Abstract
CP asymmetries for neutrino oscillations in matter can be disentangled into the matter-induced CPT-odd (T-invariant) component and the genuine T-odd (CPT-invariant) component. For their understanding in terms of the relevant ingredients, we develop a new perturbative expansion in both Δm212, |a| ≪ |Δm312| without any assumptions between Δm212 and a, and study the subtleties of the vacuum limit in the two terms of the CP asymmetry, moving from the CPT-invariant vacuum limit a → 0 to the T-invariant limit Δm212 → 0. In the experimental region of terrestrial accelerator neutrinos, we calculate their approximate expressions from which we prove that, at medium baselines, the CPT-odd component is small and nearly δ-independent, so it can be subtracted from the experimental CP asymmetry as a theoretical background, provided the hierarchy is known. At long baselines, on the other hand, we find that (i) a Hierarchy-odd term in the CPT-odd component dominates the CP asymmetry for energies above the first oscillation node, and (ii) the CPT-odd term vanishes, independent of the CP phase δ, at E = 0.92 GeV (L/1300 km) near the second oscillation maximum, where the T-odd term is almost maximal and proportional to sin δ. A measurement of the CP asymmetry in these energy regions would thus provide separate information on (i) the neutrino mass ordering, and (ii) direct evidence of genuine CP violation in the lepton sector.
Highlights
A = 2EV of the matter potential V due to charged current interactions between electron neutrinos and electrons and the genuine CPV term is generated by a phase δ in the threefamily PMNS mixing matrix, the ACαβPT and ATαβ components of the CP asymmetry have the correct behavior, for any neutrino energy E and baseline L, in these parameters: whereas ACαβPT is odd in a ∀δ, ATαβ is odd in sin δ ∀a
The transmutation of masses in vacuum to mixings in matter forces the smallness of the imaginary part of the rephasing-invariant mixing in matter at high energies. This fact does not necessarily mean that genuine CP violation is unobservable at these energies, since the genuine CPV component of the CP asymmetry contains this energy-dependent factor together with the matter-dependent oscillation function —odd in L — that depends on both energy and baseline
As the CP asymmetry is a difference between neutrino and antineutrino oscillation probabilities, we discover that ACμePT is only changing its sign under a change of hierarchy in the vanishing limit of ∆m221
Summary
Neutrino oscillations in matter are described through the effective Hamiltonian in the flavor basis [4, 7,8,9,10,11]. The absence of genuine CP violation leads to real Jαijβ and J ̄αijβ, so all transition probabilities Pαβ are L-even functions This result shows that L-odd terms in ACαβP are. Under CPT: {∆m 2ij ↔ ∆m ̄ 2ij, Jαijβ ↔ (J ̄αijβ)∗}, neutrino and antineutrino terms in ACαβPT are interchanged, so ACαβPT changes its sign This sign in ATαβ is compensated by the change of sign in both Im Jαijβ and Im J ̄αijβ, leaving ATαβ invariant. Under T: {Jαijβ → (Jαijβ)∗, J ̄αijβ → (J ̄αijβ)∗}, the only change in the asymmetries is a change of sign in all imaginary parts, changing the sign of ATαβ and leaving ACαβPT invariant These properties lead cleanly to the disentanglement of ACαβP = ACαβPT + ATαβ, where ACαβPT is T-invariant (even in sin δ) and CPT-odd in a, whereas ATαβ is CPT-invariant. These complementary behaviors of the two components of the experimental CP asymmetry identify the CPV component ATαβ as CPT-invariant and a fully genuine CPV observable, whereas the CPV component ACαβPT is T-invariant and a fully fake CPV observable
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
