# If Neutron and Proton have some diff. mass then why?

## Main Question or Discussion Point

I see that in some books, Proton and Neutron charge differ a bit. Why is it?

I thought them to be same. But...

And I am new to this forum...
Let's hope we will have a great time together studying science...

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You mean mass, right, not charge?

Yes yes!

cristo
Staff Emeritus
I'm not quite sure why you've posted this in the tutorials section, but I'm sure it'll be seen and moved soon.

I'll try and give an answer to your question, although I'm sure the experts will chime in with something more rigourous. Protons and neutrons are both made up of fundamental particles. More specifically, they are both made up of three quarks. These quarks come in different flavours, but protons and neutrons both consist of two different flavours, namely "up" and "down". A proton is made up of two up's and one down quark, whereas a neutron is made up of two down's and one up. It's the slight difference in the masses of these different types of quark that gives rise to the difference in overall mass of the proton and neutron.

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thanks

I'm not quite sure why you've posted this in the tutorials section, but I'm sure it'll be seen and moved soon.

I'll try and give an answer to your question, although I'm sure the experts will chime in with something more rigourous. Protons and neutrons are both made up of fundamental particles. More specifically, they are both made up of three quarks. These quarks come in different flavours, but protons and neutrons both consist of two different flavours, namely "up" and "down". A proton is made up of two up's and one down quark, whereas a neutron is made up of two down's and one up. It's the slight difference in the masses of these different types of quark that gives rise to the difference in overall mass of the proton and neutron.
To add a bit to cristo message. If up and down quark had exactly the same mass, protons and neutrons would have the same mass (neglecting other quarks). Then we could introduce a new symmetry with a new quantum number called isospin. In practice, this symmetry is broken.
You can find a nice article on wikipedia :
http://en.wikipedia.org/wiki/Isospin

Astronuc
Staff Emeritus
Up and down quarks are considered to have the same mass.
http://hyperphysics.phy-astr.gsu.edu/hbase/particles/quark.html

Proton is (uud) while neutron is (udd).
http://hyperphysics.phy-astr.gsu.edu/hbase/particles/proton.html

The neutron is neutral, i.e. has a 0 (or no) charge while the proton has a charge of +1e by convention.

The masses are slightly different -
The combination of up and down quarks to form protons and neutrons suggests that the u and d are of about equal mass: about 1/3 the mass of a nucleon
http://hyperphysics.phy-astr.gsu.edu/hbase/particles/qmass.html

The combination of up and down quarks to form protons and neutrons suggests that the u and d are of about equal mass: about 1/3 the mass of a nucleon
Hello,

I do not understand this sentence. Quark masses are very small, much smaller than 1/3 m(neutron) :
m(up) = [1.5, 4.0] MeV
m(down) = [3.0, 7.0] MeV
m(up)/m(down) = 0.3 to 0.6
according to PDG

In fact the proton-neutron mass split is a puzzle. As can be seen in the values given by PDG, the uncertainties in the (current) quark masses themselves are enough so that from everything down to nothing in this split can be explained by the masses of the quark. If you take the extreme, those uncertainties are even compatible with a heavier proton !

There are many models providing different interpretations for this split. You have noticed that the (current) quark masses do not add up to the nucleon (proton or neutron) masses at all, by far. This (or something slightly more technical) is called the mass-gap problem and is one of the most interesting (important) problems in (pure) mathematics today. From this point of view, it is a little to "easy" to blame the quark masses for the proton-neutron split.

The charge (electrical and magnetisation) densities in the proton and neutron are rather different, suggesting they do not have quite the exact same structures, even though very similar.

Our understanding of those problems is poor enough so that, even assuming so called "isospin" symmetry (same neutron and proton structures), we already struggle to make precise sens out of them.

BTW, talking of "constituent" quark masses as one third (approximately) of the nucleon mass is not only old-fashioned anymore. It is over simplifiying.

But if we can reproduce part of the baryon spectrum via lattice qcd, it means we have part of the answer to this puzzle, isn't it ? By the way, this "up" and "down" masses from PDG are coming from lattice results I guess.
I agree that it is one of the most interesting subject of subatomic physics. Particularly because QCD is non-pertubative and so we have to find alternative mathematical methods.

Astronuc
Staff Emeritus
Hello,

I do not understand this sentence. Quark masses are very small, much smaller than 1/3 m(neutron) :
m(up) = [1.5, 4.0] MeV
m(down) = [3.0, 7.0] MeV
m(up)/m(down) = 0.3 to 0.6
according to PDG
Thanks for pointing that out. I was oversimplifying the matter.

Does this help - http://pdg.lbl.gov/2005/reviews/quarks_q000.pdf - on the question of method?

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arivero
Gold Member
Thanks for pointing that out. I was oversimplifying the matter.

Does this help - http://pdg.lbl.gov/2005/reviews/quarks_q000.pdf - on the question of method.
Hmm the right answer should state mass formulae for the baryons, and this review only quotes (page 6) some for mesons.

Of course naively if m_u < m_d, then mass(uud)<mass(udd). But given that already in the meson mass formulae there are two terms, for QCD and electromagnetic contributions, one could cast some doubts. Of course historically it happened that the proposed mass formula was enough to fit the SU(3) flavour decuplet with some predictions, but the neutron and the proton are not there; they live in the octet.

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There is also the potential mass found in the "quark-gluon sea" found within nucleons such as proton and neutron. It has been known for some time now (since 2000) that strange quark is present within proton sea--that is, the proton is much more interesting that just saying it is made of three quarks (uud)--see this link:
http://www.sciencedaily.com/releases/2000/02/000204073943.htm

Here is a link from Jefferson Lab with lots of current research on nucleon internal structure:
http://www.jlab.org/highlights/phys.html

arivero
Gold Member
There is also the potential mass found in the "quark-gluon sea" found within nucleons such as proton and neutron. It has been known for some time now (since 2000) that strange quark is present within proton
Yeah, this is interesting for the question of the absolute value of the nucleon mass, but for the specific cuestion here (calculation of the mass difference between proton and neutron) surely it is not so relevant.