Hi! I'm Emma and I am an undergraduate student at the University of California, Berkeley majoring in Physics and Astrophysics. In the summer of 2021, as part of the CIERA REU program at Northwestern University, I worked with Dr. Andre de Gouvea on neutrino physics research with the help of Dr. Ivan Martinez-Soler and Dr. Yuber Perez-Gonzalez.
Neutrinos are weakly interacting subatomic particles that are known to exist in three different flavors. In neutrino physics, current measurements of neutrino properties have yet to achieve a level of precision to be able to rule out the possibility of a fourth, sterile neutrino. We are exploring what neutrino-oscillation information can be extracted given a high-statistics sample of proton-proton (pp) solar neutrinos (including spectral information) from the next-generation WIMP dark-matter-search experiment DARWIN. Specifically, the DARWIN collaboration claims sensitivity to solar neutrinos via electron scattering in an energy region lower than that accessed by any previous experiments. Ultimately, we are exploring DARWIN's ability to constrain different parameter values based on its sensitivity. We simulated DARWIN data and, using a simple chi-squared method, analyzed whether DARWIN could answer various physics questions; for example, setting constraints on a theorized sterile neutrino. Determining whether to expand DARWIN's mission to measure solar neutrinos will provide valuable insight into DARWIN's potential. Measuring neutrino properties with greater precision, and potentially discovering the constraints of a sterile neutrino, would be a significant contribution to understanding the Standard Model and doing so via an already planned project would be expeditious and limit costs.
Neutrinos are neutral charged leptons with spin-1/2 that only interact with matter through weak interactions (Haxton 2012). There are three distinct types, or flavors, of neutrinos identified by the charged particle that accompanies neutrino production, i.e., the electron, muon, and tauon (Haxton 2012). Neutrino oscillations describe the process by which neutrinos oscillate between flavors as they traverse, which explains the phenomenon of a neutrino being born one flavor and detected as another. Neutrinos are byproducts of nuclear reactions, and specifically, in the Sun, they are products of nuclear fusion (Bahcall 1989). Given the Sun's proximity to Earth and its large-scale production of neutrinos, we can experimentally measure neutrino properties through the detection and study of solar neutrinos. Typically, experiments are conducted using large detectors deep underground; this is essential to provide the necessary rate of events and to limit backgrounds caused by cosmic rays and natural radioactivity (Haxton 2012). The Sun produces various neutrinos from its nuclear reactions and has been studied extensively for high energies. The most recent study was Borexino, which measured the low-energy pp, 7Be, and pep component fluxes (G. Bellini et al. 2014, 2011, 2012).
Our work focuses on investigating whether more can be learned from studying neutrinos with low energies, a region where the proton-proton (pp) reaction dominates the solar energy-generating process (Bahcall 1989). Observing solar neutrinos, specifically pp neutrinos, serves as a probe to study non-standard neutrino interactions and to test the Standard Model. More accurate measurements depend on how well the experiment can measure neutrinos and how well current theories accurately reflect experimental measurements. Because DARWIN, a dark matter experiment, proposes to measure neutrinos with greater acuity and less uncertainty, and because more is known about pp neutrinos theoretically (they are the easiest to predict, as pp neutrinos do not depend on the entire pp reaction chain), an experiment of this caliber would provide more accurate measurements of neutrino properties.
The proposed liquid xenon DARWIN observatory offers the sensitivity to study solar neutrinos and more specifically to measure, via elastic scattering, the pp neutrino flux in the electron recoil energy region from a few keV to 200 keV (Aalbers et al. 2020). From such an observation, we can deduce the values of the electroweak mixing angle, a parameter in electroweak interactions, and the electron-type neutrino survival probability, the probability an electron neutrino from the Sun will remain an electron neutrino upon detection, with the projected relative precision of 5% and 4%, respectively (Aalbers et al. 2020). This high-statistics observation of pp neutrinos would be the first of its kind and presents an opportunity to learn more about neutrinos. DARWIN will measure charges produced, and the electromagnetic radiation emitted, when xenon gets hit into an excited state and is ionized. For studying neutrinos, DARWIN will detect incoming neutrinos by measuring what the xenon's electron does. In particular, DARWIN will measure the number of events that occur, where an event is a neutrino colliding with an electron. Ideally, DARWIN will measure the electron recoil energy spectrum for pp neutrinos, assuming outstanding background can be removed from radioactive xenon.
