Neutrinos, Oscillations and New Physics:An Introduction

Rex TayloeIndiana University, Dept. of Physics, Bloontington, Indiana, 47405

Abstract. An introduction to the neutrino and neutrino oscillations and their role in the standardmodel of particle physics is presented. Current results and a plan for future experiments in neutrinophysics are summarized.Keywords: neutrino oscillationsPACS: 14.60.Pq

NEUTRINO HISTORYIn the early 1900s, nuclear physics was confronted with a particularly confoundingproblem. In the decays of several nuclei such as 14N and 6Li, it appeared that energywas not conserved. It was observed in these decays that two particles were emitted.However, the measured energy of the emitted /3 particle (now known as an electron) wasnot a single value as was expected. It was a continuous distribution, consistent with a3-body decay. In 1930, Wolfgang Pauli, in his famous letter to a gathering of physiciststhat he was not able to attend, postulated a "desperate-remedy" to this problem. l.

His hypothesis was that another particle, in addition to the electron, was emitted in/3 decay. This particle must be neutral and of small mass, thus making it difficult ifnot impossible to detect. This "neutrino"2 carries some of the decay energy and is notdetected and thus saves energy conservation in /3 decay.

The chance of actually detecting a neutrino seemed quite remote. The developmentof Fermi's theory of weak interactions enabled a calculation of the neutrino interactionprobability. It was quite small. In order to get a single neutrino to interact, a target oflength measured in light-years would be required. However, it was realized that there wasa way around that problem — find a source that created neutrinos in immense numbers.The invention of the nuclear reactor provided such a source.

In 1955, the neutrino was discovered in an experiment conducted at the SavannahRiver Nuclear Plant in South Carolina. This experiment was led by Fred Reines andClyde Cowan of Los Alamos National Laboratory. The nuclear reactor provided theintense source of neutrinos which were detected in a large volume of liquid via theinverse /3 decay reaction, v -I- p -> e+ + n. This work was awarded the Nobel Prize inPhysics in 1995. This technique for neutrino detection is essentially the same as used

1 For a good summary of this story, see Ref. [1]2 Pauli originally named it "neutron". It was later renamed "neutrino" by Enrico Fermi after the moremassive "neutron" was discovered.

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ATTACHMENT CREDIT LINE (BELOW) TO BE INSERTED ON THE FIRST PAGE

OF EACH PAPER

CP842, Particles and Nuclei, Seventeenth International Conference on Particles and Nuclei

edited by P. D. Barnes, M. D. Cooper, R. A. Eisenstein, H. van Hecke, and G. J. Stephenson © 2006 American Institute of Physics 0-7354-0338-4/06/$23.00

Neutrinos, Oscillations and New Physics:An Introduction

Rex TayloeIndiana University, Dept. of Physics, Bloontington, Indiana, 47405

Abstract. An introduction to the neutrino and neutrino oscillations and their role in the standardmodel of particle physics is presented. Current results and a plan for future experiments in neutrinophysics are summarized.Keywords: neutrino oscillationsPACS: 14.60.Pq

NEUTRINO HISTORYIn the early 1900s, nuclear physics was confronted with a particularly confoundingproblem. In the decays of several nuclei such as 14N and 6Li, it appeared that energywas not conserved. It was observed in these decays that two particles were emitted.However, the measured energy of the emitted /3 particle (now known as an electron) wasnot a single value as was expected. It was a continuous distribution, consistent with a3-body decay. In 1930, Wolfgang Pauli, in his famous letter to a gathering of physiciststhat he was not able to attend, postulated a "desperate-remedy" to this problem. l.

His hypothesis was that another particle, in addition to the electron, was emitted in/3 decay. This particle must be neutral and of small mass, thus making it difficult ifnot impossible to detect. This "neutrino"2 carries some of the decay energy and is notdetected and thus saves energy conservation in /3 decay.

The chance of actually detecting a neutrino seemed quite remote. The developmentof Fermi's theory of weak interactions enabled a calculation of the neutrino interactionprobability. It was quite small. In order to get a single neutrino to interact, a target oflength measured in light-years would be required. However, it was realized that there wasa way around that problem — find a source that created neutrinos in immense numbers.The invention of the nuclear reactor provided such a source.

In 1955, the neutrino was discovered in an experiment conducted at the SavannahRiver Nuclear Plant in South Carolina. This experiment was led by Fred Reines andClyde Cowan of Los Alamos National Laboratory. The nuclear reactor provided theintense source of neutrinos which were detected in a large volume of liquid via theinverse /3 decay reaction, v -I- p -> e+ + n. This work was awarded the Nobel Prize inPhysics in 1995. This technique for neutrino detection is essentially the same as used

1 For a good summary of this story, see Ref. [1]2 Pauli originally named it "neutron". It was later renamed "neutrino" by Enrico Fermi after the moremassive "neutron" was discovered.

