Proton and Neutron mass

Hi Passion Flower.

neutron is slightly heavier

Mass of proton : 1,6726 x 10^(-27) kg
Mass of neutron: 1,6749 x 10^(-27) kg
Mass of electron: 0,00091x10^(-27) kg

The mass of a neutron is greater than the mass of a
proton because the neutron contains a proton, contains
an electron with some subatomic particles.

neutron = proton + electron + subatomic particles

 

In energy units (using E = mc^2), the masses are: Proton: 938.272 MeV, neutron:
939.566 MeV, mass difference = 1.293 MeV, electron: 0.511 Mev.

 

From Wikipedia

Outside the nucleus, free neutrons are unstable and have a mean lifetime of 885.7±0.8 s (about 14 minutes, 46 seconds); therefore the half-life for this process (which differs from the mean lifetime by a factor of ln(2) = 0.693) is 613.9±0.8 s (about 10 minutes, 14 seconds).[2] Free neutrons decay by emission of an electron and an electron antineutrino to become a proton, a process known as beta decay:[6]

n⁰ → p⁺ + e⁻ + ν_e

 

This is absolutely not correct. A proton consists of two u quarks, a d quark and a set of virtual quark pairs and gluons. A neutron looks exactly like that with a d quark substituted for one of the u quarks.

 

This model of the neutron has been known to be inaccurate for the last 45 years, which you might have realized if you kept reading on the web page you took that from.

We now understand that protons and neutrons are composed of quarks. The proton is composed of 2 up quarks and 1 down quark, while the neutron is composed of 2 down quarks and 1 up quark. There's no simple explanation for the exact difference in the mass between the proton and neutron. It's known that the down quark is slightly heavier than the up quark, so the neutron could be predicted to be slightly heavier than the proton. However, the difference between quark masses only explains a small amount of the neutron-proton mass difference.

The remaining mass difference can only be explained by the strong interaction between the constituent quarks of each particle. This interaction within the proton is stronger, since the proton is stable and the neutron is not. So the proton has more binding energy, again leading to a smaller mass than the neutron. However precisely computing the mass difference is not as simple as writing down a formula, since just about all approximation schemes break down when considering the strong interaction at low energies. Lattice QCD is the most promising computational method for answering such questions, and it gives correct results for nucleon masses to within a few percent.

 

There is no simple formula to be written down. Lattice QCD starts with the definition of QCD observables via path integrals, discretizing on a lattice (along with techniques that took many years to develop) allows these integrals to be done numerically. The resulting spectrum can be converted to (ratios) of particle masses, but I'm not familiar (and not many people outside of the experts are either) with the details. If you want to see some general ideas about lattice methods, you could take a quick look at http://arxiv.org/abs/hep-lat/0506036 One of the more recent computations of light hadron masses appears in http://arxiv.org/abs/0906.3599 but there aren't many formulas there either.

 

My understanding is that the masses of quarks would come from the Higgs mechanism, thus outside QCD. This paper is as fundamental as it gets for QCD.

 

There's a computational obstacle that I don't completely understand related to doing computations with light quark masses. Obtaining physical results is done by some sort of scaling procedure (in masses, this is separate from the lattice spacing) and they must require some extra data to complete the definitions of physical results.

Almost, but due to renormalization, the quark masses at the electroweak scale are very different from those at GeV scales. There are other papers that compute light quark masses and coupling renormalization at GeV scales, but they also use light pion masses as inputs.

I'd expect many of the lattice codes are still written in Fortran and run on parallel supercomputers. I don't think that Maple or Mathematica are well-suited yet to doing these things. While you could probably put all of the formulas into a notebook, neither program would do the computations in a particularly optimal manner. It's still better to explicitly code hard computations.

Quenched means that corrections from fermion loops are being neglected. This is because dealing with Grassmann variables on a lattice is a very hard problem in the first place and the approximation schemes that must be used are computationally intensive.

 

From the paper on computation of neutron/proton masses (light hadron masses):

Computations were performed on the Blue Gene supercomputers at FZ J¨ulich and IDRIS
and on clusters at Wuppertal and CPT. This work is supported in part by EU grant I3HP,
OTKA grants AT049652, DFG grants FO 502/1-2, SFB-TR 55, EU grants RTN contract
MRTN-CT-2006-035482 (FLAVIAnet), (FP7/2007-2013)/ERC no208740 and the CNRS’s
GDR grant 2921. Useful discussions with J. Charles and M. Knecht are acknowledged

FYI: this paper is considered a landmark culination of 3 decades or work on QCK

 

From the paper on computation of neutron/proton masses (light hadron masses):

Computations were performed on the Blue Gene supercomputers at FZ J¨ulich and IDRIS
and on clusters at Wuppertal and CPT. This work is supported in part by EU grant I3HP,
OTKA grants AT049652, DFG grants FO 502/1-2, SFB-TR 55, EU grants RTN contract
MRTN-CT-2006-035482 (FLAVIAnet), (FP7/2007-2013)/ERC no208740 and the CNRS’s
GDR grant 2921. Useful discussions with J. Charles and M. Knecht are acknowledged

FYI: this paper is considered a landmark culmination of 3 decades of work on lattice QCD methods.