We simulate DARWIN data and explore what physics questions this data could answer about neutrinos, specifically what constraints can DARWIN set on neutrino parameters. Through this analysis, we establish whether expanding DARWIN's mission to measure solar neutrinos will give valuable information to neutrino physics.
We simulated experimental measurement data of pp neutrinos from DARWIN using equations (1, 2, and 3) given by Aalbers et al. 2020. Equation (1) describes the spectral flux of the pp neutrino in β form, where ϕpp is the flux scale of the pp neutrino, A is the corresponding normalization constant, xpp = Qpp + me with Qpp being the characteristic maximal energy and me being the electron mass, and Eν the energy of the emitted neutrino (Figure 1).
Equation (2) describes the differential cross section, where gL = sin2θw-1/2 and gR = sin2θw are the coupling parameters with the assumption that sin2θw = 0.2387, and Er is the energy of the induced electron recoil (Figure 2). Taking into consideration the electron neutrino's charged current interactions, for νe, gL → gL + 1.
Equation (3) describes the elastic electron-neutrino scattering, which involves the spectral flux and differential cross section, where Nee = 2.48✕1029 is the number of target electrons per tonne of xenon, and qpp is the minimum emitted neutrino energy defined in equation (4).
From equation (3), the electron recoil spectrum was modeled to represent DARWIN data using values of ϕpp = 5.98✕1010 cm-2 s-1, Qpp = 420 keV, and Pee = 0.55 given in Aalbers et al. 2020 (Figure 3). The value of the normalization constant A was chosen to be ~27.3 keV, to match results in Aalbers et al. 2020.
To simulating DARWIN data, Er was binned by 10 keV to compute the number of events DARWIN measures. Using equation (5) for each Er bin, Figure 4 represents DARWIN's anticipated experimental measurements.
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The result of the simulation represents the data that DARWIN will produce once the experiment is active. Considering potential backgrounds that would contribute more to the event rate than pp neutrinos, we removed those energy regions for which this was true so we could disregard potential background interference in our analysis. This changed the energy spectrum to span from ~70 to ~213 keV, as opposed to its original 0 to 420 keV; below 70 keV, 124Xe dominated, and above 213 keV, radon dominated. We ignored the main source of potential background, unstable xenon isotopes, which naturally undergo double-beta decay, under the assumption that, if DARWIN were commissioned to detect solar neutrinos, these 136Xe background contributions would be removable through isotropic depletion and therefore insignificant (Aalbers et al. 2020).
We then analyzed the data, comparing it to data produced to test our hypothesis using theoretical equations. The next stage is to simulate our theoretical data to examine how well DARWIN can constrain different theoretical parameters.
The simulated DARWIN data was analyzed using a simple chi-squared test, shown in equation (6), where i is the Er bin number and assuming the expected error for each bin is given by σi = √(Di), Di represents DARWIN data, and Ti represent the theoretical data.
The chi-squared test is used to determine how much our experimental measurement differs from our theoretical predictions. For all questions analyzed, DARWIN data is modeled to measure the standard three-neutrino scenario with Pea = 1 - Pee, and the target composition for the experiment was set to 300 tonne·year for all questions.
Using the chi-squared test, we investigate how well we can measure Pee, assuming it is energy-independent and that Pea = 1 - Pee, where Pea represents the muon- and tauon-type survival probability, and the result of which resulted in a 1σ relative uncertainty of 13.6%. Because pp neutrinos have fast oscillations and short wavelengths, it is reasonable to assume energy-independence of the probabilities. Additionally, due to pp neutrino’s low energy, we assume the MSW effects for pp neutrinos were negligible. We use this result to check that our estimates were consistent with those made by the DARWIN collaboration, which got a similar result. Further, we consider how well we can measure energy-independent Pee and Pea, without imposing the constraint 1 = Pea + Pee, to test whether Pee and Pea do add up to one. The result of this test is Figure 5, which shows how well DARWIN can constrain Pee and Pea when measured together and whether it can rule out the possibility that Pea equals zero. Because Figure 5 shows an ellipse, we know that DARWIN can constrain the values of Pee and Pea with fewer assumptions made, and therefore can measure it well.