748

ATTACHMENT CREDIT LINE (BELOW) TO BE INSERTED ON THE FIRST PAGE

OF EACH PAPER

CP842, Particles and Nuclei, Seventeenth International Conference on Particles and Nuclei

edited by P. D. Barnes, M. D. Cooper, R. A. Eisenstein, H. van Hecke, and G. J. Stephenson © 2006 American Institute of Physics 0-7354-0338-4/06/$23.00

Particles

FIGURE 1. Fundamental particles within the standard model diagram [2]. The three neutrino flavorscan be seen together with their charged-lepton partners. There is a symmetric diagram for antiparticles.

today.

NEUTRINOS IN THE STANDARD MODEL

In the years since the groundbreaking Reines and Cowan experiment, an immenseamount of experimental and theoretical work has been done to understand how theneutrino fits into our standard model (SM) of particle physics. In the SM, there arethree types ("flavors") of neutral, massless neutrino, arranged in three generations alongwith their charged lepton and quark partners as shown in Fig. 1. There is a symmetricdiagram for the antiparticles (including antineutrinos) in the SM.

Measurements of Z° decays at LEP have shown that there are only three light andactive neutrinos [3]. However, this measurement does not rule out the possibility of veryheavy neutrinos or "sterile" neutrinos (particles that, effectively, do not interact withmatter). Neutrinos are left-handed, that is their spin points in a direction opposite that oftheir momentum vector. They interact only via the "weak" interaction unlike the leptonsand quarks. This interaction is truly weak, interaction probabilities are approximately 12orders of magnitude smaller than those governed by the strong nuclear force at similarenergies. 749

Particles

FIGURE 1. Fundamental particles within the standard model diagram [2]. The three neutrino flavorscan be seen together with their charged-lepton partners. There is a symmetric diagram for antiparticles.

today.

NEUTRINOS IN THE STANDARD MODEL

In the years since the groundbreaking Reines and Cowan experiment, an immenseamount of experimental and theoretical work has been done to understand how theneutrino fits into our standard model (SM) of particle physics. In the SM, there arethree types ("flavors") of neutral, massless neutrino, arranged in three generations alongwith their charged lepton and quark partners as shown in Fig. 1. There is a symmetricdiagram for the antiparticles (including antineutrinos) in the SM.

Measurements of Z° decays at LEP have shown that there are only three light andactive neutrinos [3]. However, this measurement does not rule out the possibility of veryheavy neutrinos or "sterile" neutrinos (particles that, effectively, do not interact withmatter). Neutrinos are left-handed, that is their spin points in a direction opposite that oftheir momentum vector. They interact only via the "weak" interaction unlike the leptonsand quarks. This interaction is truly weak, interaction probabilities are approximately 12orders of magnitude smaller than those governed by the strong nuclear force at similarenergies. 749

FIGURE 1. Fundamental particles within the standard model diagram [2]. The three neutrino flavorscan be seen together with their charged-lepton partners. There is a symmetric diagram for antiparticles.

today.

NEUTRINOS IN THE STANDARDMODEL

In the years since the groundbreaking Reines and Cowan experiment, an immenseamount of experimental and theoretical work has been done to understand how theneutrino fits into our standard model (SM) of particle physics. In the SM, there arethree types (“flavors”) of neutral, massless neutrino, arranged in three generations alongwith their charged lepton and quark partners as shown in Fig. 1. There is a symmetricdiagram for the antiparticles (including antineutrinos) in the SM.

Measurements of Z0 decays at LEP have shown that there are only three light andactive neutrinos [3]. However, this measurement does not rule out the possibility of veryheavy neutrinos or “sterile” neutrinos (particles that, effectively, do not interact withmatter). Neutrinos are left-handed, that is their spin points in a direction opposite that oftheir momentum vector. They interact only via the “weak” interaction unlike the leptonsand quarks. This interaction is truly weak, interaction probabilities are approximately 12orders of magnitude smaller than those governed by the strong nuclear force at similarenergies.

749

FIGURE 1. Fundamental particles within the standard model diagram [2]. The three neutrino flavorscan be seen together with their charged-lepton partners. There is a symmetric diagram for antiparticles.

today.

NEUTRINOS IN THE STANDARDMODEL

In the years since the groundbreaking Reines and Cowan experiment, an immenseamount of experimental and theoretical work has been done to understand how theneutrino fits into our standard model (SM) of particle physics. In the SM, there arethree types (“flavors”) of neutral, massless neutrino, arranged in three generations alongwith their charged lepton and quark partners as shown in Fig. 1. There is a symmetricdiagram for the antiparticles (including antineutrinos) in the SM.

Measurements of Z0 decays at LEP have shown that there are only three light andactive neutrinos [3]. However, this measurement does not rule out the possibility of veryheavy neutrinos or “sterile” neutrinos (particles that, effectively, do not interact withmatter). Neutrinos are left-handed, that is their spin points in a direction opposite that oftheir momentum vector. They interact only via the “weak” interaction unlike the leptonsand quarks. This interaction is truly weak, interaction probabilities are approximately 12orders of magnitude smaller than those governed by the strong nuclear force at similarenergies.

