However, the resulting distribution may be more complex and difficult to interpret if the individual distributions are significantly different from each other.

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