How Can The Non-unitarity Of The PMNS Matrix, As Hinted By Recent IceCube And Super-Kamiokande Data, Be Reconciled With The Perturbative Approach To Neutrino Oscillations In Matter, Particularly In The Context Of The MSW Effect, Without Violating The Principles Of Quantum Field Theory And The Standard Model Of Particle Physics?

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Reconciling the non-unitarity of the PMNS matrix with the perturbative approach to neutrino oscillations in matter, particularly the MSW effect, can be approached through the following framework:

  1. Understanding Non-Unitarity: The PMNS matrix's non-unitarity, suggested by experiments like IceCube and Super-Kamiokande, implies potential new physics beyond the Standard Model. This could involve additional neutrino states, such as sterile neutrinos, or new interactions that affect neutrino mixing.

  2. Extended Theoretical Framework: Introducing sterile neutrinos or heavy states can lead to an effective non-unitary PMNS matrix when considering only the active neutrinos. The full matrix, including all states, remains unitary, preserving quantum field theory principles.

  3. Perturbative Approach Adaptation: The perturbative method can be extended by incorporating small non-unitarity effects as higher-dimensional operators or additional terms in the Hamiltonian. These terms modify oscillation probabilities and can be treated as perturbations, allowing the use of existing methods with minor adjustments.

  4. Consistency with QFT and SM: Any extension must ensure unitarity is maintained in the full theory, preventing violations of quantum mechanics. This can be achieved by embedding non-unitarity within a larger unitary framework, such as through seesaw mechanisms or effective theories.

  5. Implications for MSW Effect: Non-unitarity may alter resonance conditions and oscillation probabilities in matter. The perturbative approach would need to account for these changes, possibly through modified potential terms in the Hamiltonian.

  6. Empirical Validation: Ongoing and future experiments should continue to test the extent of non-unitarity and its implications, guiding theoretical developments and ensuring consistency with both QFT and the Standard Model.

In conclusion, non-unitarity can be reconciled within an extended Standard Model framework, treating it as an effective phenomenon that preserves theoretical consistency while accommodating experimental observations.