749

FIGURE 1. Fundamental particles within the standard model diagram [2]. The three neutrino flavorscan be seen together with their charged-lepton partners. There is a symmetric diagram for antiparticles.

today.

NEUTRINOS IN THE STANDARDMODEL

In the years since the groundbreaking Reines and Cowan experiment, an immenseamount of experimental and theoretical work has been done to understand how theneutrino fits into our standard model (SM) of particle physics. In the SM, there arethree types (“flavors”) of neutral, massless neutrino, arranged in three generations alongwith their charged lepton and quark partners as shown in Fig. 1. There is a symmetricdiagram for the antiparticles (including antineutrinos) in the SM.

Measurements of Z0 decays at LEP have shown that there are only three light andactive neutrinos [3]. However, this measurement does not rule out the possibility of veryheavy neutrinos or “sterile” neutrinos (particles that, effectively, do not interact withmatter). Neutrinos are left-handed, that is their spin points in a direction opposite that oftheir momentum vector. They interact only via the “weak” interaction unlike the leptonsand quarks. This interaction is truly weak, interaction probabilities are approximately 12orders of magnitude smaller than those governed by the strong nuclear force at similarenergies.

749

FIGURE 1. Fundamental particles within the standard model diagram [2]. The three neutrino flavorscan be seen together with their charged-lepton partners. There is a symmetric diagram for antiparticles.

today.

NEUTRINOS IN THE STANDARDMODEL

In the years since the groundbreaking Reines and Cowan experiment, an immenseamount of experimental and theoretical work has been done to understand how theneutrino fits into our standard model (SM) of particle physics. In the SM, there arethree types (“flavors”) of neutral, massless neutrino, arranged in three generations alongwith their charged lepton and quark partners as shown in Fig. 1. There is a symmetricdiagram for the antiparticles (including antineutrinos) in the SM.

Measurements of Z0 decays at LEP have shown that there are only three light andactive neutrinos [3]. However, this measurement does not rule out the possibility of veryheavy neutrinos or “sterile” neutrinos (particles that, effectively, do not interact withmatter). Neutrinos are left-handed, that is their spin points in a direction opposite that oftheir momentum vector. They interact only via the “weak” interaction unlike the leptonsand quarks. This interaction is truly weak, interaction probabilities are approximately 12orders of magnitude smaller than those governed by the strong nuclear force at similarenergies.

749

In the SM, the charged leptons (and quarks) are given mass via the Higgs mechanismwhich couples left and right handed particles. The neutrinos do not acquire a mass asthere is no right-handed component to couple to the Higgs field.

Solar Neutrinos

The first hint that the SM, in which neutrinos are exactly massless, is not complete,surfaced in the results from the pioneering experiment of Ray Davis [5], which wasrewarded with the 2002 Nobel Prize in Physics. In this experiment, conducted approxi-mately 30 years ago, neutrinos from the sun were detected in 615 tons of perchloroethy-lene (C^Cl^) located in the Homestake Gold Mine in South Dakota. The results showedthat the number of neutrinos observed was about 1/3 that expected from models of nu-clear fusion in the sun. It took several decades and several subsequent experiments toverify, but this was the first sign that neutrinos change flavor during the journey fromthe sun to the earth. This necessitates a modification to the standard model to allow formassive neutrinos.

The Standard Model with Neutrino Oscillations

If neutrinos are massive and the neutrino eigenstates produced in the weak interactionare not eigenstates of mass (as occur with quarks and observed in neutral kaons) thenneutrinos will oscillate [4]. More formally, with mathematical notation and assumingonly two neutrino types for simplicity, the weak states (ve, v^) are superpositions of themass states (vi,V2),

sin0 W vicose J \v2

And, for example, a v^ state produced at t = 0 is, evolves to a different state at timet, according to the energies (£"1 ,£"2) of the mass states (vi , V2),

Then the probability for detecting a ve at a distance x given that a v^ was produced at

m2-m22. (3)

The probability for detecting a v^ is the complement,

P(Vp -> VM) = 1 - P(V^ -> Ve). (4)

These probabilities are illustrated schematically in Fig. 2.Thus, the probability for detecting a ve given the production of a v^ depends on the

source to detector distance jc, the neutrino energy Ev, the neutrino "mixing angle" 9, and750

In the SM, the charged leptons (and quarks) are given mass via the Higgs mechanismwhich couples left and right handed particles. The neutrinos do not acquire a mass asthere is no right-handed component to couple to the Higgs field.

Solar Neutrinos

The first hint that the SM, in which neutrinos are exactly massless, is not complete,surfaced in the results from the pioneering experiment of Ray Davis [5], which wasrewarded with the 2002 Nobel Prize in Physics. In this experiment, conducted approxi-mately 30 years ago, neutrinos from the sun were detected in 615 tons of perchloroethy-lene (C^Cl^) located in the Homestake Gold Mine in South Dakota. The results showedthat the number of neutrinos observed was about 1/3 that expected from models of nu-clear fusion in the sun. It took several decades and several subsequent experiments toverify, but this was the first sign that neutrinos change flavor during the journey fromthe sun to the earth. This necessitates a modification to the standard model to allow formassive neutrinos.

