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Introduction and Theoretical Background

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Event Classification in Liquid Scintillator Using PMT Hit Patterns

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Abstract

The neutrino was first proposed to save energy conservation in nuclear \(\beta \) decay. By 1914, Chadwick had shown that the \(\beta \) energy spectrum was continuous [1], but \(\beta \) decay was then thought to be a two body process, in which the energy of the \(\beta \) and recoiling nucleus are exactly constrained by energy conservation. What followed was many years of controversy, as people questioned the apparently impossible experimental results [1] until they were confirmed by Ellis and Wooster in 1927 [2] and Meitner proved that the missing energy could not be accounted for by neutral \(\gamma \) rays [2]. These results famously led N. Bohr to suggest that perhaps energy conservation applied only in a ‘statistical sense’ [3].

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Notes

  1. 1.

    1 SNU (solar neutrino unit) is equal to the flux that produces \(10^{-36}\) captures per second per target atom.

  2. 2.

    The smallest angle made with a vector normal to the surface of the earth.

  3. 3.

    Compared with D\(_2\)O, salt has a much larger neutron capture cross-section and produces a larger \(\gamma \) energy deposit. Both factors enhance the neutron detection efficiency.

  4. 4.

    If the oscillation length was shorter than the length of the detector, the oscillations would ‘average out’ to produce 1/3 of each flavour.

  5. 5.

    Though the octant of \(\theta _{23}\) is still poorly constrained.

  6. 6.

    As the universe expands, neutrinos collide with other particles ever less frequently. Eventually, interactions betweeen the neutrinos and the rest of the universe’s particles are too infrequent to maintain thermal equilibrium between the two and the neutrinos are thermally isolated. This is ‘freeze-out’.

  7. 7.

    An introduction to Lorentz group representations and spin 1/2 fields is given in [103].

  8. 8.

    Where \(\mathcal {C} = i\gamma ^{2}\gamma ^{0}\).

  9. 9.

    References [2, 105] serve as a good introductions for the following two sections.

  10. 10.

    The largest mass currently allowed by cosmology.

  11. 11.

    Fermion fields carry dimension \([E]^{\frac{3}{2}}\), so the Majorana mass term carries dimension \([E]^{3}\) whilst boson fields carry dimension [E]. Two Higgs fields in the interaction term would give it dimension 5, Lagrangian terms of dimension greater than 4 are non-renormalisable.

  12. 12.

    This is just the same helicity suppression that causes \(\pi ^\pm \) to decay predominantly to \(\upmu \).

  13. 13.

    This is the ‘pairing’ term of the semi-empirical mass formula for nuclei.

  14. 14.

    Neglecting the neutrino mass.

  15. 15.

    The exception is the \(\alpha \) emitter \(^{238}\)U for which the half-life was measured radio-chemically [116].

  16. 16.

    Part of which is not ruled out by cosmology.

  17. 17.

    Ignoring the neutrino mass.

  18. 18.

    Assuming G\(^{0\nu } = 3.96\times 10^{-14}\), M\(^{0\nu } = 4.03\).

  19. 19.

    In the limit that the number of background counts is Gaussian.

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Dunger, J. (2019). Introduction and Theoretical Background. In: Event Classification in Liquid Scintillator Using PMT Hit Patterns. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-31616-7_1

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