[Paper Review] Photon-neutrino interactions in magnetic fields

Rashid Shaisultanov|ArXiv.org|Sep 22, 1997

Neutrino Physics Research3 citations

TL;DR

This paper investigates low-energy photon-neutrino interactions in the presence of a homogeneous magnetic field, demonstrating that cross sections for processes like γγ → νν̄ are enhanced by a factor of ∼(m_W/m_e)^4 × (B/B_c)^2 compared to vacuum. The energy-loss rate for photons due to this process is derived, showing significant implications for astrophysical environments with strong magnetic fields, such as neutron stars.

ABSTRACT

The low-energy two neutrino-two photon interactions in the presence of homogeneous magnetic field are studied. The cross sections in external magnetic field are shown to be larger than in vacuum by factor $\sim (m_W /m_e) ^4(B/B_c) ^2$. The energy-loss rate due to the process $γγ o ν\barν$ in magnetic field is obtained.

Motivation & Objective

• To analyze low-energy two-photon, two-neutrino interactions in the presence of a homogeneous magnetic field.
• To determine how external magnetic fields modify neutrino production and photon absorption cross sections compared to vacuum processes.
• To calculate the energy-loss rate for photons due to the γγ → νν̄ process in strong magnetic fields.
• To assess the astrophysical relevance of these interactions in environments with extreme magnetic fields, such as magnetars.
• To provide a theoretical framework for photon-neutrino scattering in external fields beyond standard model vacuum QED.

Proposed method

• The study employs quantum field theory techniques in external electromagnetic fields, focusing on the effective Lagrangian approach for low-energy processes.
• It considers the interaction Hamiltonian for photons and neutrinos in a constant, uniform magnetic field, using perturbative QFT to compute scattering amplitudes.
• The cross section is calculated using the matrix element squared and phase space integration for the process γγ → νν̄ in a magnetic field.
• The energy-loss rate is derived from the cross section by averaging over photon energies and including the magnetic field dependence via the critical field B_c.
• The analysis includes the leading-order contribution from virtual W-boson exchange, with the magnetic field modifying the effective coupling strength.
• The results are expressed in terms of the ratio of the magnetic field to the critical quantum electrodynamic field B_c ∼ 4.4 × 10^13 T.

Experimental results

Research questions

• RQ1 How does a homogeneous magnetic field enhance the cross section for the γγ → νν̄ process compared to vacuum?
• RQ2 What is the energy-loss rate for photons due to this process in strong magnetic fields?
• RQ3 What is the dependence of the cross section on the magnetic field strength and the W-boson mass?
• RQ4 How do these interactions affect photon propagation in magnetized astrophysical environments?
• RQ5 What is the role of virtual W-boson exchange in mediating photon-neutrino interactions in external fields?

Key findings

• The cross section for γγ → νν̄ is enhanced by a factor of ∼(m_W/m_e)^4 × (B/B_c)^2 in the presence of a magnetic field compared to vacuum.
• The enhancement arises due to the modification of the effective coupling between photons and neutrinos via virtual W-boson exchange in the external field.
• The energy-loss rate for photons due to this process is found to be significant in strong magnetic fields, particularly in neutron star environments.
• The derived energy-loss rate scales with the square of the magnetic field strength, indicating a strong dependence on B.
• The results suggest that photon-neutrino interactions in magnetic fields could play a role in the radiative cooling of magnetized compact objects.
• The cross section enhancement is most pronounced at low photon energies and high magnetic fields, consistent with conditions in magnetars.