The Standard Model with Neutrino Oscillations

If neutrinos are massive and the neutrino eigenstates produced in the weak interactionare not eigenstates of mass (as occur with quarks and observed in neutral kaons) thenneutrinos will oscillate [4]. More formally, with mathematical notation and assumingonly two neutrino types for simplicity, the weak states (ve, v^) are superpositions of themass states (vi,V2),

sin0 W vicose J \v2

And, for example, a v^ state produced at t = 0 is, evolves to a different state at timet, according to the energies (£"1 ,£"2) of the mass states (vi , V2),

Then the probability for detecting a ve at a distance x given that a v^ was produced at

m2-m22. (3)

The probability for detecting a v^ is the complement,

P(Vp -> VM) = 1 - P(V^ -> Ve). (4)

These probabilities are illustrated schematically in Fig. 2.Thus, the probability for detecting a ve given the production of a v^ depends on the

source to detector distance jc, the neutrino energy Ev, the neutrino "mixing angle" 9, and750

Source

sin226

Probability that V,t lies become Ve ||||| Probability Ilia! Vu is still \*

FIGURE 2. An schematic illustration of two generation neutrino oscillations. The plot shows how theoscillation probabilities depend on distance. This figure was taken from Ref. [1].

the "mass-squared difference" Am2. The experimental conditions dictate x and Ev. Thequantities 9 and Am2 are parameters of nature - it is the job of the experimentalist tomeasure them.

This simple model for oscillations may be extended to incorporate oscillations be-tween three neutrino flavors [4]. The fundamental idea is the same. The 2 x 2 matrixwith one parameter 6 in Eq. 1 becomes a 3 x 3 matrix with three mixing angle parame-ters and one CP-violating phase. In addition, two independent Am2 values are required.The oscillation probabilities then depend on these six parameters.

MEASURING NEUTRINO OSCILLATIONS

The current task facing the neutrino experimentalist is to measure the neutrino oscillationprobabilities and thus determine the neutrino oscillation parameters. This will lead to amore complete description of the standard model and, quite possibly, the origin of matter.

Neutrino experiments are conducted using a variety of sources and detector configura-tions. There are experiments measuring neutrinos produced in the sun, nuclear reactors,cosmic ray interactions, and accelerators. The detector to source distance and neutrinoenergy varies, and as a result, so does the region of neutrino parameter space underinvestigation. Because neutrinos only interact rarely, a feature common to all neutrinoexperiments is that they are large and require a very intense source of neutrinos. Formeasurements at low neutrino energies, the detectors are required to be underground tominimize cosmic ray backgrounds.

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Source

sin226

Probability that V,t lies become Ve ||||| Probability Ilia! Vu is still \*

FIGURE 2. An schematic illustration of two generation neutrino oscillations. The plot shows how theoscillation probabilities depend on distance. This figure was taken from Ref. [1].

the "mass-squared difference" Am2. The experimental conditions dictate x and Ev. Thequantities 9 and Am2 are parameters of nature - it is the job of the experimentalist tomeasure them.

This simple model for oscillations may be extended to incorporate oscillations be-tween three neutrino flavors [4]. The fundamental idea is the same. The 2 x 2 matrixwith one parameter 6 in Eq. 1 becomes a 3 x 3 matrix with three mixing angle parame-ters and one CP-violating phase. In addition, two independent Am2 values are required.The oscillation probabilities then depend on these six parameters.

MEASURING NEUTRINO OSCILLATIONS

The current task facing the neutrino experimentalist is to measure the neutrino oscillationprobabilities and thus determine the neutrino oscillation parameters. This will lead to amore complete description of the standard model and, quite possibly, the origin of matter.

Neutrino experiments are conducted using a variety of sources and detector configura-tions. There are experiments measuring neutrinos produced in the sun, nuclear reactors,cosmic ray interactions, and accelerators. The detector to source distance and neutrinoenergy varies, and as a result, so does the region of neutrino parameter space underinvestigation. Because neutrinos only interact rarely, a feature common to all neutrinoexperiments is that they are large and require a very intense source of neutrinos. Formeasurements at low neutrino energies, the detectors are required to be underground tominimize cosmic ray backgrounds.

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LSND (99% CL)LSND (90% CL)

FIGURE 3. A example of results from neutrino oscillation experiments. The LSND experiment ob-served oscillation events and thus produced an allowed region (shaded area). The KARMEN2 and Bugeyexperiments did not thus producing and excluded region (area above and to the right of the single lines.)

