Abstract
In Chap. 2 we saw that searching for a nonzero θ13 is one of the main priorities in the field of neutrino physics. In this chapter, after reviewing the motivation for θ13 in the first part of Sect. 4.1 we explain how MINOS can access this mixing angle by searching for νe appearance, together with the main challenges involved in that search. Section 4.2 then lays out the strategy for the analysis, by introducing the different methods involved and by giving an overview of their roles. The subsequent chapters, which are referenced throughout Sect. 4.2, provide more detail on each of the steps of the analysis.
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- 1.
This expression is good to first order in the mass hierarchy parameter \(\alpha\) and to second order in \(\hbox{sin}\,\theta_{13}\). Also, the probability is calculated based on the assumption that neutrinos travel in matter of constant electron density \(n_{e}\), which is a very good approximation in our case as neutrinos go only through the earth’s crust [4]. Eq. 4.2 is thus accurate for all practical purposes, even though for the analysis we used the full expression for \(P(\nu_{\mu} \rightarrow \nu_{e})\), which takes more than one page to write fully but is easy for a computer to evaluate.
- 2.
This statement is not strictly correct when we consider the full expression for \(P(\nu_{\mu} \rightarrow \nu_{e})\). As a matter of fact, the next term in the expansion is \(\alpha^2 \hbox{sin}^2 2\theta_{12} \hbox{sin}^2 \theta_{23} {{\hbox{sin}^2 A\Updelta}\over {A^2}}\) [5], which is not dependent on \(\theta_{13}\). However \(P(\nu_{\mu} \rightarrow \nu_{e})\) in the case of \(\theta_{13} =0 \) is ∼0.002 at \(1\) GeV and decreases exponentially at higher energies, thus being completely negligible experimentally.
- 3.
This corresponds to the MINOS recorded dataset as of this writing.
- 4.
The effective radiation length and the effective Molière radius are calculated considering that a normally incident electron goes through \(42.7\%\) of steel, \(16.8\%\) of scintillator and \(40.5\%\) of air. In the case of the radiation length for example, from the values in Table 4.1 we obtain \(X_{{\rm eff}}= (0.427/1.76 + 0.168/47.9 + 0.405/3.04\times10^{4})^{-1} = 4.06\,\hbox{cm}\).
- 5.
Throughout this thesis we use the term “hadronic shower" in its broad sense, i.e., as the shower initiated by the transfer of energy from the neutrino to the struck nucleus in the detector. These showers consist mostly of hadrons although, as discussed in this section, can contain particles that do not interact through the strong interaction.
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Ochoa Ricoux, J.P. (2011). Measuring \(\theta_{13}\) in MINOS. In: A Search for Muon Neutrino to Electron Neutrino Oscillations in the MINOS Experiment. Springer Theses. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7949-0_4
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