The desired parity operator would be . If is part of a continuous symmetry group then exists, but if it is part of a discrete symmetry then this element need not exist and such a redefinition may not be possible. The Standard Model exhibits a symmetry, where is the fermion number operator counting how many fermions are in a state. Since all particles in the Standard Model satisfy , the discrete symmetry is also part of the continuous symmetry group. If the parity operator satisfied , then it can be redefined to give a new parity operator satisfying . But if the Standard Model is extended by incorporating Majorana neutrinos, which have and , then the discrete symmetry is no longer part of the continuous symmetry group and the desired redefinition of the parity operator cannot be performed. Instead it satisfies so the Majorana neutrinos would have intrinsic parities of . Parity of the pion In 1954, a paper by William Chinowsky and Jack Steinberger demonstrated that the pion has negative parity. They studied the decay of an "atom" made from a deuteron () and a negatively charged pion () in a state with zero orbital angular momentum into two neutrons (). Neutrons are fermions and so obey Fermi–Dirac statistics, which implies that the final state is antisymmetric. Using the fact that the deuteron has spin one and the pion spin zero together with the antisymmetry of the final state they concluded that the two neutrons must have orbital angular momentum The total parity is the product of the intrinsic parities of the particles and the extrinsic parity of the spherical harmonic function Since the orbital momentum changes from zero to one in this process, if the process is to conserve the total parity then the products of the intrinsic parities of the initial and final particles must have opposite sign. A deuteron nucleus is made from a proton and a neutron, and so using the aforementioned convention that protons and neutrons have intrinsic parities equal to they argued that the parity of the pion is equal to minus the product of the parities of the two neutrons divided by that of the proton and neutron in the deuteron, explicitly from which they concluded that the pion is a pseudoscalar particle. Parity violation Although parity is conserved in electromagnetism and gravity, it is violated in weak interactions, and perhaps to