# Atomic Model of Hadrons mass of excited particles

1. May 3, 2014

### cooev769

So in a lecture i'm reading up on we are given questions to answer during the lectures with no answers, and for this particular lecture the answer has been omitted and it is in none of our textbooks.

But basically it says that a proton and a sigma plus, both have the same quark composition and hence should have the same mass, but the sigma + has a great mass than the proton. Basically the sigma + has a greater energy, but this seems weird to me because as an object gains energy does that necessarily mean it gains mass? I thought that was only in relativity as the variable mass, which is actually fallacious and that mass is actually a lorentz scalar.

Can anybody explain this difference in mass to me clearly?

Thanks :)

2. May 3, 2014

### cooev769

Like in an atom when the electrons are in excited states, higher energy levels, I've never heard that this means that the electrons have a greater mass. When you accelerate an electron and it gains energy i've never heard that it gains mass.

3. May 3, 2014

### cooev769

Sorry I mean delta plus not sigma plus.

4. May 4, 2014

### JustinLevy

"mass" can mean a lot of things. The equation
E=mc^2
only holds for a system at rest, otherwise we need to include the momentum terms.
E^2 -(pc)^2 = (mc^2)^2

That "m" there is indeed a Lorentz scalar as you mentioned. It is also called the rest mass.

So for an atom, the rest mass _does_ depend on what energy level the electrons are in. It just turns out this energy difference is very small compared to the rest mass of the atom's nucleus and so it is basically negligible. For the light baryons though, the mass of the quarks is quite small compared to the 'strong field' interaction energy. So it shouldn't be too much of a surprise that the energy level difference (and hence mass difference) of different excited states is a sizable fraction of the ground state.

5. May 4, 2014

### Staff: Mentor

You cannot treat the particles as separate entities when bound together in an atom. They compose a system and it is the system as a whole, aka the whole atom, that gains mass.

6. May 4, 2014

### Staff: Mentor

No. Why should they? They are different particles, and most of their rest energy (and therefore most of the mass) comes from QCD anyway.

An excited atom is heavier than an atom in its ground-state, but the difference is extremely tiny (of the order of 10-9 of the total mass).