Leptonic CP violation

An accelerator sends muon-type neutrinos toward a distant detector, where some are detected as electron-type neutrinos. It can repeat the experiment with antineutrinos, their antimatter counterparts. Are the changes intrinsically different after allowing for the ordinary matter they cross? That would violate charge–parity, or CP, symmetry: the rule relating a particle process to its antimatter counterpart with space reflected.[1] [2] [5]

A muon-neutrino beam produces electron-neutrino events after travelling to a distant detector. The corresponding antineutrino beam gives another energy-dependent event pattern. Do these patterns require an intrinsic charge–parity, or CP, asymmetry in three-flavour neutrino mixing once matter and experimental effects are accounted for?

CP compares a process with its antimatter counterpart after a spatial reflection. The Dirac CP phase $\delta_{\rm CP}$ sets a relative angle in the mixing of mass states, changing how their quantum components interfere. Its CP-conserving values are $0$ and $\pi$, modulo a full turn. This oscillation phase is distinct from the Majorana phases that may accompany neutrino mass; those phases do not enter these oscillation probabilities.

Ordinary matter contains electrons rather than an equal mixture of electrons and positrons. Its effect on propagation can therefore create a neutrino–antineutrino difference even at a CP-conserving phase. Beam fluxes, neutrino interactions with detector nuclei and event selection must also be modeled before counts become constraints on a probability. Near-detector measurements help control these experimental uncertainties. T2K and NOvA use different energies and travel distances, so their joint fit helps separate phase and ordering effects; the stated CP evidence still depends on the ordering assumption.[1] [2] [4] [5]

A decisive measurement of this intrinsic asymmetry is still missing.[1] [2] [3]

Joint fits give evidence conditional on an assumed inverted ordering; the cited results do not constitute an unconditional discovery.[1] [2] [3]

Masses and mixing strengths do not fully specify how neutrinos behave. An intrinsic matter–antimatter asymmetry would reveal an additional feature of their interactions, giving theories of neutrino mixing another quantity to explain.[1] [5]

A CP phase supplies information about lepton interactions that mass splittings and mixing angles cannot supply alone. Its measurement would test whether a symmetry survives in this part of particle physics and constrain models of neutrino mixing. Such symmetry violation is relevant to some accounts of the cosmic matter excess, but the measured oscillation phase by itself would not demonstrate any one production mechanism.[1] [5]