Kinetic energy of quarks in a baryon

[ValeForce46]

If we say that a proton has a kinetic energy of ##50## GeV, can we say that each of the three quarks that compose it have roughly a mean energy of ##\approx\frac{50}{3}=17## GeV?

If not, what can we say about the energy of each individual quark inside a baryon with a known energy?

 

[Orodruin]

This is usually described by the parton distribution functions that essentially describe the probability distribution of finding a particular quark (or gluon) with a fraction x of the total energy.

https://en.wikipedia.org/wiki/Parton_(particle_physics)#Parton_distribution_functions

 

[ohwilleke]

This is usually described by the parton distribution functions that essentially describe the probability distribution of finding a particular quark (or gluon) with a fraction x of the total energy.

https://en.wikipedia.org/wiki/Parton_(particle_physics)#Parton_distribution_functions

For clarity, it is worth observing that the parton distribution function is largely a function of intra-proton quarks and gluons within the proton system. It is not meaningfully dependent upon the velocity of the proton system (together with the particle impacting it in a collision) as a whole relative to the world outside the proton.

By virtue of the equivalence of mass and energy, the total mass and energy of a proton (adding up all possible parton distribution function possible outputs), including internal kinetic energy and gluon field energy and the mass of its quarks arising from their Higgs field interactions, add up to the total mass of the proton when the proton is in equilibrium. High energy collisions involve particles, such as two protons, colliding at high energies relative to each other, without regard to their kinetic energies in a frame of reference that is relative to the world outside of the colliding particle system.

Also, gluons, in principle, since they are massless, don't have kinetic energy. Each gluon, in principle, has a well defined energy which is a function of its frequency, much like a photon, but not kinetic energy. Only quarks and other fermions and W and Z bosons and Higgs bosons in the parton distribution function have kinetic energy because only that have mass.

So, saying that a proton has 50 GeV of kinetic energy is an ill-defined statement until you choose a suitable frame of reference.

Protons in equilibrium never have 50 GeV of kinetic energy in their own internal frame of reference (e.g. relative to their center of mass or electromagnetic charge). The total mass-energy inside a proton system in equilibrium is a hair less than 1 GeV in most circumstances (although the effective total is partially a function of the energy transfer in the collision due to renormalization but that only varies very slowly, roughly speaking, as a log of energy transfer scale that gets smaller at higher energy transfer of collision scales).