Neutrino Astrophysics

Evidence for Electron Neutrino Flavor Change Through Measurement of the ⁸B Solar Neutrino Flux at SNO

Synopsis

The Solar Neutrino Problem refers to the large deficit of solar neutrinos observed on earth relative to the predictions from solar models and particle physics. It has been known since the 1960’s that only about 1/3 of the predicted flux of solar electron neutrinos with energy above a few MeV (resulting from a fusion chain involving ⁸B) is observed on earth.

My analysis of 169.3 live-days of data from the Sudbury Neutrino Observatory (SNO) experiment provided first direct evidence for electron neutrino flavor change, resolving the decades-long Solar Neutrino Problem in the form of neutrino mass and mixing. The analysis presented in the first SNO paper was based on my thesis work, although many scientists collaborated to design, build and commission the SNO detector and collect and analyze data from the experiment.

This result lead to the 2015 Nobel Prize in Physics (A. McDonald, shared with T. Kajita) for observation of v_e flavor change at SNO and to the 2016 Breakthrough Prize in Fundamental Physics.

Technical Description

The Sun sustains life on Earth through nuclear fusion of hydrogen to produce helium and sunlight. A large flux of neutrinos is produced as a by-product of these thermonuclear reactions within the Sun. In fact, more than 60 billion solar neutrinos pass through each square centimeter of your body every second. These neutrinos also pass straight through Earth (unlike photons and other particles which are normally absorbed) owing to the fact the neutrinos are only very weakly interacting with matter. This weakly interacting property also makes neutrinos one of the most poorly understood of the fundamental particles in nature because they are so difficult to detect.

On the other hand, this difficulty affords researchers an opportunity to use neutrinos to probe the deep interior of stars where they are produced. This is just what John Bahcall and Ray Davis Jr. had in mind in 1964 when they submitted two PRL articles proposing the use of a large chlorine detector to observe neutrinos which “can enable us to see into the interior of a star and thus verify...nuclear energy generation in stars.” The chlorine experiment mentioned in their papers and also other experiments that followed established the neutrino flux reaching detectors on Earth to be 30-60% of solar model predictions. Initially, this discrepancy was thought by most people to be due to problems in the solar models themselves, as calculating accurate, detailed properties of astrophysical systems is notoriously difficult. However, as solar model calculations were refined and showed a high level of agreement (better than 0.1%) with helioseismological measurements of solar acoustic oscillations, people began taking the neutrino flux deficit - the “Solar Neutrino Problem” as it would become known - very seriously. Scientists now began asking the tantalizing question, “what are solar neutrinos telling us about particle physics?” rather than “what are solar neutrinos telling us about our lack of understanding of how the Sun works?”

Neutrinos are known to exist in three different types or “flavors” which characterize the type of charged lepton (electron, muon, tau) they are associated with (more accurately, the charged lepton with which they couple to the $W^{\pm}$ boson). Some have also raised the possibility that one or more “sterile” neutrinos might exist (motivated by results from the LSND experiment) which, unlike the active neutrinos just mentioned, do not have weak interactions but can still mix with other neutrinos to produce observable effects. The previous experiments which established the solar neutrino deficit were primarily only sensitive to electron-type neutrinos ($\nu_e$), which are the same type of neutrinos generated by the nuclear fusion processes in the solar interior. Theories developed over the years that sought to explain the solar neutrino deficit as a consequence of mixing between massive neutrino species - “neutrino oscillations”. In this scenario, the correct flux of electron neutrinos is being generated in the Sun but these $\nu_e$’s are oscillating into other neutrino species - $\nu_\mu$ (muon), $\nu_\tau$ (tau), and/or $\nu_s$ (sterile) neutrinos - before reaching detectors on earth which have little or no sensitivity to non-electron neutrinos. Since neutrinos are assumed to be massless in our current best theory of fundamental particles and their interactions, the “Standard Model”, observation of solar neutrino oscillation which requires neutrino mass and mixing would constitute a window into exciting new physics. Convincing evidence for $\nu_\mu \rightarrow \nu_\tau$ oscillations of atmospheric neutrinos demonstrated by SuperKamiokande in recent years lends further plausibility to an explanation of the Solar Neutrino Problem in terms of neutrino oscillations.