Similarly, we explore how well we can measure energy-independent Pee and Pes assuming the constraint 1 = Pee + Pes, where Pes represents the survival probability of an oscillation into a hypothetical sterile neutrino. Figure 6 shows the result of the chi-squared test for this exploration, which indicates that DARWIN can set an upper bound on Pee and Pes when measuring both at the same time.
Additionally, we investigated how well we could constrain Pes given a measurement from DARWIN. To do so, we needed Pes alone; this was achieved by marginalizing the chi-squared equation over Pee, resulting in Figure 7.
In the context of three-neutrino-oscillations, given the assumption that oscillations are essentially energy-independent for pp-neutrinos and what is known about the mass-squared differences of neutrinos, we investigate how well DARWIN can measure the neutrino-oscillation mixing parameters sin2θ12 and sin2θ13. A measurement of sin2θ13 using only solar neutrinos would be the first of its kind, as this parameter has only been measured using nuclear reactors, unlike sin2θ12, which has been measured using solar neutrinos. Because pp solar neutrinos have a large degeneracy in sin2θ12 and sin2θ13 parameter space, to consider a "solar neutrinos-only" measurement of the mixing parameters, a prior must be included from the current, mostly 8B measurement. We include a prior on sin2θ12 to account for this, using the NuFit results. The result of this analysis is Figure 8, which shows that DARWIN can effectively constrain the mixing parameters and therefore a measurement of this type would be valuable. This result is non-trivial even with the prior set on sin2θ12 because the contour levels do not cross zero.
To determine what physics questions DARWIN could answer about a fourth flavor neutrino, oscillation probability equations are derived for a hypothetical fourth neutrino using the standard three-neutrino lepton mixing matrix, resulting in equations (7) and (8) for the oscillation probabilities,
where Pes represents the oscillation probability of a sterile neutrino, |Ue1|2 = cos2θ12cos2θ13, |Ue2|2 = sin2θ12cos2θ13, and |Ue3|2 = sin2θ13, L is the travel distance (from the Sun to Earth), θ14 is the lepton mixing angle between electron-type and sterile neutrino, and Δm412 is the mass-difference between electron-type and sterile neutrino. These equations are derived under the assumption that the components of the four-flavor lepton mixing matrix |Us2| and |Us3| vanish so that there are only two new-physics parameters, sin22θ14 and Δm412.
Using equations (7) and (8) to generate our theoretical data for the chi-squared method in the context of four-neutrinos, we considered constraining sin22θ14 in the limit that Δm412 is large, such that oscillations driven by the Δm412 term average out. To do this, we fix the values of sin2θ12 and sin2θ13 to their best-fit values using the NuFit results to generate Figure 9, which shows how a measurement form DARWIN could constrain the parameter sin22θ14 when Δm412 is large.
Additionally, we explored constraining Δm412 in the limit that sin22θ14 is large, such that oscillations driven by the Δm412 term are significant. To do this, we fix the values of sin2θ12 and sin2θ13 to their best-fit values using the NuFit results to generate Figure 10, which shows how a measurement form DARWIN could constrain the parameter Δm412 when sin22θ14 is large.
Lastly, we survey how well we can constrain sin22θ14 and Δm412 when Δm412 is exceedingly small (less than ~10-10 eV2), so that Δm412 driven oscillations are visible. Again, we fix the values of 12 and sin2θ13 to their best-fit values using the NuFit results to produce Figure 11, which shows how a measurement from DARWIN can constrain the values of sin22θ14 and Δm412 simultaneously.
The results of our work are reflected in the figures above, which show how well measurements from DARWIN should constrain different neutrino parameters. These figures justify the expansion of DARWIN's mission to include the detection and study of solar neutrinos, as DARWIN will provide the opportunity to measure sin2θ13 using solar neutrinos, which would be the first of its kind. Additionally, assuming a sterile neutrino exists, we examined the limits at which DARWIN will be able to determine its existence. Meaning, for what values do our parameters have to be smaller for DARWIN to lack sufficient sensitivity to detect the sterile neutrino's possible presence. This is to say that if the sterile neutrino's properties are larger than this threshold, DARWIN will have the sensitivity to detect it. Our figures indicate that DARWIN has the potential to set the best bounds (to date) on a sterile neutrino, where Δm412 is small, because of DARWIN's ability to probe an energy region lower than any other past experiment.
This material is based upon work supported by the National Science Foundation under grant No. AST-1757792.
