# Quark vs. Hardron mass

Why are Hadrons so much heavier than their quark components? For example, the components of the proton have a combined mass of 12 MeV but the proton is ~950 MeV. If we look at binding energy:

$$B=\sum{m_{components}}-m_{whole}$$ so the Binding Energy must be a large negative number. Is this right? If so, why?

Yes its right. It would take that much energy to separate them.

In Nuclear Physics $$m_{whole}\leq\sum{m_{components}}$$ correct? So in this case it is the other way around. What is the significance of that?

To put it more succinctly: What does it mean to have a negative Binding Energy?

Staff Emeritus
In a hydrogen atom, the mass is equal to the mass of the proton plus the mass of the electron plus the mass of the energy stored in the electromagnetic field, less the binding energy.

For the hydrogen atom, the energy stored in the electromagnetic field is tiny - parts per million. For a proton, the energy stored in the gluon field is huge: 99% of the mass of the proton.

Why are Hadrons so much heavier than their quark components? For example, the components of the proton have a combined mass of 12 MeV but the proton is ~950 MeV. If we look at binding energy:

$$B=\sum{m_{components}}-m_{whole}$$ so the Binding Energy must be a large negative number. Is this right? If so, why?

Well the case of the nucleus mass being smaller then the constituent nuclei is indeed due to the negative binding energy. This is shown by the semi-empirical mass formula. The nucleon-nucleon potential becomes repulsive at very short distances.

Inside the nucleon things are totally different though :

The sum of the constituent quarkmasses is much smaller then the mass of the hadron. The extra mass comes from the potential and kinetic energy of the quarks and also from dynamical quarks.

For example the proton contains three valence quarks of three different colours (red, green and blue), but it also contains dynamical (sea) quarks. These are quark-antiquark pairs that appear and disappear through energy fluctuations in the vacuum.

These dynamical quarkpairs will generate mass. The mass of a hadron is bigger then the sum of the masses of the constituent quarks (the three quarks of the proton). But the dynamical quarks also generate mass (via symmetry breaking) , so in the end the mass of a proton is BIGGER then the sum of the three quark masses.

marlon

Hi,

as you noted correctly, the mass default calculated as such is negative. In principle, we imagine that separating them would produce energy.

However, this mass default has no physical meaning, because quarks are premanently confined. Therefore, you can not interpret you result as the stored potential energy. There is no "asymptotic state at infinity" to perform the difference.

In addition, you must be careful when you talk about quark masses. There are current quark masses appearing in the lagrangian, and hose are (I think) the one you quote. Basically what you do is that you use symetries to find relation between ratios of different masses (quarks and hadrons). And there are constituent quark masses which are used in various models of bound states.

An intriguing possibility is that the naked current quark mass measured at high energy is really the same at the constituent quark mass, but renomalized at a lower energy. This is not an easy topic however.

Well the case of the nucleus mass being smaller then the constituent nuclei is indeed due to the negative binding energy. This is shown by the semi-empirical mass formula. The nucleon-nucleon potential becomes repulsive at very short distances.

Hi,

do we explain why nucleon-nucleon potential becomes repulsive at very short distances ?
Or is it only phenomenologic ?

do we explain why nucleon-nucleon potential becomes repulsive at very short distances ?
Or is it only phenomenologic ?
Did you try to compare nuclei/nucleon radii ? It is a quite interesting game

malawi_glenn
Homework Helper
Hi,

do we explain why nucleon-nucleon potential becomes repulsive at very short distances ?
Or is it only phenomenologic ?

the most fundamental reason I can give you is the Pauli principle. In comparison, you can't put two atoms to close to each other.

Thanks,

I found some interesting information on wikipedia : http://en.wikipedia.org/wiki/Internucleon_interaction
but they do not explain shot distance repealing.
Pauli principle should not exclude having two nucleons with opposite spins at the same position.

malawi_glenn
Homework Helper
no but what is considered are the quarks that builds up the nucleons.

Pauli principle should not exclude having two nucleons with opposite spins at the same position.
I think we are oversimplifying here. You don't need spin for Pauli principle not to exclude two nucleons at the same positions. They just can have different momenta.

In addition, isospin comes into game as well, and nucleons in a nuclei do form pairs indeed.

I think we are oversimplifying here. You don't need spin for Pauli principle not to exclude two nucleons at the same positions. They just can have different momenta.

In addition, isospin comes into game as well, and nucleons in a nuclei do form pairs indeed.

Spin or isospin, the question remains : where this short repulsive force is coming from ?

Spin or isospin, the question remains : where this short repulsive force is coming from ?
Nobody knows ! And it is very interesting

Now, if you have pairing, very grosso-modo, you have two nucleons at the same position with opposite momenta (reminds you of BCS model of superconductivity ?). This situation is dubbed "short-range correlation". It is very well observed. It implies that nucleons are going to behave just as if they were repelling at short distances (but really, they are so much attracted to each other that they form a bosonic pair !).

Another model : One Boson Exchange Potential "phenomenological" models. You have a light scalar and isoscalar sigma meson for long range attraction, and a heavier omega isoscalar vector meson for repulsion. You also put in a rho isovector vector for isospin dependent effects. All is great, you have a relativistic mean field theory of the nuclear structure. But wait ! Where are the pions ? What is this sigma !?

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Another model : One Boson Exchange Potential "phenomenological" models. You have a light scalar and isoscalar sigma meson for long range attraction, and a heavier omega isoscalar vector meson for repulsion. You also put in a rho isovector vector for isospin dependent effects. All is great, you have a relativistic mean field theory of the nuclear structure. But wait ! Where are the pions ? What is this sigma !?

Thanks ! That model looks interesting.
Hope some day nuclear physicists can run a big simulation with Lattice QCD to check 2 nucleous hypothesis.