While there can be no argument that we gain much useful insight and direction from theory, observation gets the final word in physics. We would like to probe whether it is new neutrino physics behind the Solar Neutrino Problem or rather a more mundane explanation (from a particle physicists’ perspective!) of misunderstood solar physics or experimental systematics. Fortunately, there are quite a few signatures of neutrino oscillation which can be observed with the proper experiment. An experiment able to separately measure the total active neutrino flux ($\nu_e$ + $\nu_\mu$ + $\nu_\tau$) and the $\nu_e$-only flux could directly observe electron neutrino flavor change into other active flavors, demonstrating new physics in the (solar) neutrino sector. Many oscillation solutions also predict significant deviation of the neutrino energy spectrum from robust predictions based on standard nuclear physics alone, as well as temporal dependence of the observed $\nu_e$ flux (e.g. day/night differences arising from earth matter effects or seasonal dependence due to changing neutrino path length) after correcting for effects due to the earth’s orbital eccentricity.

The importance of an experiment having both charged current ($W^{\pm}$ exchange, flavor dependent) and neutral current ($Z^0$ exchange, flavor independent) sensitivity in directly resolving the Solar Neutrino Problem was stressed in 1985 by H. Chen. He further pointed out that a heavy water ($D_2O$) Cerenkov detector could be used for such an experiment, provided stringent background requirements inherent to the use could be achieved. Out of these and other ideas came the Sudbury Neutrino Observatory (SNO) after more than a decade of construction by physicists and engineers at institutions throughout United States, Canada, and the United Kingdom.

I began working with the SNO group under direction of Professor Eugene Beier in the summer before my first year of graduate school at the University of Pennsylvania in 1994. Because this was roughly five years before the start of data taking, I was able to become heavily involved in the SNO detector building and commissioning as well as early analysis of the data. By the time I completed my thesis in 2001, I had made significant contributions at nearly all stages of the experiment - from Monte Carlo simulation, to detector design, construction, and commissioning, to a complete analysis leading to a major publication.

The SNO detector is located at the 6800 ft level of the INCO, Ltd Creighton mine near Sudbury, Ontario, Canada. It is designed to study $^8$B solar neutrinos with the principal purpose of understanding the origin of the Solar Neutrino Problem. Neutrinos are primarily detected through their interactions with one kiloton of heavy water contained in a 12 m diameter acrylic vessel. The vessel is surrounded by $\sim 9500$ photomultiplier tubes (PMTs) mounted on a 17 m diameter geodesic support structure. These PMTs collect Cerenkov light generated by the fast-moving charged particles produced by neutrino interactions in the detector. The remaining detector volume is filled with ultra-pure acting as a shield against naturally occurring radioactivity from the cavity walls and detector materials. Because intrinsic radioactivity can produce Cerenkov light that is a background to our solar neutrino signals of interest, the entire lab must be operated as a clean room - a real challenge in the dirty environment of a nickel mine 2 km underground.

Through its use of heavy water as the interaction and detection medium, the SNO experiment is able to directly observe transformation of solar $\nu_e$’s into other active neutrino flavors. The is because SNO is able to separately measure the total solar $\nu_e$ flux through the charged-current (CC) reaction

$\nu_e + d \rightarrow p + p + e^-$

which only occurs for electron neutrinos, and also the total active neutrino flux from the neutral-current (NC) reaction

$\nu_x + d \rightarrow n + p + \nu_x$

which occurs at the same rate independent of which active neutrino ($\nu_x$ $\equiv$ $\nu_e$, $\nu_\mu$, or $\nu_\tau$) initiates the reaction. Comparison of the CC and NC rates (corrected for differences in cross section, signal efficiency, etc.) provides a direct measure of $\nu_e$ flavor change into $\nu_\mu$ + $\nu_\tau$ (denoted $\nu_{\mu\tau}$). If the CC rate is less than the NC rate, then solar $\nu_e$’s are changing into other active flavors en route to Earth. If, in addition, the NC rate also agrees with total flux predicted by solar model calculations, we can consider the Solar Neutrino Problem most simply explained by $\nu_e$$\rightarrow$$\nu_{\mu\tau}$ flavor transformations. If the CC and NC rates are equal and the NC rate is significantly lower than solar model predictions, this would point toward $\nu_e \rightarrow \nu_s$ (sterile) as the explanation of the Solar Neutrino Problem.

