Relation between momentum and mass of quarks

In summary: QFT in mind). Off-shell mass is a mathematical trick which helps in the calculations for Feynman diagrams, and is only an approximation of the true mass of a quark.
  • #1
Hluf
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We say on-shell and off-shell mass of quarks. 1) What is the difference on-shell and off-shell mass of quarks. 2) At lab. center of mass frame for lepton particles p2= -m2. Can we apply this equation for quarks.
Thank you!
 
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  • #2
Hi Hluf! :smile:
Hluf said:
We say on-shell and off-shell mass of quarks. 1) What is the difference on-shell and off-shell mass of quarks.

a quark always has on-shell mass (usually just called "mass")

a quark never has off-shell mass

off-shell mass is a mathematical trick which helps in the calculations for Feynman diagrams
2) At lab. center of mass frame for lepton particles p2= -m2. Can we apply this equation for quarks.

(p is the four-momentum)

yes this applies to everything (and in any frame): leptons hadrons and photons

you can regard it as the definition of m (the mass) :wink:
 
  • #3
tiny-tim said:
off-shell mass is a mathematical trick which helps in the calculations for Feynman diagrams
If it works once, it's a trick. If it works twice, it's a method!
 
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  • #4
Bill_K said:
If it works once, it's a trick. If it works twice, it's a method!

But if you don't know how it works, it's magic! o:)
 
  • #5
tiny-tim said:
But if you don't know how it works, it's magic! o:)
If you don't know how it works, go to school to learn how.
Quarks can appear as intermediate particles in Feynman diagrams, where they are
'off-shell'.
 
  • #6
tiny-tim said:
yes this applies to everything (and in any frame): leptons hadrons and photons

you can regard it as the definition of m (the mass) :wink:
Well, there is no center of mass frame for (single) photons.
 
  • #7
tiny-tim said:
a quark always has on-shell mass (usually just called "mass")

a quark never has off-shell mass

Some people would argue the complete opposite. The longer time a particle lives for, the more probably that its mass would be measured to be almost exactly the on-shell mass, but really the whole universe is quantum mechanical and every process a "little bit" virtual, so everything is always off-shell, the exact on-shell mass occupying measure zero of the probability distribution :p.
 
  • #8
Yes, some people will make this argument. Some people find quibbling entertaining. It's not a very good argument for promoting understanding of QFT to people new to it, though.

There really is a difference between real and virtual, and to quote Potter Stewart, "I know it when I see it"
 

1. What is momentum and mass in relation to quarks?

Momentum is a measure of an object's motion, while mass is a measure of an object's resistance to change in motion. In the context of quarks, momentum refers to the quark's speed and direction of motion, while mass refers to the amount of matter contained in the quark.

2. How are momentum and mass related in the context of quarks?

The momentum of a quark is directly proportional to its mass. This means that as the mass of a quark increases, its momentum also increases. However, the exact relationship between momentum and mass of quarks is complex and is described by the theory of quantum chromodynamics.

3. Can the momentum and mass of quarks change?

Yes, the momentum and mass of quarks can change. This is because quarks can interact with other particles and exchange energy, which can alter their momentum and mass. In addition, the mass of a quark can also change due to the process of quark confinement, where quarks are bound together to form larger particles.

4. How do scientists measure the momentum and mass of quarks?

Scientists use high-energy particle colliders, such as the Large Hadron Collider, to study the behavior of quarks. By accelerating particles to high speeds and colliding them, scientists can measure the properties of quarks, including their momentum and mass, through the detection of secondary particles produced in these collisions.

5. Is there a limit to the momentum and mass of quarks?

According to current theories, quarks have a finite mass and can only reach a certain maximum momentum. This is due to the nature of the strong nuclear force, which binds quarks together. However, there is ongoing research to understand the properties of quarks and their limits more deeply.

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