M.D. Sheppeard – CPT Violation and the MINOS Experiment
This is a guest post from a unemployed theoretical physicist from New Zealand, Marni Dee Sheppeard. Marni is currently dabbling in quantum gravity research in Wellington. After a variety of jobs in experimental and particle physics, and also outside science, Marni completed a PhD in quantum gravity at Canterbury University in 2007. Jobs held since then include a Oxford University postdoc. She regularly discusses physics on her blog, Arcadian Pseudofunctor. I (T.D.) invited Marni to produce a guest post for this blog. Please find it below.
In the Standard Model of particle physics, there are three basic symmetries, namely
C: the interchange of positive and negative electric charge,
P: parity, associated to reflections of spatial coordinates,
T: the time reversal operation.
In quantum mechanics, each of these operations acts on a quantum state, and the reversal of the operation leads to a state that is closely related to the original one. In radioactive beta decay, a neutron always produces a proton, an electron and an electron antineutrino. A violation of CP symmetry was first observed in 1956 in the beta decay of cobalt-60, by Chien-Shiung Wu and her team. This demonstrates that our universe differentiates between a beta decay process and its mirror image, by favouring antineutrinos of a definite handedness in the weak interactions that we observe. But although the combined CP symmetry is not respected by nature, a combined CPT operation is supposed to behave nicely. This is because the CPT symmetry is understood in terms of Lorentz symmetry, which describes the behaviour of spacetime using the well tested theory of special relativity.
Although many theorists believe that the geometry of spacetime should emerge from more fundamental gravitational degrees of freedom, it is still generally thought that the CPT symmetry will be respected by nature. However, in a theory that does not begin with the classical description of spacetime, an apparent violation of CPT symmetry need not be directly associated to a breaking of the Lorentz symmetry, as we demonstrate.
A fundamental fermion is initially specified by a list (q,m,h) where m is its rest mass, q its charge and h its chirality, or handedness, which for a massless particle notes whether or not the spin is aligned with the direction of propagation. With massive particles we need to be more careful in describing propagation because their velocity is relative to the observer, as special relativity tells us. Still, chirality has two basic states: left and right. If we assume that all left and right states exist in nature, then the allowed values of the list (q,m,h) almost account for the fundamental fermions: the leptons and quarks. There remains a question about the antiparticles of neutral leptons. For a charged particle, the antiparticle has opposite charge, so the two particles cannot be confused. For the neutral neutrinos, however, it is not immediately clear that an antineutrino is a distinct state. Consider the possibility that all particles have distinct antiparticles. Charged particles have antiparticles of opposite charge, the same chirality and equal mass, but neutral antiparticles have like charge and like mass, so there could also be a neutral particle of like chirality with distinct mass. But by definition all particles have equal mass antiparticles with which they annihilate to photons, and one would like to claim that there is no CPT violation in the usual sense.
However, what we usually call a neutrino and an antineutrino might really be called a neutrino and a mirror neutrino, where the mirror neutrino has a distinct mass to the neutrino. The nomenclature is important, because in this case the neutrino and antineutrino can be the same particle!
The MINOS experiment has observed distinct masses for neutrinos and the so called antineutrinos, which we now call mirror neutrinos. In preliminary results released in 2010, MINOS claim that the total difference in masses squared for neutrinos is around 0.00232 eV2, while for mirror neutrinos it is 0.00336 eV2. Given our new mirror particle zoo, can we say anything about these numbers?
The ordinary neutrinos come in three possible mass states. In 2006, Carl Brannen fitted these three masses to a simple formula, resembling the Koide formula for the three charged lepton masses. First discovered by Yoshio Koide in 1981, this exact relation between the masses of the electron, muon and tau particles was used to predict the tau mass from the more accurately known electron and muon masses. The prediction was correct, and the formula remains in agreement with experimental results. Brannen’s prediction for the neutrino masses was based on the observation that the Koide formula is expressed in terms of a certain matrix. This matrix map is a quantum Fourier transform of the square roots of the three masses. In quantum information theory, this map is a three dimensional analogue of the qubit Hadamard gate, which is built from two elementary Pauli spin operators. The neutrino scale is selected so that the sum of mass squares is around 0.00232 eV2, as observed. Ignoring the choice of mass units, there are two remaining parameters in the neutrino matrix. One parameter is identical to the charged lepton case. The single remaining parameter appears to differ from the charged lepton case by π/12. That is, there is a complex phase parameter of exp(2i/9) for the charged leptons, and exp(2i/9+ πi/12) for the neutrinos. Both of these phases were then used to fit hadron masses into triplets, according to a theoretical analysis based on measurement algebras rather than traditional wave functions.
In the Fourier matrix, a conjugation of phases leaves the set of three masses unchanged. For the equal mass charged leptons and antileptons, the phases exp(±2i/9) give equal masses. Are the phase signs associated to elementary quantum data, such as the charge q? After the release of the MINOS results, many theorists were wondering about the possibility of CPT violation in the neutrino sector. Let us choose phases so that particle and antiparticle phases sum to zero, which is the phase associated to a boson set of three identical masses. The neutrino phase now has two sign components, so we may double the allowed mass sets for the neutral particles by choosing a sign mismatch, as in exp(2i/9- πi/12). With this phase, at the same scale as the neutrinos, the difference of mass squares for the mirror neutrinos is around 0.00336 eV2, as observed.
The mirror mass prediction corresponding to the lightest neutrino mass is now 0.00117 eV. Very soon after I posted this calculation on my blog last June, keen astronomer Graham Dungworth pointed out that the thermal equivalent of 0.00117 eV under the law for black body radiation is 2.73K, which is precisely the temperature of the cosmic microwave background. But that is a subject for another day.
If the CPT symmetry is respected, CP violation may be paired to T violation as it is in the working Standard Model. Neutrinos come in left and right handed states, just like the other leptons. Ordinary beta decay, however, produces mirror neutrinos, introducing a pervasive coupling between ordinary matter and the mirror world.