Although extracting the CC signal from the data stream of a complex detector like SNO is no simple task, it is easier than determining the rate of NC events for several reasons. The Cerenkov light yield from the electron produced in the CC reaction is greater than that which results from capture of the free neutron produced in the NC reaction. This gives a better separation of CC events from dominant radioactive backgrounds at low energy than is the case with events from the NC reaction. Also, free neutrons can be produced in the by sources other than neutrinos, particularly from photodisintigration of deuterons by low energy radioactive backgrounds. Any measurement of the total active neutrino flux via the NC reaction must accurately account for all sources of background neutrons. For this reason, great care has gone into maintaining the highest level cleanliness during not only the construction but also routine operation of the SNO detector.

Fortunately, SNO can also detect neutrinos from neutrino-electron elastic scattering (ES)

$\nu_x + e^- \rightarrow \nu_x + e^-$

for which CC ($\nu_e$ only) and NC (flavor independent) interactions both contribute to the scattering. For this reason, the ES occurs at rate approximately six times greater for $\nu_e$’s than for $\nu_\mu$’s or $\nu_\tau$’s. The scattered electron direction (which can be estimated from the pattern of PMT hits) is also highly correlated to the incident neutrino direction (i.e. direction to the Sun) allowing the ES signal to be more easily extracted from the data than either the CC or NC signals. The ES reaction is not specific to heavy water - it occurs throughout both the and regions of the SNO detector. It is also the primary method of solar neutrino detection in light water experiments such as SuperKamiokande and therefore gives these experiments weak neutral-current sensitivity without requiring expensive heavy water.

SNO began production neutrino data taking in November 1999. My thesis entitled “Evidence for Electron Neutrino Flavor Change Through Measurement of the $^8$B Solar Neutrino Flux at SNO” presents an analysis of the neutrino data set over a livetime of 169.3 days. I measured the $^8$B $\nu_e$ flux from the CC reaction to be $1.78^{+0.13}_{-0.14} \times 10^6$ cm$^{-2}$ s$^{-1}$, which is 34.6% of the flux expected from solar model calculations by Bahcall, et al (BP00 Standard Solar Model). This confirms of solar neutrino deficit, however for the first time by measuring exclusively the $\nu_e$ flux in $^8$B neutrinos. I have also measured the ES rate in SNO which, under the assumption that the $^8$B is solely comprised of electron neutrinos, is $2.56^{+0.48}_{-0.45} \times 10^6$cm$^{-2}$ s$^{-1}$ or 49.8% of expected flux. This ES result is consistent with that obtained by the light water experiments. It is also higher than the flux obtained from the CC rate which is exactly what one would expect for $\nu_e \rightarrow \nu_\mu\tau$ flavor transformations. However, the significance of the SNO-only CC-ES difference is quite low (2.0$\sigma$), with the error on the difference dominated by low ES statistics.

The SuperKamiokande experiment had nearly ten times the statistics on ES at the time I finished my analysis, with a published $^8$B neutrino flux after 1258 days of $2.32^{+0.09}_{-0.08} \times 10^6$cm$^{-2}$ s$^{-1}$. The $^8$B $\nu_e$ flux from my measurement the SNO CC rate is smaller than the $\nu_e$ flux inferred from SuperKamiokande’s ES results by 3.4$\sigma$. Because the ES reaction has known relative sensitivity to the active neutrino flavors, the flux of non-$\nu_e$ active neutrinos ($\phi_{\nu_{\mu,\tau}}$) in the $^8$B can be deduced and is measured for the first time to be

$\phi_{\nu_{\mu,\tau}} = 3.62^{+1.06}_{-1.08} \times 10^6$cm$^{-2}$ s$^{-1}$

providing evidence for $\nu_e \rightarrow \nu_{\mu,\tau}$ flavor transformations at greater than 99.7% confidence level. In addition, the total $^8$B neutrino flux ($\phi_{tot}$) was measured for the first time to be

