Quark mixing and energy conservation

In summary: We should see no b production, and yet the small coupling of the b to the d and the s implies we should have a small chance of seeing a b produced.
  • #1
Jezza
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We've recently been looking at the hadronic decays of the W boson. In this one example, we looked at possible decays for the W boson being produced near its resonance peak, meaning the centre of mass energy is sufficient to produce u,d,c,s & b quarks. However, because we're below the mass of the top quark, and the coupling of the b to the u and c quarks is tiny, we neglected it in our calculations. Nonetheless, there is still a small chance of getting a b in the decay owing to the small but non-zero coupling of the b to the d and the s.

What confuses me is that all the discussions I've seen so far make no reference to energy conservation. Suppose we observe the decays of (virtual) W bosons at a centre of mass energy above the mass of the c but below the mass of the b. (I am assuming we can observe such processes). Energy conservation implies we should see no b production, and yet the small coupling of the b to the d and the s implies we should have a small chance of seeing a b produced. i.e. the coupling doesn't seem to necessarily satisfy energy conservation.

So my question: What happens to the coupling of the b to the d and s quarks at centre of mass energies below the mass of the b quark?
 
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  • #2
The coupling stays the same. You just don't get any events in that channel, just as you don't get (real) W decays to t+b.
 
  • #3
Hmm... I've been viewing this 'coupling' as the probability amplitude of a quantum superposition. That is the W decays (for example) into an u and an anti-d', where d' is a superposition of the d, s and b with mostly d, some s and a small amount of b. For us to not get any events with a b, that means the amount of b in d' must be zero, implying the coupling of the bottom to the down is now zero. Is this then the wrong way to think about it?
 
  • #4
Yes, it's the wrong way. The probability of interaction is the matrix element (including the coupling) squared multiplied by phase space. The probability is zero if the matrix element is zero, but it's also zero if the phase space is zero.
 
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  • #5
Jezza said:
Suppose we observe the decays of (virtual) W bosons at a centre of mass energy above the mass of the c but below the mass of the b. (I am assuming we can observe such processes).
Decays of b-hadrons have this case if there is no lighter b-hadron to decay to.
 

1. What is quark mixing?

Quark mixing, also known as quark flavor mixing or CKM mixing, is a phenomenon in particle physics where the flavor eigenstates of quarks (up, down, strange, charm, top, and bottom) mix with each other, resulting in a superposition of different flavor states in a particle.

2. How does quark mixing affect energy conservation?

Quark mixing does not affect energy conservation in the traditional sense, as energy is still conserved in all interactions involving quarks. However, it does play a role in the decay processes of particles, as the mixing of quark flavors can change the probabilities of certain decay modes and affect the overall energy distribution of the decay products.

3. What is the significance of quark mixing in the Standard Model?

Quark mixing is an essential part of the Standard Model of particle physics, which is the most widely accepted theory describing the fundamental particles and their interactions. It helps explain the observed variety of particles and their decay patterns, and is crucial for predicting and interpreting experimental results.

4. Are there any experimental evidences for quark mixing?

Yes, there are many experimental evidences for quark mixing. One of the most famous is the observation of CP violation in the decay of neutral kaons, which is a direct consequence of quark mixing. Additionally, precise measurements of quark mixing parameters have been made at various particle colliders, providing strong evidence for its existence.

5. Can quark mixing be explained by the conservation of other quantum numbers?

No, quark mixing is a unique phenomenon that cannot be explained by the conservation of other quantum numbers. It is a consequence of the structure of the Standard Model and the properties of quarks, and cannot be derived from other principles such as electric charge or baryon number conservation.

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