The charmonium P-wave states are the spin singlet with and the spin triplet

PHYSICS · Subjective · Fermi University Physics · Particle Physics & Quantum Fields · Symmetry, groups and the quark model · Symmetry, groups and the quark model

Symmetry and Flavour, Ch Hadron spectroscopy: quarkonium, orbital excitations and exotic states

Problem

The charmonium P-wave states are the spin singlet

h_c(1P)

with

J^{PC}=1^{+-}

and the spin triplet

\chi_{c0}(1P)

\chi_{c1}(1P)

and

\chi_{c2}(1P)

with

J^{PC}=0^{++}

1^{++}

and

2^{++}

. A single photon has

C=-1

. The Landau-Yang theorem, asserted here from the theory of angular momentum and gauge invariance applied to two on-shell photons, forbids a state with total angular momentum

J=1

from decaying into two photons. State, with a one-line reason in each case, whether each of the four can decay to two photons.

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