$\phi_{\nu_{tot}} = 5.39^{+1.07}_{-1.09} \times 10^6$cm$^{-2}$ s$^{-1}$

in agreement with BP00 solar model calculations and confirmed by recent NC rate measurements by SNO. “I feel like dancing,” said Dr. Bahcall [June 19, 2001 NYTimes article] after the first SNO results confirmed his solar model calculations. As a result, we can rule out exclusive oscillation of $\nu_e$ into a sterile neutrino as an explanation of the Solar Neutrino Problem. Instead, we now know that  2/3 of all $^8$B electron neutrinos change flavor into and/or before reaching the Earth and that the total active neutrino flux agrees with Standard Solar Model calculations (see Figure below).

Aside from some wiggle room allowing for simultaneous transformation of $\nu_e$ into $\nu_{\mu\tau}$ and $\nu_s$, the Solar Neutrino Problem has been solved - the missing neutrinos were there the whole time, we just needed to know how to look. In fact, the light water solar neutrino experiments had been detecting these missing neutrino all along, but there was just no way for them to know!

The majority of analysis effort for my thesis was focused on careful study of solar neutrino backgrounds at high energy (above $\sim$7 MeV) and of systematics from energy, event reconstruction, and trigger efficiency. The largest systematic error on CC and ES rate measurements above my chosen energy threshold is determination of the absolute energy scale because this directly affects the number of events one expects to observe in the data above threshold for a given solar neutrino flux. SNO’s energy response is determined by modeling the detector geometry and Cerenkov light generation with input from calibration of detector optical properties. The energy response model is tested with calibration sources (e.g triggered 6 MeV $\gamma$-rays from the decay of $^{16}$N) but only in a discrete sampling of source locations, therefore a typical neutrino analysis will rely heavily upon accuracy of the model. Systematic uncertainties on the optical calibrations were not finalized when I was analyzing the neutrino data set, so I developed a new method of interpolating energy scale between $^{16}$N calibration data points which greatly reduces sensitivity to optical uncertainties. Accuracy of the interpolated energy variable used in my extraction of the solar neutrino signals was tested using additional calibrations sources and shown to be robust against a variety of detector effects (e.g. rate effects, time stability) and extreme optical parameters which proved crucial to the success of my analysis.

Estimating the location and direction of Cerenkov light-producing particles in the detector is a critical part of solar neutrino analysis in SNO. This is because many backgrounds originate (by design) in the outer regions of the detector and the only way to separate them from neutrino events is to locate them outside of the target volume or demonstrate their inconsistency with the PMT time and angle distribution expected from Cerenkov light. In an effort to have the best reconstruction for my analysis which uses as much event information as possible, I developed a new maximum likelihood fitter using PMT time and angle information to find the most likely vertex and direction of events under the hypothesis of the Cerenkov light from a single electron. Consistency with the fitting hypothesis is then tested to reject bad fits of “good” events from Cerenkov light as well background events from other sources of light and instrumental effects. Based upon performance on Monte Carlo simulation and calibration data, this fitter was chosen by the collaboration as the primary event reconstruction method for analysis during the phase of operation.

In the context of background studies, I developed the method adopted by SNO for limiting external high energy $\gamma$-ray backgrounds. These are important backgrounds to study because they have energies that extend into the $^8$B solar neutrino energy range and therefore cannot simply be removed by a cut on energy (unlike internal $\beta$-$\gamma$s, for example). A far larger solar neutrino background in the raw data above 7 MeV are backgrounds from the detector instrumentation itself. In particular, spontaneous emission of light from the PMTs (“PMT flashers”) is the dominant solar neutrino background at high energy and therefore much analysis effort has gone into learning how to remove these events. I developed two cuts which take advantage of the short time duration of Cerenkov light initiated by neutrino interactions in SNO compared to flashers and other instrumental backgrounds. These cuts described in my thesis are used in first-pass filtering of the SNO production data stream.

