# Lambda decay, momentum of the pion and proton

## Homework Statement

I have a lambda decaying into a pion and a proton. The lambda is moving with velocity 0.9c and I know the mass of the lambda as well as the pion and proton (these are known constants). I need to find the momentum of the pion and the proton after the decay happens.

## Homework Equations

Conservation of momentum and conservation of energy

## The Attempt at a Solution

I don't know at this point which momentum to choose out of the two. I solved the math using a software so I would assume it is right.

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Orodruin
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There are two solutions because I assume you solve kind of the quadratic equation (so + or - the square root)
But I am having trouble realizing which answer is "wrong" since none of them give anything negative

Orodruin
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Why would either be wrong? What are the possible decays in the Lambda rest frame.

Edit: I suggest you do the computation in the Lambda rest frame first and then interpret your solutions there.

Edit: I suggest you do the computation in the Lambda rest frame first and then interpret your solutions there.
That's kind of the first problem I am working on, the lambda is at rest and I need to find the momentums of the other particles.
I end up getting that the momentum is equal to the mass, which seems wrong to me. They don't have the same mass and if the momentum of particle A (mother) is 0, then Pb=-Pc ... so this can't be right.

Orodruin
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Please show your computations in the Lambda rest frame. No, I am not referring to the possible decay channels, I am referring to the possible momenta of this particular decay.

Please show your computations in the Lambda rest frame. No, I am not referring to the possible decay channels, I am referring to the possible momenta of this particular decay.
https://imgur.com/rbiJNbT

In this page I tried kind of two different things and at one point got Pc=mc and then the other got a factor of sqrt2/2

Orodruin
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I am sorry, but it is impossible to tell what you have tried to do from that photo. Please write it out here along with argumentation describing what you are doing and why.

I am sorry, but it is impossible to tell what you have tried to do from that photo. Please write it out here along with argumentation describing what you are doing and why.
Basically I was trying to apply this logic

Where I can write expressions for the momentum because it will be conserved, it will be a sum. Then I wanted to solve for an expression for the energy which I could equate to the more commonly known

And solve for the momentum, substituting as necessary since I can find an expression for Pa, and it is equal to 0 anyways

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Orodruin
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I am sorry, it is still unclear. It is not clear from your handwriting what $p$s represent 4-momenta and what $p$s represent 3-momenta. Perhaps you are even mixing them up. This is why I suggest that you write down your entire reasoning again here, taking care to explain what you are doing in every step.

I am sorry, it is still unclear. It is not clear from your handwriting what $p$s represent 4-momenta and what $p$s represent 3-momenta. Perhaps you are even mixing them up. This is why I suggest that you write down your entire reasoning again here, taking care to explain what you are doing in every step.
This is the best I can do by myself. I haven't learned this stuff formally so trying to learn as I go, it's for a project and not even homework it will not be graded.

It's just a lot of algebra and I thought maybe there was an easier way, there must be some concepts I just don't understand properly like the four vectors that I could apply here.

If I fill this in with the values of the lambda decay, I get that Pc=0.1485 Gev/c which is roughly the mass of the pion.

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Orodruin
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If I fill this in with the values of the lambda decay, I get that Pc=0.1485 which is roughly the mass of the pion.
No, you get $\pm$ that.

No, you get $\pm$ that.
Yes, and Pb=-Pc.

I'm not sure what I'm missing out on here

Orodruin
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How do you interpret the $\pm$?