A neutrino oscillation experiment results in a measurement of an oscillation probabil-ity. An observed excess of oscillation events over background can be used to determinethe oscillation parameters. If only two neutrinos are participating in the oscillations,which may be true for certain combinations of distance and energy, this determination ismade with the assumption of two oscillation parameters 9 and Am2. Because of exper-imental errors, the oscillation parameters can not be determined exactly and the rate ofoscillation events is used to determine an "allowed" region in the space of 9 and Am2.If an experiment observes no oscillation events, an "exclusion" region is produced. Anexample of this situation is shown in Fig. 3. The LSND [6] experiment observed a sig-nal for neutrino oscillations and produced an allowed region for the parameters 9 andAm2. Two other experiments (KARMEN2 [7] and Bugey [8]), at similar distances andenergies, saw no oscillations and produced an exclusion region.

EVIDENCE FOR NEUTRINO OSCILLATIONS

There is evidence for neutrino oscillations at three distinctly different Am2 values. Eachof these different Am2 values has labeled based on the neutrino source used for the firstobservation (i.e. solar, atmospheric, LSND). However, several of the Am2 values have752

LSND (99% CL)LSND (90% CL)

FIGURE 3. A example of results from neutrino oscillation experiments. The LSND experiment ob-served oscillation events and thus produced an allowed region (shaded area). The KARMEN2 and Bugeyexperiments did not thus producing and excluded region (area above and to the right of the single lines.)

A neutrino oscillation experiment results in a measurement of an oscillation probabil-ity. An observed excess of oscillation events over background can be used to determinethe oscillation parameters. If only two neutrinos are participating in the oscillations,which may be true for certain combinations of distance and energy, this determination ismade with the assumption of two oscillation parameters 9 and Am2. Because of exper-imental errors, the oscillation parameters can not be determined exactly and the rate ofoscillation events is used to determine an "allowed" region in the space of 9 and Am2.If an experiment observes no oscillation events, an "exclusion" region is produced. Anexample of this situation is shown in Fig. 3. The LSND [6] experiment observed a sig-nal for neutrino oscillations and produced an allowed region for the parameters 9 andAm2. Two other experiments (KARMEN2 [7] and Bugey [8]), at similar distances andenergies, saw no oscillations and produced an exclusion region.

EVIDENCE FOR NEUTRINO OSCILLATIONS

There is evidence for neutrino oscillations at three distinctly different Am2 values. Eachof these different Am2 values has labeled based on the neutrino source used for the firstobservation (i.e. solar, atmospheric, LSND). However, several of the Am2 values have752

FIGURE 3. A example of results from neutrino oscillation experiments. The LSND experiment ob-served oscillation events and thus produced an allowed region (shaded area). The KARMEN2 and Bugeyexperiments did not thus producing and excluded region (area above and to the right of the single lines.)

A neutrino oscillation experiment results in a measurement of an oscillation probabil-ity. An observed excess of oscillation events over background can be used to determinethe oscillation parameters. If only two neutrinos are participating in the oscillations,which may be true for certain combinations of distance and energy, this determination ismade with the assumption of two oscillation parameters # and &m2. Because of exper-imental errors, the oscillation parameters can not be determined exactly and the rate ofoscillation events is used to determine an “allowed” region in the space of # and &m2.If an experiment observes no oscillation events, an “exclusion” region is produced. Anexample of this situation is shown in Fig. 3. The LSND [6] experiment observed a sig-nal for neutrino oscillations and produced an allowed region for the parameters # and&m2. Two other experiments (KARMEN2 [7] and Bugey [8]), at similar distances andenergies, saw no oscillations and produced an exclusion region.

EVIDENCE FOR NEUTRINO OSCILLATIONS

There is evidence for neutrino oscillations at three distinctly different &m2 values. Eachof these different &m2 values has labeled based on the neutrino source used for the firstobservation (i.e. solar, atmospheric, LSND). However, several of the &m2 values have

752

FIGURE 3. A example of results from neutrino oscillation experiments. The LSND experiment ob-served oscillation events and thus produced an allowed region (shaded area). The KARMEN2 and Bugeyexperiments did not thus producing and excluded region (area above and to the right of the single lines.)

A neutrino oscillation experiment results in a measurement of an oscillation probabil-ity. An observed excess of oscillation events over background can be used to determinethe oscillation parameters. If only two neutrinos are participating in the oscillations,which may be true for certain combinations of distance and energy, this determination ismade with the assumption of two oscillation parameters # and &m2. Because of exper-imental errors, the oscillation parameters can not be determined exactly and the rate ofoscillation events is used to determine an “allowed” region in the space of # and &m2.If an experiment observes no oscillation events, an “exclusion” region is produced. Anexample of this situation is shown in Fig. 3. The LSND [6] experiment observed a sig-nal for neutrino oscillations and produced an allowed region for the parameters # and&m2. Two other experiments (KARMEN2 [7] and Bugey [8]), at similar distances andenergies, saw no oscillations and produced an exclusion region.

EVIDENCE FOR NEUTRINO OSCILLATIONS

There is evidence for neutrino oscillations at three distinctly different &m2 values. Eachof these different &m2 values has labeled based on the neutrino source used for the firstobservation (i.e. solar, atmospheric, LSND). However, several of the &m2 values have

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been confirmed with a neutrino source different from that used for the first observation.