My work on SNO’s trigger system (for which I was primarily responsible for design and commissioning of the digital system) naturally led to consideration of trigger efficiency. Loosely speaking, the trigger efficiency is the probability of triggering SNO in response to time-correlated PMT hits from Cerenkov light, for example. In addition to being a crucial input to physics analyses, the trigger efficiency also has a profound impact on how the data is collected. The ability to collect quality neutrino data at as low an energy threshold as possible depends critically on being both very efficient at triggering on events above hardware threshold and very inefficient at triggering on events below threshold where radioactive backgrounds become exponentially large. The combination of a highly efficient trigger ($\sim$3.5 Nhit turn-on from 10% to 90%) and very low backgrounds currently allows SNO to run with a hardware trigger threshold of 16 ($<$2 MeV) - a level never before achieved by water a Cerenkov experiment. I developed the methods for determining trigger efficiency and performed SNO’s official trigger efficiency measurement. I measured the trigger to be $>$99.9% efficient for 22 or more hits in-time which demonstrates that trigger efficiency represents a negligible source of systematic uncertainty in all SNO neutrino analyses to date.

In summary, the primary result of my thesis is a demonstration solar neutrino flavor change. This provides a resolution of the Solar Neutrino Problem, but what does it mean for particle physics? The most natural and therefore favored framework for explaining neutrino flavor change is neutrino oscillation - neutrinos are massive and mix with one another. This now represents the second strong piece of evidence for neutrino oscillation and neutrino mass, the other being the Kamiokande and SuperKamiokande atmospheric neutrino results (the LSND signal is as of yet unconfirmed). While neutrinos are assumed massless in the Standard Model and therefore these results provide evidence for physics beyond it, extensions to the Standard model such as those implicit in some Grand Unified Theories and more exotic scenarios like extra dimensions naturally incorporate neutrino mass into their theoretical framework. It is clear that there are still many questions to be answered, however. In what ways are neutrino mixing and quark mixing similar and are there unifying principles relating the two at work? One significant difference between the two (aside from the mass scales involved) is that while there is small mixing between the quark flavors (i.e. the CKM matrix is nearly diagonal), small mixing angles for atmospheric and solar neutrino are ruled out (the latter with the addition of SNO data). Why is neutrino mixing maximal or nearly maximal while quark mixing is small? Are neutrinos their own antiparticles (i.e. Majorana particles)? Further information from SNO and future experiments will constrain the allowed parameter space for neutrino oscillations to narrow down which, if any, of the new theories are realized in Nature.

Popular Summary

We all know that the Sun’s warming presence sustains life on Earth, but how many of us really take time to think about our Sun? Maybe in the morning when it takes us from a deep sleep into a disgruntled stupor? Or possibly for a fleeting moment when we put on our sunglasses? We almost certainly forget about it at night when the Earth shields us from all but the Sun’s pull of gravity, right? Not quite. We may not get sunburn at night, but you can be assured that the Sun is still shining on you. No, this is not just the sort of motivational malarkey you find inside a fortune cookie. As a by-product of the energy-generating nuclear fusion processes occurring deep inside the Sun, a very large number of ghostly particles having no electric charge and little mass called “neutrinos” whiz through your body - both day and night. You should not lose any sleep over this tonight - more than 60 billion solar neutrinos pass harmlessly through each square centimeter of your body every second without you ever noticing. These timid particles also pass straight through the entire Earth (unlike sunlight which gets absorbed) due to the fact the neutrinos are only very weakly interacting with matter. Because they are so difficult to detect, neutrinos are one of the most poorly understood of the fundamental particles in Nature.

On the other hand, this weakly interacting property affords researchers an opportunity to use neutrinos to probe the deep interior of stars. This is because neutrinos produced deep inside the Sun can propagate directly to the Earth, while photons, the particles of sunlight, bounce around for thousands of years after being created in the solar core before leaving the solar surface. This is just what Dr. John Bahcall, now at the Institute of Advanced Study in Princeton, N.J., and Dr. Raymond Davis Jr. of Brookhaven National Laboratory and the University of Pennsylvania had in mind in 1964 when they published two articles in Physical Review Letters proposing the use of a large underground chlorine detector to observe neutrinos which “can enable us to see into the interior of a star and thus verify...nuclear energy generation in stars.” The pioneering chlorine experiment mentioned in their papers came to a rather striking conclusion - only about 30% of the predicted number of solar neutrinos are reaching the Earth!

