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Concept# C parity

Summary

In physics, the C parity or charge parity is a multiplicative quantum number of some particles that describes their behavior under the symmetry operation of charge conjugation.
Charge conjugation changes the sign of all quantum charges (that is, additive quantum numbers), including the electrical charge, baryon number and lepton number, and the flavor charges strangeness, charm, bottomness, topness and Isospin (I3). In contrast, it doesn't affect the mass, linear momentum or spin of a particle.
Consider an operation that transforms a particle into its antiparticle,
Both states must be normalizable, so that
which implies that is unitary,
By acting on the particle twice with the operator,
we see that and . Putting this all together, we see that
meaning that the charge conjugation operator is Hermitian and therefore a physically observable quantity.
For the eigenstates of charge conjugation,
As with parity transformations, applying twice must leave the particle's state unchanged,
allowing only eigenvalues of the so-called C-parity or charge parity of the particle.
The above implies that for eigenstates, . Since antiparticles and particles have charges of opposite sign, only states with all quantum charges equal to zero, such as the photon and particle–antiparticle bound states like the neutral pion, η or positronium, are eigenstates of .
For a system of free particles, the C parity is the product of C parities for each particle.
In a pair of bound mesons there is an additional component due to the orbital angular momentum. For example, in a bound state of two pions, π+ π− with an orbital angular momentum L, exchanging π+ and π− inverts the relative position vector, which is identical to a parity operation. Under this operation, the angular part of the spatial wave function contributes a phase factor of (−1)L, where L is the angular momentum quantum number associated with L.
With a two-fermion system, two extra factors appear: one comes from the spin part of the wave function, and the second from the exchange of a fermion by its antifermion.

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