Chirality (physics)

A chiral phenomenon is one that is not identical to its mirror image (see the article on mathematical chirality). The spin of a particle may be used to define a handedness, or helicity, for that particle, which, in the case of a massless particle, is the same as chirality. A symmetry transformation between the two is called parity transformation. Invariance under parity transformation by a Dirac fermion is called chiral symmetry. A chiral phenomenon is one that is not identical to its mirror image (see the article on mathematical chirality). The spin of a particle may be used to define a handedness, or helicity, for that particle, which, in the case of a massless particle, is the same as chirality. A symmetry transformation between the two is called parity transformation. Invariance under parity transformation by a Dirac fermion is called chiral symmetry. The helicity of a particle is right-handed if the direction of its spin is the same as the direction of its motion. It is left-handed if the directions of spin and motion are opposite. So a standard clock, with its spin vector defined by the rotation of its hands, tossed with its face directed forwards, has left-handed helicity. Mathematically, helicity is the sign of the projection of the spin vector onto the momentum vector: “left” is negative, “right” is positive. The chirality of a particle is more abstract: It is determined by whether the particle transforms in a right- or left-handed representation of the Poincaré group. For massless particles – photons, gluons, and (hypothetical) gravitons – chirality is the same as helicity; a given massless particle appears to spin in the same direction along its axis of motion regardless of point of view of the observer. For massive particles – such as electrons, quarks, and neutrinos – chirality and helicity must be distinguished: In the case of these particles, it is possible for an observer to change to a reference frame moving faster than the spinning particle, in which case the particle will then appear to move backwards, and its helicity (which may be thought of as “apparent chirality”) will be reversed. A massless particle moves with the speed of light, so no real observer (who must always travel at less than the speed of light) can be in any reference frame where the particle appears to reverse its relative direction of spin, meaning that all real observers see the same helicity. Because of this, the direction of spin of massless particles is not affected by a change of viewpoint (Lorentz boost) in the direction of motion of the particle, and the sign of the projection (helicity) is fixed for all reference frames: The helicity of massless particles is a relativistic invariant (a quantity whose value is the same in all inertial reference frames) which always matches the massless particles' chirality. The discovery of neutrino oscillation implies that neutrinos have mass, so the only observed massless particle is the photon. The gluon is also expected to be massless, although the assumption that it is has not been conclusively tested. Hence, these are the only two particles now known for which helicity could be identical to chirality, and only one of them has been confirmed by measurement. All other observed particles have mass and thus may have different helicities in different reference frames. It is still possible that as-yet unobserved particles, like the graviton, might be massless, and hence have invariant helicity that matches their chirality, like the photon. Only left-handed fermions and right-handed antifermions interact with the weak interaction.In most circumstances, two left-handed fermions interact more strongly than right-handed or opposite-handed fermions, implying that the universe has a preference for left-handed chirality, which violates a symmetry of the other forces of nature.