Exploration of CPT violation via time-dependent geometric quantities embedded in neutrino oscillation through fluctuating matter

Abstract

We propose a new approach to explore CPT violation of neutrino oscillations through a fluctuating matter based on time-dependent geometric quantities. By mapping the neutrino oscillations onto a Poincaré sphere structure, we obtain an analytic solution of master equation and further define the geometric quantities, i.e., radius of Poincaré sphere and geometric phase. We find that the mixing process between electron and muon neutrinos can be described by the radius of Poincaré sphere that depends on the intrinsic CP-violating angle. Such a radius reveals a dynamic mechanism of CPTviolation, i.e., both spontaneous symmetry breaking and Majorana-Dirac neutrino confusion. We show that the time-dependent geometric phase can be used to find the neutrino nature and observe the CPT-violation because it is strongly enhanced under the neutrino propagation. We further show that the time-dependent geometric phase can be easily detected by simulating the neutrino oscillation based on fluctuating magnetic fields in nuclear magnetic resonance, which makes the experimental observation of CPT-violation possible in the neutrino mixing and oscillations. PACS numbers: 14.60.Pq,03.65.Vf, 03.65.Yz I. INTRODUCE Neutrino mixing and oscillations are important to investigate new physics beyond the Standard Model of elementary particle physics, and also involve in hot issues on both astro-particle physics and cosmology [1-3]. Experimentally and theoretically, a set of important and fundamental problems, such as the neutrino mass, the nature of the Dirac vs Majorana neutrino or Majorana-Dirac confusion theorem [4], and the validity of CPT symmetry, has been under the debate [5][6][7][8][9]. The interference of the neutrino oscillations [10,11] can be used to test the CPT symmetry and the neutrino nature based effectively on the geometric phase, which provides an unconventional approach to probe CPT-violation beside the neutron electric dipole moment [12].The evolution of neutrinos involved the weak interactions leads to the CP-violation in a given flavor space, where the extrinsic CP-violating phases can mimic the characteristics of intrinsic CP-violating phases in the leptonic mixing matrix [13,[13][14][15][16].The neutrino oscillations observed so far can be explained in terms of three flavor space, i.e., active electron neutrino ν e , muon neutrino ν µ and τ neutrino ν τ , where the extrinsic CP violation is disentangled from the intrinsic one by the CP-violating observable [17]. An alternative method to treat neutrino oscillations has attracted extensive interests * zishengwang@yahoo.com † huipan@umac.mo

Discerning the Nature of Neutrinos: Decoherence and Geometric Phases

“…Geometric phases and, more generally, geometric invariants, have also been studied in connection with the particle mixing phenomena [45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60]. Here we focus on the geometric phases associated to the propagation of neutrinos and show that they can be a valuable tool to tell Dirac and Majorana neutrinos apart.…”

Noncyclic geometric phases and helicity transitions for neutrino oscillations in a magnetic field

“…In this approach quantum systems that cannot be accessed experimentally are simulated using a controllable physical system underlying the same mathematical model [76]. The possibility of studying neutrino systems by quantum simulation has been explored in [42,77]. In [42] it was proposed to detect the neutrino geometric phases using the nuclear magnetic resonance (NMR) setup with a controllable range of parameters.…”

“…Associated with the phenomenon of neutrino oscillations in vacuum, matter, and magnetic fields is the emergence of geometric phase, which has been explored by many authors in various settings [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42]. The concept of geometric phase emerges from the idea that the phase factor acquired by the wavefunction of a system undergoing quantum evolution has a part that is dynamical * sjoshi@barc.gov.in † srjain@barc.gov.in arXiv:1703.05027v2 [hep-ph]…”

“…For the case of Majorana neutrinos, even though diagonal magnetic moments vanish [6], there could be nonzero off-diagonal magnetic moments which result in transitions between neutrinos of different flavors and helicities, commonly termed as ν ↔ν transitions. The spin and spin-flavor oscillations may also lead to resonant conversion mechanisms, similar to the Mikheyev-Smirnov-Wolfenstein effect [7], the possibility of which has been extensively discussed in various scenarios including solar [8][9][10][11][12][13][14][15][16][17][18] and supernova neutrinos [19][20][21][22][23][24](see [25] for a detailed list of references).Associated with the phenomenon of neutrino oscillations in vacuum, matter, and magnetic fields is the emergence of geometric phase, which has been explored by many authors in various settings [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42]. The concept of geometric phase emerges from the idea that the phase factor acquired by the wavefunction of a system undergoing quantum evolution has a part that is dynamical * sjoshi@barc.gov.in † srjain@barc.gov.in arXiv:1703.05027v2 [hep-ph]…”

Gravity-Induced Geometric Phases and Entanglement in Spinors and Neutrinos: Gravitational Zeeman Effect

“…There are many other explorations over the years in various contexts of geometric phase and entanglement in neutrinos, including those with CPT violation and fluctuating matter, non-linear refraction, magnetic field, dissipative matter, etc. [17][18][19][20][21][22][23][24].…”