# Weak Decay of Hyperon: Explained!

• vertices
In summary, the conversation discusses the assumption that qc (where q is the momentum transfer) is of the order of the hyperon's rest mass energy and the discrepancy between the rest mass energy of the W boson and the hyperon. The speaker also questions whether or not qc can be neglected and if the hyperon's ultra-relativistic speed affects the momentum transfer. The responder clarifies that the underlying physics of the decay cannot be changed by the hyperon's speed and likens it to the observation of a collision from different frames.

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I attach a solution to a problem. I don't understand the highlighted bit:

I mean, firstly why can we assume that qc (where q is the momentum transfer) is of the order of the hyperons rest mass energy?

And secondly, why is the rest mass energy of the W boson MORE than the rest mass energy of the hyperon. Erm, does this not violate energy conservation? (doesn't the hyperon 'decay' to a W- boson AND a proton?)

Thanks:)

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• decay of hyperon.pdf
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vertices said:
I attach a solution to a problem. I don't understand the highlighted bit:

I mean, firstly why can we assume that qc (where q is the momentum transfer) is of the order of the hyperons rest mass energy?
This is an order of magnitude type of problem. The only energy scale you have at your disposal is th erest mass energy of the hyperon so the momentum transfer must of that order. You would not expect it to be 100 times larger or 100 times smaller.
And secondly, why is the rest mass energy of the W boson MORE than the rest mass energy of the hyperon.
I am not sure I understand.
Erm, does this not violate energy conservation? (doesn't the hyperon 'decay' to a W- boson AND a proton?)

Thanks:)
The W boson is a virtual particle. Energy is conserved at the vertices but it does not mean that the energy of the W boson must be equal to its rest mass energy since it is virtual. I am not sure I understand the problem, sorry.

thanks nrqed:)

nrqed said:
I am not sure I understand.
The W boson is a virtual particle. Energy is conserved at the vertices but it does not mean that the energy of the W boson must be equal to its rest mass energy since it is virtual. I am not sure I understand the problem, sorry.

Yes, ofcourse, it's virtual so it can violate energy conservation for a little bit as long as it satisfies HUP. I can be really silly sometimes:(

Actually, I'm goint to backtrack on this one.

The question is can we really neglect qc? The hyperon could be going ultra relativistically, in which case, it must transfer way more more momentum than its mass*c because it has way more momentum to start off with (this kind of makes sense intuitivly, but I'm not sure how to prove it) - so the qc term in the propagator could exceed the M_x^2c^2 term (could it not?) and hence it would not make sense to neglect it..

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vertices said:
The hyperon could be going ultra relativistically, in which case, it must transfer way more more momentum than its mass*c because it has way more momentum to start off with

Whoa!

It helps to study relativistic kinematics before studying particle physics. Making the hyperon go faster is the same as observing an at-rest hyperon from a fast-moving frame. That can't change the underlying physics of the decay.

The same thing happens in elementary physics. Imagine two cars colliding. Observers moving at different non-relativistic velocities will disagree with how much kinetic energy each car has, but they will not disagree on how much energy is transferred during the collision.

It helps to study relativistic kinematics before studying particle physics. Making the hyperon go faster is the same as observing an at-rest hyperon from a fast-moving frame. That can't change the underlying physics of the decay.

Yes, ofcourse!

I forgot it was a decay!

## 1. What is weak decay of hyperon?

The weak decay of hyperon is a type of nuclear decay in which a hyperon particle decays into another particle through the weak nuclear force. This process involves the emission of a W boson and results in the transformation of the original hyperon into a different particle.

## 2. How does weak decay of hyperon occur?

Weak decay of hyperon occurs when a hyperon particle, which is made up of three quarks, transforms into a different particle by changing one of its constituent quarks. This change is mediated by the weak nuclear force, which is responsible for the decay of subatomic particles.

## 3. What is the significance of weak decay of hyperon in nuclear physics?

Weak decay of hyperon is significant in nuclear physics because it helps us understand the behavior of subatomic particles and their interactions. It also plays a crucial role in the stability and radioactive decay of atomic nuclei.

## 4. Can weak decay of hyperon be observed in nature?

Yes, weak decay of hyperon can be observed in nature. It is a natural process that occurs in the decay of certain subatomic particles, such as hyperons and mesons. Scientists can also produce and observe this type of decay in laboratory experiments.

## 5. What are some applications of weak decay of hyperon?

One application of weak decay of hyperon is in medical imaging, where it is used to produce positron-emission tomography (PET) scans. It is also used in particle accelerators to study the properties of subatomic particles and in nuclear reactors to understand and control nuclear reactions.