Low-Am2 (solar) oscillations

The result from the Homestake experiment that neutrinos oscillate on their way fromthe sun to the earth has been confirmed in subsequent solar neutrino experiments in-cluding Super-Kamiokande [9] and SNO [10]. This result has also been confirmed bythe Kami and experiment using antineutrinos from nuclear reactors. These results indi-cate that ve are oscillating to v^ (and perhaps vr). The measured oscillation parametervalues are Am2 « 8 x 10~5 eV2 and sin2 9 « 0.8

Recent results from the Sudbury Neutrino Observatory (SNO) in Canada has recentlyproduced results that confirm the oscillations of ve from the sun as observed by theHomestake. They have also made the important observation that the number of neutrinosof all three flavors is consistent with the number of ve predicted by the standard solarmodel. This leads to the conclusion that solar neutrinos are oscillating within the threeactive flavors of neutrinos and do not require the existence of a sterile neutrino.

The Kamland experiment in Japan has recently reported results that antineutrinos(ve) from reactors oscillate with parameters consistent with those observed in solarneutrino oscillations. This was effectively an observation of solar neutrino oscillationsconducted on earth. And, they added the important piece of information that anti-neutrino oscillations occur with same parameters as with neutrinos.

Intermediate-Am2 (atmospheric) oscillations

Neutrinos produced in the atmosphere as the result of cosmic ray interactions havebeen observed to oscillate. The most recent measurements have been produced bythe Super-Kamiokande [12] detector in Japan. There measurements indicate that v^neutrinos are oscillating to vr neutrinos with A/n2 w 2 x 10~3 eV2 and sin20 « 1.0A measurement consistent with this result has been produced by the K2K experimentusing neutrinos produced with a proton accelerator and the same Super-Kamiokandedetector.

High-Am2 (LSND) oscillations

The third Am2 value observed in neutrino oscillations comes from the LSND exper-iment conducted at Los Alamos National Lab in the U.S. In this experiment, v^ wereobserved to oscillate to ve with Am2 « 1 eV2 and sin2 9 « 3 x 10~3. This result hasyet to be verified by another experiment. It is very important to check this result since,if correct, the SM would have to be modified to include additional neutrinos (or someother exotic effect).

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been confirmed with a neutrino source different from that used for the first observation.

Low-Am2 (solar) oscillations

The result from the Homestake experiment that neutrinos oscillate on their way fromthe sun to the earth has been confirmed in subsequent solar neutrino experiments in-cluding Super-Kamiokande [9] and SNO [10]. This result has also been confirmed bythe Kami and experiment using antineutrinos from nuclear reactors. These results indi-cate that ve are oscillating to v^ (and perhaps vr). The measured oscillation parametervalues are Am2 « 8 x 10~5 eV2 and sin2 9 « 0.8

Recent results from the Sudbury Neutrino Observatory (SNO) in Canada has recentlyproduced results that confirm the oscillations of ve from the sun as observed by theHomestake. They have also made the important observation that the number of neutrinosof all three flavors is consistent with the number of ve predicted by the standard solarmodel. This leads to the conclusion that solar neutrinos are oscillating within the threeactive flavors of neutrinos and do not require the existence of a sterile neutrino.

The Kamland experiment in Japan has recently reported results that antineutrinos(ve) from reactors oscillate with parameters consistent with those observed in solarneutrino oscillations. This was effectively an observation of solar neutrino oscillationsconducted on earth. And, they added the important piece of information that anti-neutrino oscillations occur with same parameters as with neutrinos.

Intermediate-Am2 (atmospheric) oscillations

Neutrinos produced in the atmosphere as the result of cosmic ray interactions havebeen observed to oscillate. The most recent measurements have been produced bythe Super-Kamiokande [12] detector in Japan. There measurements indicate that v^neutrinos are oscillating to vr neutrinos with A/n2 w 2 x 10~3 eV2 and sin20 « 1.0A measurement consistent with this result has been produced by the K2K experimentusing neutrinos produced with a proton accelerator and the same Super-Kamiokandedetector.

High-Am2 (LSND) oscillations

The third Am2 value observed in neutrino oscillations comes from the LSND exper-iment conducted at Los Alamos National Lab in the U.S. In this experiment, v^ wereobserved to oscillate to ve with Am2 « 1 eV2 and sin2 9 « 3 x 10~3. This result hasyet to be verified by another experiment. It is very important to check this result since,if correct, the SM would have to be modified to include additional neutrinos (or someother exotic effect).

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THE STANDARD MODEL WITH NEUTRINO OSCILLATIONS - II

If the LSND result is shown to be incorrect, the SM can be modified to include neutrinomass but without the addition of sterile neutrinos. The masses of the neutrinos would bearranged in either a "normal" hierarchy with the v\ mass state as the lightest and v$ asthe heaviest with the mass differences between the states as indicated by the solar andatmospheric results. An "inverted" hierarchy is also possible, with the mass orderinginverted. In either of these scenarios, the absolute value of the masses is unknown asneutrino oscillations are only sensitive to mass differences. The average mass of theneutrinos may be as large as 2.2 eV as allowed by experiments searching for neutrinomass via /3 decay.

