Energy conservation concerns in the weak interaction

[Asgrrr]

I have a few questions:

Can a u quark turn into a d quark (heavier) via the weak interaction? If so, how is the mass/energy shortfall made up?

How can the (supermassive) carrier bosons (W, Z) be called into being? Where does the energy come from? Or is the energy bill unpaid because they are virtual particles, on the verge of existence? Is it akin to a tunneling effect?

Thank you.

 

[mfb]

Quarks don't exist as isolated objects. There is no u->d process without "context".

How can the (supermassive) carrier bosons (W, Z) be called into being?

In radioactive decays: They don't. There are just virtual W, not real particles.
In particle accelerators: We give the particles enough energy.

 

[Asgrrr]

Quarks don't exist as isolated objects. There is no u->d process without "context".

The context is within a nucleon in a nucleus, e.g. electron capture.

 

[Asgrrr]

.In radioactive decays: They don't. There are just virtual W, not real particles.

Thank you. I already had that. I guess I could just write "they are not real" but that seems to me an unsatisfactory explanation. What is meant by a virtual particle? Is it just an arbitrary expedient, like when explaining lightning saying "Thor does it"? There has to be something more to be said.

 

[snorkack]

I have a few questions:

Can a u quark turn into a d quark (heavier) via the weak interaction? If so, how is the mass/energy shortfall made up?

A proton turning into neutron is caused by one u quark turning into d quark. And a neutron is heavier.
The mass/energy shortfall is made up by the (larger) binding energy of the neutron/d quark.

How can the (supermassive) carrier bosons (W, Z) be called into being? Where does the energy come from? Or is the energy bill unpaid because they are virtual particles, on the verge of existence? Is it akin to a tunneling effect?

Yes, tunnelling is a good comparison for virtual particles.

 

[Asgrrr]

Thank you Snorkack!

If nobody contradicts, I may be onto something here.

 

[mfb]

What is meant by a virtual particle?

A mathematical concept in perturbation theory, which is a tool to calculate approximations to processes.
It is not "Thor does it", because we can calculate how often what happens.

The context is within a nucleon in a nucleus, e.g. electron capture.

Then it can be possible, it depends on the nucleus and the binding energy of the initial and potential final nucleus.

 

[snorkack]

I am not sure that

we can calculate how often what happens

For the simplest example of what a virtual particle is, consider virtual photon.
Electromagnetic field includes electromagnetic waves. They are freely propagating, carry energy, momentum and angular momentum independent of the source and eventual recipient.
They are also observably quantized into real photons.
But not all electromagnetic field is free waves.
Electromagnetic field also includes electrostatic and magnetostatic fields.
As well as evanescent waves. Oscillating electric fields exist in directions and volumes of space into which they are not freely propagating.
The concept of "virtual particle" is based on the idea of treating unfree fields as quantized like the freely propagating waves are.
If you look at the electrostatic field of a point charge, you can define the total strength of the field lines included. But can you break down the electrostatic field of a point charge into a countable number of virtual photons, the way you can in theory count the radio wave real photons emitted by an antenna?

 

[mfb]

But can you break down the electrostatic field of a point charge into a countable number of virtual photons

No.

How is your post related to the part you quoted?
"How often what happens" is about physical processes, e. g. decays, cross sections and so on.

 

[snorkack]

No.

How is your post related to the part you quoted?
"How often what happens" is about physical processes, e. g. decays, cross sections and so on.

Ah, the real final outcome?
But do you need virtual particles for that?

 

[vanhees71]

To make it very clear: "Virtual particles" is a confusing buzzword for propagators in Feynman diagrams, depicted there by internal lines. They are not interpretable as particles at all. That's only possible in the sense of asymptotic free states, and sometimes even those are not as simple as it looks in the standard procedure idealizing them to free plane-wave states. For a full understanding you have to study relativistic quantum field theory and deal with pretty mind-boggling conceptual problems, related to the definition of asymptotic states, LSZ reduction (named after Lehmann, Symanzik, and Zimmermann), and all that.

 

[mfb]

But do you need virtual particles for that?

No, there are calculation methods that do not have virtual particles. Lattice calculations for example.