## Thursday, December 19, 2013

### Proton and Neutron and Electron Masses In Various Formats

Relative Mass

Neutron = 1
Proton = 0.99862349 (99.862349%)
N-P= 0.00137651 (0.137651%)
Electron = 0.00054386734

Neutron = 1838.6837
Proton = 1836.1527
N-P = 2.53096
Electron = 1

Kilograms

Neutron = 1.6749286*10-27 kg
Proton = 1.6726231*10-27 kg
N-P= 2.3052*10-30 kg
Electron = 9.1093897*10-31 kg

MeV

Neutron = 939.56563 MeV
Proton = 938.27231 MeV
N-P= 1.29332 MeV
Electron = 0.51099906 MeV

The relevant portion of the relevant PDG entry states:

 u-QUARK MASS 2.3 +0.7−0.5 MeV d-QUARK MASS 4.8 +0.5−0.3 MeV m¯¯¯ = (mu+md)/2 3.5 +0.7−0.2 MeV mu/md MASS RATIO 0.38−0.58

As a first order approximation, hadron masses are equal to the sum of the masses of the constituent quarks plus an amount that is roughly the same for any hadron with the same number of quarks that has the same spin.  Thus, this binding energy contribution is roughly the same for all spin-3/2 baryons.  This approximation understates hadron mass by an amount that is a function of the particular quarks in the hadron which increases, but less than linearly, with the sum of the constituent quark masses (and possibly also varies slightly with combinations of quark charges in the hadron).

I have seen a paper (which I will try to find a reference for) which suggests that QCD models predict a proton-neutron mass of 870 MeV in the a model with massless up quarks and down quarks - the portion of the mass purely attributable to gluon interactions via the color force between the three light quarks in each nucleon.  The mass of the component quarks in the proton is about 9.3 MeV, and the mass of the component quarks in the neutron is about 11.8 MeV, a difference of about 2.5 MeV (using PDG values).  Thus, the presence of massive quarks in the proton has a non-linear contribution to proton mass of about 59 MeV and a non-linear contribution to neutron mass of about 58 MeV.

#### 1 comment:

andrew said...

The PDG value for down quark mass minus up quark mass is 2.5 MeV, while the neutron mass minus the proton mass is about 1.3 MeV. Thus, differences in gluon source mass between the neutron and proton buffer the difference between the component quark masses.

Given that so little of the mass of the proton and neutron are attributed to the three light quarks in each of them, one would naively expect the differences in the component quark masses to also be only a small percentage of the total difference (perhaps 0.1 MeV or less?). But, that is not what current estimates suggest.