Physicists are skeptical people by nature. Few thought that this discrepancy had anything fundamental to do with the properties of elementary particles like neutrinos. Instead, the models of the Sun used to calculate the expected solar neutrino flux (the number of particles per unit area per unit time reaching Earth) were called into question. After all, calculating detailed, accurate properties of astrophysical systems is notoriously difficult. However, as solar model calculations were refined and other solar neutrino experiments using very different methods confirmed the results, people began taking the neutrino flux deficit - the “Solar Neutrino Problem” as it would become known - very seriously. Scientists now began asking the tantalizing question, “what are solar neutrinos telling us about particle physics?” rather than “what are solar neutrinos telling us about our lack of understanding of how the Sun works?”

Neutrinos are known to exist in three different types or “flavors” - electron-type (), muon-type (), and tau-type () which characterize the type of heavy, charged particle - electron, muon, and tau - with which they associate. Only electron-type neutrinos are generated by the Sun, so previous solar neutrino experiments were primarily sensitive to this type of neutrino. In an attempt to explain the results from these experiments, theories developed over the years that describe the deficit as resulting from transformations or “mixing” between massive neutrino species. This is referred to as “neutrino oscillation” because the neutrino species appear to change back and forth into one another in a wave-like manner as they propagate though space. The chance of seeing a given neutrino type depends on where in the wave you happen to be looking. In this way, electron neutrinos generated in the Sun could be seen as changing into other neutrinos (and/or ) when their wave washes up on Earth. Since previous experiments have had little or no sensitivity to neutrinos other than , this neutrino flavor change is interpreted as a solar neutrino deficit. Neutrinos are incorporated as massless particles into our current best theory of fundamental particles and their interactions, the “Standard Model”. Therefore, observation of solar neutrino oscillation requiring neutrino mass and mixing would constitute a window into exciting new physics.

There are several signatures of neutrino oscillation which can be observed with the properly designed experiment. An experiment able to separately measure the total flux of all neutrinos (+ + ) and the -only flux could directly observe electron neutrino flavor change into other flavors. Some oscillation scenarios also predict a significant deviation of neutrino energies observed at the Earth from those known to be generated in the Sun by standard nuclear fusion processes. Neutrino oscillation can also cause the solar neutrino rate measured in a given experiment to depend on the time of day (e.g. different day/night rates) or the time of the year (e.g. different summer/winter rates), after correcting for known effects related to the Earth’s motion around the Sun.

The importance of an experiment capable of making separate flavor-specific and neutrino flavor-independent measurements of the solar neutrino flux in directly solving the Solar Neutrino Problem was stressed in 1985 by the late Professor Herb Chen of the University of California at Irvine. He further pointed out that heavy water () could be used for such an experiment, provided stringent purity requirements inherent to the use could be achieved. Compared to the hydrogen nuclei in normal water (), heavy water contains additional loosely bound neutrons that make an excellent target for solar neutrino detection. The dream of a heavy water solar neutrino detector was finally realized with the Sudbury Neutrino Observatory (SNO) after more than a decade of construction by physicists and engineers at institutions throughout United States, Canada, and the United Kingdom.

The SNO detector is located inside a large (22 m $\times$ 30 m) cavity 6800 ft underground in the INCO, Ltd Creighton mine near Sudbury, Ontario, Canada. It is designed to study solar neutrinos with the principal purpose of understanding the origin of the Solar Neutrino Problem. Using SNO, one is able to study neutrinos from a rare but high energy (hence easier to detect) component of the solar neutrino flux referred to as neutrinos, named after the parent nucleus from which they are produced. Neutrinos are primarily detected in SNO through their interactions with 1000 tons of heavy water contained in a 12 m diameter acrylic vessel. The vessel is surrounded by $\sim 9500$ sensitive light detectors called photomultiplier tubes (or PMTs) mounted on a 17 m diameter geodesic support structure. These PMTs collect Cherenkov light generated by the fast-moving charged particles resulting from neutrino interactions inside the detector. The remaining detector volume is filled with ultra-pure acting as a shield against naturally occurring radioactivity from the cavity walls and detector materials. Because intrinsic radioactivity can produce Cherenkov light that is a background to our solar neutrino signals of interest, the entire laboratory must be operated as a clean room - a real challenge in the dirty environment of a nickel mine located 2 km underground.

