For neutral pions, the existence of the decay
[tex]\pi^{0} \longrightarrow 2\gamma[/tex]
proves that the pion spin must be integral (since Sy = 1) and that [itex]s_\pi \neq 1[/itex], from the following argument. It can be proved as a consequence of relativistic invariance that for any massless particle of spin s, there are only two possible spin substates, [itex]S_z = \pm s[/itex], where z is the direction of motion. Taking the common line of flight of the photons in the pion rest frame as the quantisation axis, the z-component of total photon spin in the above decay can thus have the values Sz = 0 or 2. Suppose [itex]s_\pi = 1[/itex]; then only [itex]S_z = 0[/itex] is possible, and the two-photon amplitude must behave under rotation like the polynomial [itex]P_{l}^{m}(\cos \theta)[/itex] with m = 0, where [itex]\theta[/itex] is the angle of the photon relative to the z-axis.
xepma said:Conservation of angular momentum. two is larger than one!
The spin of a pion is a quantum mechanical property that describes its intrinsic angular momentum. It is a fundamental property of subatomic particles and is measured in units of Planck's constant (h-bar).
The spin of a pion can be determined through experiments, such as measuring its decay products. In the case of neutral pions, their spin can be determined by analyzing their decay into two photons, which is only possible for particles with integral spin.
A particle with integral spin means that its spin value is a whole number, such as 0, 1, 2, etc. This is in contrast to particles with half-integral spin, which have spin values of 1/2, 3/2, 5/2, etc. Integral spin particles follow different rules and behaviors compared to half-integral spin particles.
The neutral decay of pions into two photons is only possible if the pion has integral spin. This is because the conservation of angular momentum requires that the total spin of the decay products must be equal to the spin of the parent particle. Since photons have a spin of 1, the spin of the pion must also be 1 in order for the decay to be possible.
The spin of a pion, and other subatomic particles, provides important information about their fundamental properties and interactions. It is also a key factor in understanding the structure of matter and the fundamental forces of the universe. By studying the spin of pions, scientists can gain a better understanding of the underlying principles of the universe.