Protons and Neutrons

Given the previous and somewhat technical discussion about QCD, lets look at what we know exists in nature. We know that the lightest spin ${1\over 2}$ strongly interacting particles that can be made in the laboratory are the proton and neutron. The proton has mass $M_p~=~938.27231~{\rm MeV}$, and $M_n~=~939.56563~{\rm MeV}$ There are other properties that have been measured, and can be found in the particle data group compilation[3]. There you can find, for the proton

$$M_p~=~938.27231\pm 0.00023~{\rm MeV}\qquad {\rm Mass}$$

$$\mu_p~=~2.79284739\pm 0.00000006 \mu_N\qquad {\rm Magnetic\ Moment}$$

$$d_p~=~\left(-4\pm 6\right)\times 10^{-4}~{\rm e\ cm}\qquad {\rm Electric\ Dipole\ Moment}$$

$$\overline{\alpha}_p~=~\left(12.1\pm 0.9\right)\times 10^{-4}~{\rm fm}\qquad {\rm Electric\ Polarizability}$$

$$\overline{\beta}_p~=~\left(2.1\pm 0.9\right)\times 10^{-4}~{\rm fm}\qquad {\rm Magnetic\ Polarizability}$$

$$\tau_p > 1.6\times 10^{25}~{\rm yrs}\qquad {\rm Mean\ Lifetime}$$

$$r_p~=~0.862\pm 0.012~{\rm fm}\qquad {\rm Charge\ Radius} \ \ \ ,$$ (9)

and for the neutron

$$M_n~=~939.56563\pm 0.00028~{\rm MeV}\qquad {\rm Mass}$$

$$M_n-M_p~=~1.293318\pm 0.000009~{\rm MeV}$$

$$\mu_n~=~-1.9130428\pm 0.0000005 \mu_N\qquad {\rm Magnetic\ Moment}$$

$$d_p < 0.97\times 10^{-25}~{\rm e\ cm}\qquad {\rm Electric\ Dipole\ Moment}$$

$$\overline{\alpha}_p~=~\left(9.8\pm 2.1\right)\times 10^{-4}~{\rm fm}\qquad {\rm Electric\ Polarizability}$$

$$\tau_n~=~ 886.7\pm 1.9~{\rm s}\qquad {\rm Mean\ Lifetime}$$

$$r_n^2~=~-0.119\pm 0.0016~{\rm fm}\qquad {\rm Charge\ Radius} \ \ \ .$$ (10)

Some comments:

1.

The masses of the neutron and proton are very similar, differing at the $10^{-3}$ level. Now, perhaps most fortunately for us, the neutron is slightly heavier than the proton, so that $n\rightarrow pe\overline{\nu}$ in free space, and not $p\rightarrow n\overline{e}\nu$ as would happen if $M_n < M_p$. This scenario would mean that there is no stable hydrogen, and hence a very different universe than the one we live in!

2.

So far an electric dipole for neither the proton $d_p$ nor the neutron $d_n$ has been measured. Such a quantity violates time-reversal invariance, a symmetry that we expect to satisfied in nature to a very high precision. However, the present limit on $d_n$ is close to where some extensions to the standard model of electroweak interactions would may produce a value for $d_n$. The standard model is estimated to give a $d_n$ a few orders of magnitude lower.

3.

It is clear from the fact that both the neutron and proton have non-zero charge radii (for a review see [4]) and also non-zero electric and magnetic polarizabilities, $\overline{\alpha}_p$, $\overline{\alpha}_n$ that the neutron and proton are not point like objects, and have an extended size not so much smaller than $1~{\rm fm}$. A plot of the proton charge form factor can be seen in fig. (2). If the proton wa s apoint object then we would expect the curve to behave like $Q^4$, which clearly it doesn't!

  

Figure: The proton charge form factor $F_1(Q^2)$ multiplied by $Q^4$. Data is from the E136 experiment at SLAC (reproduced without permission).