Pions

One of the implications of our understanding of QCD and the spontaneous breaking of chiral symmetry, is that there should be a nearly massless strongly interacting spin-zero particle, a pseudo-Goldstone particle. When we say nearly massless, we mean that the mass is much less than typical strong interaction length scales $\Lambda_\chi$. In the limit that the up and down quark masses were to vanish then this particle would have exactly zero mass. The pion ($\pi$) has been identified with this particle and it will play a significant role in our discussions of nuclear physics. There are three different charge states, $\pi^+$, $\pi^0$ and the $\pi^-$. The properties of the $\pi^+$ and $\pi^-$ are identical by the CPT theorem (Field Theory). In [3] you will find

$$M_{\pi^\pm}~=~139.5679\pm 0.0007~{\rm MeV}$$

$$M_{\pi^0}~=~134.9743\pm0.0008~{\rm MeV} \qquad {\rm Mass}$$

$$\tau_{\pi^\pm}~=~\left(2.6030\pm 0.0024\right)\times 10^{-8}~{\rm s}$$

$$\tau_{\pi^0}~=~\left(8.4\pm 0.06\right)\times 10^{-17}~{\rm s} \qquad {\rm Mean\ Lifetime}$$

$$\overline{\alpha}_{\pi^\pi}~=~\left(6.8\pm 1.4\right)\times 10^{-4}~{\rm fm}\qquad {\rm Electric\ Polarizability}$$

$$\overline{\beta}_{\pi^\pm}~=~-\left(5.4\pm 4.5\right)\times 10^{-4}~{\rm fm}\qquad {\rm Magnetic\ Polarizability}$$

$$r_{\pi^\pm}~=~0.66\pm 0.03~{\rm fm}\qquad {\rm Charge\ Radius} \ \ \ .$$ (11)

It is clear that the $\pi$'s are also very interesting objects. In fact a large part of nuclear and hadronic physics has been spent better understanding exactly what a pion is! We will not really get into this area during this course, but may step toward that during the next quarter.