In this scenario, two of the three neutrino mixing parameters, 9\2 and 023, may beassigned with reasonable uncertainty based on current results. The third, $13, is knownonly to be small. The CP violating phase, 6, that appears in the three generation neutrinomixing matrix is completely unmeasured.

If the LSND result is shown to be correct, additional and substantial modifications tothe SM would be required. One possible modification would be the addition of a fourthtype of neutrino that does not interact via the standard weak interaction - a "sterile"neutrino.

To complete the SM in either of these scenarios, many questions still need to beanswered by additional experiments.

• What are the values of #13 and 6?• Is the neutrino mass hierarchy normal or inverted?• What are the (absolute) neutrino masses?• Are there more than three generations of neutrinos?• Do we understand matter-enhanced oscillations completely?• Are neutrinos their own antiparticles?• Are neutrinos a window into some other exotic effect such as Lorentz violation?

These and many other questions are to be addressed in future experiments.

FUTURE

Several near-term experiments will provide answers to some of these questions. Theremainder will be addressed by subsequent experiments. The MiniBooNE experimentis running at Fermilab in the U.S. to check the LSND result and, therefore, determineif something beyond a three neutrino model is required. The MINOS [13] experimentis currently running at Fermilab and in the Soudan mine in Minnesota. This experimentwill provide better precision for the atmospheric oscillation parameters. Also, the SNO,Kamland, and Super-Kamiokande experiments continue to run, providing additionalchecks to existing results.

The American Physical Society conducted a multi-divisional study [15] to address thecurrent experimental situation and to prioritize future neutrino experiments with U.S.

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THE STANDARD MODEL WITH NEUTRINO OSCILLATIONS - II

If the LSND result is shown to be incorrect, the SM can be modified to include neutrinomass but without the addition of sterile neutrinos. The masses of the neutrinos would bearranged in either a "normal" hierarchy with the v\ mass state as the lightest and v$ asthe heaviest with the mass differences between the states as indicated by the solar andatmospheric results. An "inverted" hierarchy is also possible, with the mass orderinginverted. In either of these scenarios, the absolute value of the masses is unknown asneutrino oscillations are only sensitive to mass differences. The average mass of theneutrinos may be as large as 2.2 eV as allowed by experiments searching for neutrinomass via /3 decay.

In this scenario, two of the three neutrino mixing parameters, 9\2 and 023, may beassigned with reasonable uncertainty based on current results. The third, $13, is knownonly to be small. The CP violating phase, 6, that appears in the three generation neutrinomixing matrix is completely unmeasured.

If the LSND result is shown to be correct, additional and substantial modifications tothe SM would be required. One possible modification would be the addition of a fourthtype of neutrino that does not interact via the standard weak interaction - a "sterile"neutrino.

To complete the SM in either of these scenarios, many questions still need to beanswered by additional experiments.

• What are the values of #13 and 6?• Is the neutrino mass hierarchy normal or inverted?• What are the (absolute) neutrino masses?• Are there more than three generations of neutrinos?• Do we understand matter-enhanced oscillations completely?• Are neutrinos their own antiparticles?• Are neutrinos a window into some other exotic effect such as Lorentz violation?

These and many other questions are to be addressed in future experiments.

FUTURE

Several near-term experiments will provide answers to some of these questions. Theremainder will be addressed by subsequent experiments. The MiniBooNE experimentis running at Fermilab in the U.S. to check the LSND result and, therefore, determineif something beyond a three neutrino model is required. The MINOS [13] experimentis currently running at Fermilab and in the Soudan mine in Minnesota. This experimentwill provide better precision for the atmospheric oscillation parameters. Also, the SNO,Kamland, and Super-Kamiokande experiments continue to run, providing additionalchecks to existing results.

The American Physical Society conducted a multi-divisional study [15] to address thecurrent experimental situation and to prioritize future neutrino experiments with U.S.

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participation. This study concluded with three major recommendations:

• A program of sensitive searches for neutrinoless double /3 decay. This will addressthe question of whether neutrinos are their own antiparticles and thus, a new formof matter.

• A comprehensive program to investigate neutrino masses, mixing, and CP-violation.

• Development of a detector that is capable of measuring the energy spectrum of theprimary pp solar neutrino flux.

Physicists are working on the planning and R&D necessary to realize these recom-mendations3. There are many double J3 decay experiments in various stages of devel-opment with several choices of isotopes. The program to investigate neutrino masses,mixing, and CP-violation will require a reactor experiment, a long-baseline acceleratorexperiment capable of investigating matter effects, and a megawatt class, neutrino "su-perbeam" coupled with a very large detector at a large distance from the source. Effortsare also underway to build detectors capable of measuring the flux of neutrinos fromthe primary pp fusion process. This requires completely new techniques and will needa deep underground location to shield the device from background.

