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P -parity

P -parity is left-right parity, or spatial parity, and was the first of several "parities" discovered, and so is often called just "parity". If the universe were reflected in a mirror, most laws of physics would be identical—things would behave the same way regardless of what we call "left" and what we call "right". This concept of mirror reflection is called parity (P). Gravity, the electromagnetic force, and the strong interaction all behave in the same way regardless of whether or not the universe is reflected in a mirror, and thus are said to conserve parity (P -symmetry). However, the weak interaction does distinguish "left" from "right", a phenomenon called parity violation (P -violation).

Based on this, one might think that, if the wavefunction for each particle (more precisely, the quantum field for each particle type) were simultaneously mirror-reversed, then the new set of wavefunctions would perfectly satisfy the laws of physics (apart from the weak interaction). It turns out that this is not quite true: In order for the equations to be satisfied, the wavefunctions of certain types of particles have to be multiplied by −1, in addition to being mirror-reversed. Such particle types are said to have negative or odd parity (P = −1, or alternatively P = −), whereas the other particles are said to have positive or even parity (P = +1, or alternatively P = +).

For mesons, parity is related to the orbital angular momentum by the relation:

where the L is a result of the parity of the corresponding spherical harmonic of the wavefunction. The "+1" comes from the fact that, according to the Dirac equation, a quark and an antiquark have opposite intrinsic parities. Therefore, the intrinsic parity of a meson is the product of the intrinsic parities of the quark (+1) and antiquark (−1). As these are different, their product is −1, and so it contributes the "+1" that appears in the exponent.

As a consequence, all mesons with no orbital angular momentum (L = 0) have odd parity (P = −1).