Solar neutrinos primarily interact with heavy water in two ways - the “charged-current” (CC) reaction which only occurs for electron neutrinos and the “neutral-current” (NC) reaction which has the same rate independent of neutrino flavor. Comparison of the CC and NC rates (corrected for differences in neutrino interaction probability, signal acceptance, etc.) provides a direct measure of flavor change into + (denoted ). If the CC rate is less than the NC rate, then solar ’s are changing into other flavors en route to Earth. If, in addition, the NC rate also agrees with total flux predicted by solar model calculations, we can consider the Solar Neutrino Problem most simply explained by $\rightarrow$flavor transformations.

SNO can also detect neutrinos which scatter elastically from atomic electrons in the water, much like a cue ball striking another billiard ball. This “elastic scattering” (ES) has both CC (only) and NC (neutrino flavor independent) components. For this reason, the ES occurs at a rate approximately six times greater for than for or . The ES reaction is not specific to heavy water - it occurs throughout both the and regions of the SNO detector. It is also the primary method of solar neutrino detection in light water () experiments, Kamiokande and Super-Kamiokande. This gives these experiments weak neutral-current sensitivity without requiring expensive heavy water - a sort of “poor man’s NC.”

I set out in my doctoral thesis to solve the Solar Neutrino Problem using SNO data collected over a period of 14 months beginning in November 1999. My strategy was to first confirm that there really is a Solar Neutrino Problem by measuring the flux via the CC reaction and then to compare my measurement of the CC and ES rates to look for possible neutrino flavor change behind the solar deficit. If the flux determined from the measured CC rate is smaller than that inferred from the ES rate (assuming no flavor transformation), then one has observed solar $\rightarrow$change.

In order to make these CC and ES measurements, one needs a model of how the detector responds to solar neutrinos. The model includes how much Cherenkov light is generated by energetic charged particles produced in solar neutrino interactions (directly related to the energy of those charged particles), the location and direction of the generated light, how much of that light is absorbed and scattered before being detected by the PMTs (i.e. detector optics), and how the instrumentation responds to Cherenkov light incident onto the PMTs. The validity of the model is tested as thoroughly as possible using calibration sources of energetic charged particles providing known energies and locations inside the detector. One then uses this model to extract the CC and ES signal rates from data after backgrounds have been removed and the position/direction of charged particles in the data sample have been estimated. The CC and ES rates are corrected for the fraction of each signal retained in the full analysis using the model. The rates are then compared to solar model expectations.

Of course, there are many pieces of analysis which need to be stitched together to implement such a strategy. In the case of my thesis, there were also significant challenges along the way that required unique solutions to be pursued and implemented. The detector optics that directly affect energy response were not completely calibrated when I performed my analysis, so I developed analysis techniques which explicitly used calibration data to reduce sensitivity to optical model uncertainties. The success of this approach proved critical to the accuracy of my results as energy scale (i.e. the number of PMT hits per unit of charged particle energy) is the largest systematic uncertainty on my measurements. Another serious hurdle in my solar neutrino analysis was backgrounds in the high energy region where neutrinos are to be found. It was discovered even before we put water in the detector that spontaneous emission of light from our PMTs was swamping our solar neutrino signal by more than two orders of magnitude under steady-state conditions (frequent bursts were worse yet). My early analysis on this light emission was important for devising ways to remove these backgrounds and resulted in two rejection algorithms used in first-pass filtering of the SNO production data stream.

Reconstructing the position and direction of energetic charged particles in SNO from the PMT information is an important part of the analysis because many solar neutrino backgrounds can only be removed from the data sample by locating them outside of the region. Because I felt that event reconstruction was an area where much improvement could be made in SNO, I developed a new reconstruction algorithm which was chosen as the primary event reconstruction method used in SNO analyses.

