Relation between momentum and mass of quarks

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Discussion Overview

The discussion revolves around the concepts of on-shell and off-shell mass of quarks, exploring their definitions and implications in the context of quantum field theory (QFT) and Feynman diagrams. Participants also examine the application of certain equations in different particle frames, particularly in relation to quarks and leptons.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants assert that a quark always has on-shell mass, while it never has off-shell mass, describing off-shell mass as a mathematical tool for Feynman diagram calculations.
  • Others argue that the distinction between real and virtual particles is significant, suggesting that all particles are somewhat off-shell due to quantum mechanical effects.
  • There is a discussion about the applicability of the equation p² = -m² in the lab center of mass frame for quarks, with some asserting it applies universally to all particles, while noting that there is no center of mass frame for single photons.
  • One participant humorously notes that if one does not understand how off-shell mass works, it may seem like magic.
  • Another participant highlights that the longer a particle exists, the more likely its mass will be measured close to its on-shell mass, but emphasizes the quantum mechanical nature of particles.

Areas of Agreement / Disagreement

Participants express differing views on the nature of off-shell mass and its implications, indicating that multiple competing perspectives remain without a clear consensus.

Contextual Notes

The discussion includes assumptions about the definitions of on-shell and off-shell mass, as well as the implications of quantum mechanics on particle behavior, which remain unresolved.

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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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:
 
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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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:)
 
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'.
 
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.
 
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.
 
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"
 

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