Parity-doublet representation of Majorana fermions and neutron oscillation

Abstract

We present a parity-doublet theorem for the representation of the intrinsic parity of Majorana fermions, which is expected to be useful also in condensed matter physics, and it is illustrated to provide a criterion of neutron-antineutron oscillation in a Bardeen-Cooper-Schrieffer type of effective theory with ΔB ¼ 2 baryon number-violating terms. The CP violation in the present effective theory causes no direct CP-violating effects in the oscillation itself, which is demonstrated by the exact solution, although it influences the neutron electric dipole moment in the leading order of small ΔB ¼ 2 parameters. An analog of Bogoliubov transformation, which preserves P and CP, is crucial in the analysis.

A quest for new physics inside the neutron

“…The deeper insight into the problem requires rather elaborate technique: Majorana fermions, inclusion of external fields, the spin dependence, Bogolyubov transformation, etc. [20,22]. The general conclusion remains the same: the appearance of nn oscillations does not in itself break CP.…”

“…We start by quoting the conclusions from [18] and [19]: "neutron-antineutron oscillation implies breaking of CP along with baryon number violation" [18], and "the neutron-antineutron oscillation per se does not necessarily imply CP violation" [19]. Below we follow in an oversimplified form the arguments presented in [19,20]. A reasonable assumption is that Lorentz invariance and CPT are valid in a healthy field theory.…”

“…This question was raised in [18] and followed by a vivid discussion [19,20,22]. We start by quoting the conclusions from [18] and [19]: "neutron-antineutron oscillation implies breaking of CP along with baryon number violation" [18], and "the neutron-antineutron oscillation per se does not necessarily imply CP violation" [19].…”

“…Physics seem to depend on phase rotation! In other words, the CP property of ∆B = 2 term is ill-defined [19]. The deeper insight into the problem requires rather elaborate technique: Majorana fermions, inclusion of external fields, the spin dependence, Bogolyubov transformation, etc.…”

“…In principle, one can add an extra mass term (−m ′n iγ 5 n) which we discard, see [18][19][20][21]. The first term in (4.1) is invariant under P , C and T .…”