With the key analysis pieces in place, I was able to extract CC and ES solar neutrino signals from the data and estimate my errors on the measured rates. I measured the CC rate to be 35% of the solar model prediction, confirming that the solar deficit is also seen using SNO. My measured ES rate is 50% of the predicted rate assuming no neutrino flavor change, higher than the CC rate by two standard deviations. Although the higher ES rate is what one would expect if ’s were transforming into other neutrino flavors, the statistics on the SNO ES signal for my data set is too to low to conclude this with high confidence. The Super-Kamiokande experiment has made measurements of the same solar neutrinos using neutrino-electron elastic scattering with much higher statistics than is currently available in SNO. Using their published ES results, I find that the flux inferred from the ES rate is larger than the CC rate by 3.5 standard deviations. My measurements provide evidence for solar neutrino flavor change at greater than 99.98% confidence. This conclusion is summed up in the title of my thesis - Evidence for Electron Neutrino Flavor Change Through Measurement of the Solar Neutrino Flux at SNO.

Since the sensitivity of the ES rate to and is known (it is about six times smaller than ), one can calculate the total neutrino flux from the measured CC and ES rates. Performing this calculation, I find that the total flux is in perfect agreement with the solar model predictions! “I feel like dancing,” said Dr. Bahcall [June 19, 2001 NYTimes article] after the first SNO results confirmed his solar model calculations. As a result, we now know that  2/3 of all electron neutrinos change flavor into and/or before reaching the Earth. The Solar Neutrino Problem has been solved - the missing neutrinos were there the whole time, we just needed to know how to look. In fact, the light water solar neutrino experiments had been detecting these missing neutrino all along, but there was just no way for them to know!

In summary, the primary results of my thesis are a demonstration neutrino flavor change and a measurement of the tolar solar neutrino flux. For the first time ever, the Sun can be consider a calibrated neutrino source! This provides a resolution of the Solar Neutrino Problem, but what does it mean for particle physics? While there are many theories describing neutrino flavor change, neutrino oscillation appears to be the most natural and therefore plausible explanation. This thesis now represents the second strong indication of neutrino oscillation and neutrino mass, with the other being interpretation of Kamiokande and SuperKamiokande data on neutrinos produced in the atmosphere. While neutrinos are assumed massless in the Standard Model and therefore these results provide evidence for physics beyond it, many extensions to the Standard model are able to naturally accommodate massive neutrinos. Even so, it is clear that there are still many questions to be answered. One particularly striking observation is the way neutrinos mix with one another. Within the Standard Model, other much more massive particles called “quarks” comprising nuclear matter have been known to mix with each other for quite some time now. However, the intrinsic mixing between quarks is far smaller than that of the neutrinos, where the mixing is large (the latter for solar neutrinos is now known with the addition of SNO results). It is as if Nature has two different blender settings - Stir/Chop for quarks and Puree/Liquefy for neutrinos. The question then becomes, “are they both in the same kind of blender?” That is, in what ways are neutrino mixing and quark mixing similar and are there unifying principles relating the two at work? Is there a reason why neutrino masses are so tiny compared to other particles? Is neutrino matter and antimatter the same? Further information from SNO and future experiments will constrain the allowed parameter space for neutrino oscillations to narrow down which, if any, of the new theories are realized in Nature.

As a historical aside, I began working on the SNO experiment under direction of Professor Eugene Beier in the summer before my first year of graduate school at the University of Pennsylvania in 1994. Because this was roughly five years before the start of data taking, I was able to become heavily involved in the SNO detector building and commissioning as well as early analysis of the data. By the time I completed my doctoral thesis in June 2001, I had made significant contributions at nearly all stages of the experiment - from detector simulation, design, construction, and commissioning, to a complete analysis leading to a major publication. It is my impression that very few graduate students in recent times get this type of experience on a particle physics experiment with the same level of scientific impact as SNO.

I also got the opportunity to show the late Stephen Hawking around the SNO electronics during his visit to Sudbury in 2000 for the official opening of the experiment. Above is a picture of me as a graduate student with Stephen Hawking and his medial staff.

Further Reading

1. Q. R., Ahmad et al. [SNO Collaboration], “Measurement of the rate of ν_e + d –> p + p + e interactions produced by ⁸B solar neutrinos at the Sudbury Neutrino Observatory”, Phys. Rev. Lett. 87, 071301 (2001).