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Meaningful Details: the Value of Adding Baseline Dependence to the Neutrino-Dark Matter Effect

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Abstract

The possible effect on the flavour spectra of astronomical neutrinos from a neutrino-dark matter interaction has been investigated for decoherent neutrinos de Salas et al., (Phys. Rev. D 94(12), 123001 2016). In this work, we report results calculated for coherent neutrinos. This was done with two different models for the neutrino dark-matter interactions: a flavor eigenstate coupling, as for the weak interaction in the Standard Model, and a mass eigenstate coupling, which is predicted by certain non-Standard Models (specifically Scotogenic models). It was found that using a coherent analysis dramatically increased the explorable parameter space for the neutrino-dark matter interaction. However, the detection of coherent astronomical neutrinos presents a significant challenge to experimentalists, because such a detection would require an improvement in energy resolution by at least six orders of magnitude, with similar improvements in astronomical distance determinations.

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Notes

  1. A note about the effective mass eigenstates: The mass basis is the basis in which the vacuum propagation Hamiltonian is diagonal, meaning the mass eigenstates are the diagonal elements. In the presence of a medium, the propagation Hamiltonian is changed. The effective mass basis is the one in which the adjusted Hamiltonian is diagonal, with the effective mass eigenstates being the new diagonal elements. If the interaction inducing the shift is not uniform across species, then there will be shifts in the effective mass-squared differences leading to shifts in the oscillation patterns. This is explained further below.

  2. Δm2 is the larger of the two mass-squared differences, as that is the dominant factor. Also, the convention = c = 1 has been used.

  3. The black hole under consideration, A0620-00, is estimated to have a mass of 6.6 ± 0.25 solar masses [24], which gives it a Schwarzschild radius of approximately 20 km. By contrast, the short wavelength oscillations for the 1 PeV neutrinos under consideration are approximately 5-6 AU in length, with 1 AU ≈ 1.5 × 108 km. Even though it can be safely assumed that the production region is much larger than the Schwarzchild radius, it is still probably much smaller than the oscillation wavelength.

  4. Since baseline will have an uncertainty, σL, associated with it, the middle term in (7) should be σE E + σE E σL L. Given that the requirement on the baseline uncertainty was already established as σLlosc, the correction of the energy resolution from baseline uncertainty is negligible.

  5. These are interactions where the dark matter particles couple to the flavor eigenstates, in a manner analogous to the Weak Interaction.

  6. The mixing angles used in calculations were:𝜃12 = 0.5944, 𝜃13 = 0.1515, and 𝜃23 = 0.7854.

  7. The mass-squared differences used in calculatons were: δm12 = 7.59 × 10− 5 and δm13 = 2.43 × 10− 3.

  8. Since the diagonalization was done numerically, the actual computations replaced ΔM1322E with δλij, the difference between diagonal terms λi and λj in eff. Thus, (1) becomes

    $$ f_{\beta}=\displaystyle{\sum}_{\alpha=e,\mu,\tau}{\left|\displaystyle\sum\limits_{i=1}^{3}W_{{\beta}i}^{}W_{i{\alpha}}^{\dagger}\mathrm{e}^{-\mathrm{i}\lambda_{i}t}\right|}^2f_{\alpha}. $$
  9. This seemingly coincidental convergence with the amount of improvement in energy resolution required in order to make this measurement is not particularly surprising given that both quantities scale with baseline. Thus, a one order of magnitude increase in baseline will require a one order of magnitude improvement in both energy resolution and distance measurement, separately, with the benefit of a one order of magnitude improvement in interaction sensitivity.

  10. In the radiative mass models, the neutrino mass is generated by radiative corrections involving non-standard interactions. These are analogous to the See-Saw models which occur at tree-level. Part of the motivation for such models is to have the heavy partner of the neutrino be lower mass than is allowed by the See-Saw models and thus potentially detectable.

  11. Both Hamiltonians are presented in the mass basis representation, which is the canonical basis for the propagation Hamiltonian.

  12. In [14], the cosmological constraints are given as cross-sections. However, a close examination will reveal that the mass of the speculative dark matter particle is included as a parameter. The potentials are thus a product of the mass-dependent cross-section and the average energy density of DM in the appropriate environment (the galaxy for astronomical neutrinos, the universe for blazar neutrinos).

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Correspondence to William S. Marks.

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Marks, W.S., Cao, FG. Meaningful Details: the Value of Adding Baseline Dependence to the Neutrino-Dark Matter Effect. Int J Theor Phys 59, 3951–3966 (2020). https://doi.org/10.1007/s10773-020-04645-4

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