# Relation between momentum and mass of quarks

by Hluf
Tags: mass, momentum, off-shell, quarks, relation
 P: 20 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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P: 26,167
Hi Hluf!
 Quote by Hluf 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)
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P: 3,856
 Quote by tiny-tim 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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P: 26,167

## Relation between momentum and mass of quarks

 Quote by Bill_K 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!
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P: 1,937
 Quote by tiny-tim But if you don't know how it works, it's magic!
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'.
Mentor
P: 10,840
 Quote by tiny-tim yes this applies to everything (and in any frame): leptons hadrons and photons you can regard it as the definition of m (the mass)
Well, there is no center of mass frame for (single) photons.
P: 313
 Quote by tiny-tim 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.
 Mentor P: 15,619 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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