The realization of this comprehensive program will take many dedicated physicists,substantial funding, and several decades. However it will culminate in understanding theneutrino, its role in the standard model, and the nature of matter in the universe. It is animportant pursuit.

REFERENCES1. "Celebrating the Neutrino", N. Cooper ed, Los Alamos Science 25, (Los Alamos National Labora-

tory, 1997), http://library.lanl.gov/cgi-bin/getfilePnumber25.htm.2. http://quarknet.f nal.gov/run2/standard.html3. D. Karlen, "The Number of Light Neutrino Types from collider experiments", Phys. Lett. B592: 445

(2004).4. B. Kaiser, "Neutrino Mass, Mixing, and Flavor Change", Phys. Lett. B592: 145 (2004).5. R. Davis, Prog. Part. Nucl. Phys. 32,13 (1994).6. A.A. Aguilar et al [LSND Collaboration], Phys. Rev. D 64,112007 (2001)7. B. Armbruster et al. [KARMEN Collaboration], Phys. Rev. D 65,112001 (2002).8. B. Achkar et al [Bugey Collaboration], Phys. Rev. Lett. B 374, 243 (1996).9. M. B. Smy et al [Super-Kamiokande Collaboration], Phys. Rev. D 69,011104 (2004).10. B. Aharmim et al [SNO Collaboration], Phys. Rev. C 72, 055502 (2005).11. T. Araki et al [KamLAND Collaboration], Phys. Rev. Lett. 94, 081801 (2005).12. Y. Ashie et al [Super-Kamiokande Collaboration], Phys. Rev. Lett. 93, 101801 (2004).13. http://www-numi.fnal.gov.14. "The neutrino oscillation industry",

http://www.hep.anl.gov/ndk/hypertext/nu_industry.html.15. "Joint Study on the Future of Neutrino Physics: The Neutrino Matrix", http://www.aps.org/neutrino/,

2005.

See Ref. [14] for links to many of these experiments.755

participation. This study concluded with three major recommendations:

• A program of sensitive searches for neutrinoless double /3 decay. This will addressthe question of whether neutrinos are their own antiparticles and thus, a new formof matter.

• A comprehensive program to investigate neutrino masses, mixing, and CP-violation.

• Development of a detector that is capable of measuring the energy spectrum of theprimary pp solar neutrino flux.

Physicists are working on the planning and R&D necessary to realize these recom-mendations3. There are many double J3 decay experiments in various stages of devel-opment with several choices of isotopes. The program to investigate neutrino masses,mixing, and CP-violation will require a reactor experiment, a long-baseline acceleratorexperiment capable of investigating matter effects, and a megawatt class, neutrino "su-perbeam" coupled with a very large detector at a large distance from the source. Effortsare also underway to build detectors capable of measuring the flux of neutrinos fromthe primary pp fusion process. This requires completely new techniques and will needa deep underground location to shield the device from background.

The realization of this comprehensive program will take many dedicated physicists,substantial funding, and several decades. However it will culminate in understanding theneutrino, its role in the standard model, and the nature of matter in the universe. It is animportant pursuit.

REFERENCES1. "Celebrating the Neutrino", N. Cooper ed, Los Alamos Science 25, (Los Alamos National Labora-

tory, 1997), http://library.lanl.gov/cgi-bin/getfilePnumber25.htm.2. http://quarknet.f nal.gov/run2/standard.html3. D. Karlen, "The Number of Light Neutrino Types from collider experiments", Phys. Lett. B592: 445

(2004).4. B. Kaiser, "Neutrino Mass, Mixing, and Flavor Change", Phys. Lett. B592: 145 (2004).5. R. Davis, Prog. Part. Nucl. Phys. 32,13 (1994).6. A.A. Aguilar et al [LSND Collaboration], Phys. Rev. D 64,112007 (2001)7. B. Armbruster et al. [KARMEN Collaboration], Phys. Rev. D 65,112001 (2002).8. B. Achkar et al [Bugey Collaboration], Phys. Rev. Lett. B 374, 243 (1996).9. M. B. Smy et al [Super-Kamiokande Collaboration], Phys. Rev. D 69,011104 (2004).10. B. Aharmim et al [SNO Collaboration], Phys. Rev. C 72, 055502 (2005).11. T. Araki et al [KamLAND Collaboration], Phys. Rev. Lett. 94, 081801 (2005).12. Y. Ashie et al [Super-Kamiokande Collaboration], Phys. Rev. Lett. 93, 101801 (2004).13. http://www-numi.fnal.gov.14. "The neutrino oscillation industry",

http://www.hep.anl.gov/ndk/hypertext/nu_industry.html.15. "Joint Study on the Future of Neutrino Physics: The Neutrino Matrix", http://www.aps.org/neutrino/,

2005.

See Ref. [14] for links to many of these experiments.755