# Hadron component mass

Quarks are imprisoned in hadrons, and have large binding and kinetic energies at all times. Ditto about gluons.

How can inertial mass of quarks inside hadrons be measured?

Also, how is it proven that gluons are massless? What effects would happen if gluons had rest mass, as much as up to a few MeV?

## Answers and Replies

mfb
Mentor
For the top-quark, you can use the invariant mass of W + b-jet, as it decays before it forms hadrons.
The masses of charm- and bottom-mesons are dominated by the heavy quark, too.

For other quark masses: Compare theory predictions (based on the quark masses) with experimental results and use the comparison as indirect measurement of the masses.

I think massive gluons would give serious theoretic problems.

I think massive gluons would give serious theoretic problems.

So can someone explain just which the theoretical results are?

mfb
Mentor
Quantum field theory uses fundamental symmetries to construct interactions between particles. To have those symmetries, bosons have to be massless.
The masses of W and Z bosons (weak interaction) were a serious issue, until Higgs and some other theoreticians developed the Higgs mechanism - it breaks the symmetry and adds mass to those bosons.
If you want to add masses to gluons, too, you need something similar for the strong interaction.

Oh, and then there are experimental limits: 1 2

tom.stoer
With massive gluons there would be no confinement! There is no confinement due to the el.-weak force which differes from QCD in i) an additional U(1), ii) SU(2) instead of SU(3) and iii) W- and Z-masses; i) is irrelevant for confinement, ii) yields a confining theory as we know from lattice calculations, iii) is the major difference and spoils confinement

Photons are massless, yet electrons are not confined in atoms.

mfb
Mentor
Photons have no self-interaction, and the electromagnetic interaction is weak.

Precisely how does the force of strong interaction (gluon chain) depend on distance for large distances?

tom.stoer
Precisely how does the force of strong interaction (gluon chain) depend on distance for large distances?
It's not possible to write down a "classical potential" for the strong interaction mediated by gluons. The expression which can be derived is viable only as a non-local operator acting on a Hilbert space. One can extract something like a "potential" between "static valence quarks" mediated by gluons which has V(x) ~ x asymptotics for large x, but this is not a fundamemtal expression.

If you like I can post the exact expression just to convince you that it's not an ordinary potential ;-)

The more interesting analysis is that of a barrier against tunnel creation of a quark-antiquark pair, cutting the gluon chain.

If a hadron contains at least two up or down quarks then the lowest barrier path to snap the gluon chain is pion creation, with 140 MeV energy.

Of course, after snapping the chain, the halves are STILL stretched... where does the energy gain driving the gluon chain snapping come from?

mfb
Mentor
That is a very classical picture, and its application is limited - the system is quantum mechanical. To "cut the chain", you do not have to create a bound hadron state (pion). A quark-antiquark pair is enough, with an energy of ~2 times the quark masses (~2*5 MeV).