# The Physics Behind No$$\nu$$a

Abstract

The $${\rm NO}\nu{\rm A}$$ experiment is a long-term experiment looking to study neutrino oscillations using the newly upgraded NuMI (Neutrinos at the Main Injector) beam at Fermilab, allowing for more sensitive measurements than possible before. Following the non-zero measurement of the mixing angle ($$\theta_{13}$$), there is hope that the collider can now be used to study the neutrino mass hierarchy with more certainity, as well as put a limit on the CP violating phase ($$\delta_{cp}$$). In this paper, I will briefly introduce neutrino oscillations and the planned measurement of the mixing angle and mass hierarchy at $${\rm NO}\nu{\rm A}$$ as well as its implications on neutrino physics.

# Introduction

In 1934, when the parts of the standard model were first being pieced together, Enrico Fermi introduced a massless particle called a neutrino that is fermionic in nature and does not ineract with baryonic matter, in order to explain how beta decay could convserve fundamental quantities (energy, spin, etc.) (Wilson 1968). For a while, only electron neutrinos were thought to exist. However, fifty years later in 1988, Lederman, Schwartz, and Steinberger earned the Nobel Prize in physics for work they did in 1962 at the Alternating Gradient Synchotron at the Brookhaven National Laboratory. In their paper, the group from Columbia reported that they had found a second kind of neutrino that did not couple to the electron like the one proposed by Fermi, but instead to muons produced by their beam in upstate New York(Danby 1962). Another forty years passed before the third generation of neutrino was dicovered in 2000 by the DONUT collaboration at Fermilab near Chicago, Illinois(Kodama 2001). For a long while, these various “flavors” of neutrinos were thought to not couple with anything apart from their respective fermion. However, people reasoned that it wasn’t impossible that these neutrinos could interact with other forms of matter.

## Neutrino Oscillations

\label{sect:osc-motiv} In 1958, Bruno Pontecorvo, an assistant of Fermi’s, suggested that if neutrinos did in fact have a mass (unlike what Fermi claimed) then the neutrinos we encounter might be a particle mixture of more fundamental mass states. Consequently, Pontecorvo argued, there is some probability of transitioning between neutrino and its associated anti-neutrino (Pontecorvo 1957). Around the same time, a variety of experiments reported similar discrepancies between the measured number of neutrinos created in solar rays and what they expected.

Coupled with the discovery of the muon neutrino, Pontecorvo accredited this so-called “solar neutrino problem” to the oscillation of neutrinos between various flavor states due to a non zero mass. In 1967 he wrote that “from the point of view of detection possibilities ... if the oscillation length is much smaller than the radius of the solar region which effectively produces neutrinos ... it will be impossible to detect directly oscillations of the solar neutrino [with current technology].” He continues to say that “the only effect at the surface of the earth would consist in the fact that the flux of observable solar neutrinos would be half as large as the total flux of solar neutrinos” (Pontecorvo 1968). It was not until 1998 that the oscillation of neutrinos between various states was observed by the Super-Kamiokande Collaboration in Japan, giving substantial evidence to believe that neutrinos do in fact have a non-zero mass like Pontecorvo suggested 40 years earlier (Fukuda 1998).

## The NO$$\nu$$A Experiment

NO$$\nu$$A is the latest in the long, rich history of particle detectors specialized to study neutrinos. It is a long baseline experiment managed by the Fermi National Accelerator Laboratory (Fermilab) in Batavia, Illinois and takes advantage of the NuMI (Neutrinos at Main Injector) neutrino beam that was constructed for the MINOS project. With the start of NO$$\nu$$A, along with other improvements, the NuMI beam was upgraded to nearly twice the power with a new graphite target and magnetic horns to provide a narrow-band neutrino beam with a high intensity whose energy peaks at the maximum probability for neutrino oscillation (Paley 2012).