Here, | u ⟩ ⟩ is the up quark flavour eigenstate, and | d ⟩ ⟩ is the down quark flavour eigenstate, while | ↑ ↑ ⟩ and | ↓ ↓ ⟩ are the eigenstates of S z . Although these superpositions are the technically correct way of denoting a proton and neutron in terms of quark flavour and spin eigenstates, for brevity, they are often simply referred to as "uud" and "udd". The derivation above assumes exact isospin symmetry and is modified by SU(2)-breaking terms.