1. Lecture 1: Neutrinos and their masses
Recent advances in physics and astronomy --- our current understanding of the Universe
Gang Li, IGPP, UCR
Lecture 1: Neutrinos and their masses

2. About units and constants
In this course, we will discuss materials from the infinitesimal elementary particles to the gigantic universe itself. This corresponds to an enormous range of the length scales.
Length units: 1 fm = 10-15m, 1 A = m,
1AU =1.5* 1011m, 1 ly = 9.46*1015m, 1pc = 3.26 lr.
Velocity units: speed of light, c = 3*108m/s.
Energy: eV, 1 eV = 1.6*10-19 J. 1 MeV = 106 eV
Einstein’s E-m relation: E = mc2
Natural unit: h = 1 and c = 1.
Mp = 938 MeV, Me =0.511 MeV, M= 0.

3. Science News of the year

4. The 2002 Nobel Prize Laureates in Physics
Raymond Davis Jr.
Masatoshi Koshiba
Riccardo Giacconi
"for pioneering contributions to astrophysics, which have led to the discovery of cosmic X-ray sources"
                               
                               
"for pioneering contributions to astrophysics, in particular for the detection of cosmic neutrinos"

5. The need for neutrinos Nuclear  decays.
In 1902, Pierre and Marie Curie found that some radioactive nuclei can transmute to other nuclei through  decays, where an electron is always detected. The energy of these radiated electrons, however, is not single valued. Rather, the spectrum is continuous. Among suggested explanations, a quite notorious one is the violation of energy conservation. Quite bothered by this idea, Wolfgang Pauli proposed that there must be a second particles alongside with the emitted electron. This particle must be very light and neutral, so that it is very hard to detect. Later, Enrico Fermi named it neutrino. Indeed,
today we know that neutrinos are very light and they only participate in Weak Interaction and Gravitation.

6. Beta decay spectrum
This beta decay spectrum shows a continuous distribution for the emitted electrons. The y-axis is the intensity which reflects the probability of finding electrons at the corresponding kinetic energy. The ending point at the far right represents the total radiated energy. To insure energy conservation, there must be another undetected particle. This leaded Pauli to propose neutrinos.
                                                   
G. J. Neary, Proc. Phys. Soc. (London), A175, 71 (1940). The solid line is the prediction from Fermi’s theory.

7. The discovery of neutrinos
Wolfgang Pauli: Considered by Albert Einstein an exceptional theoretic physicist, he was awarded the Nobel Prize in 1945 for the discovery of the Exclusion Principle, also known as the Pauli Principle. In 1930, he postulated the existence of neutrino as a remedy for avoiding violation of energy conservation in nuclear beta decays.
In 1953, Frederick Reines and Clyde Cowan did the first neutrino experiment. Their targets are the anti-neutrinos from the nuclear plant at Hanford, Washington. However, they did not obtain convincing signals until 1956, when they redid the experiment. This time, at Savannah River, South Carolina.
Reines was awarded the 1995 Nobel Prize for the discovery of neutrino. Unfortunately, Cowan died in 1974.

8. The first detection of neutrino – schematics
positron and a neutron. The positron then annihilate with an electron and gives two photons simultaneously. The neutron, after 15s, will be captured by a cadmium nucleus, generating another photon. Detecting all these photons, with a 15s interval, signals the presence of (anti) neutrinos.
Experiment principles: a target of 400 liters of water mixed with cadmium chloride is used. Neutrinos from nearby nuclear plant interacts with a proton of the target, releasing a

9. Sun-- a super nuclear reactor
Sun as seen by SOHO
Sun as seen by a neutrino telescope

10. Star burning process— CNO vs pp chain
Stars represent a delicate balance between gravity and gas pressure due to the burning of the core. The net effect of the burning is to convert 4 protons to a helium atom, plus an excess of energy. Two major cycles are in operation depending on the mass of the star. In the case of our sun, the pp chain is the dominant. During the burning process, plenty neutrinos are produced.
The pp chain
Stars are constantly burning hydrogen and convert it to helium to sustain its own weight. Accompanying to this process, enormous energies are released.
The Proton-Proton or PP Chain, which is important in stars the mass of the Sun and less.
The CNO cycle, which is important in more massive stars

11. The CNO cycle
For stars with masses larger than 1.1 solar mass, the major cycle of converting 4 protons to a helium is through the CNO cycle. Neutrinos can come from 1) decay of 15O, with a maximum energy of 1.7 MeV and 2) decay of 13C, with a Maximum energy of 1.2 MeV.

12. The pp chain– steps 1-3

13. The pp chain– steps 4-7

14. The pp chain– steps 8–11

15. Sun as a neutrino factory

16. Solar neutrinos and their production location

17. Solar-neutrino spectrum

18. Detecting neutrinos from Sun
Ray Davis began to look for solar neutrinos, start in 1969, at Homestake mine. The site is 3km underground. 600 tons of chlorine solvent are used. Neutrinos above 1 MeV is detected.
Detection principles:
Reverse of beta decay, detecting the radioactive product. Homestake and GALLAX.
Rely on Cherenkov radiation. Super K and SNO.

19. Solar neutrino experiments (1) -- HOMESTAKE
The first solar neutrino detector ever built, the target is a 615 tons of tetrachloroethylene. When bombarded by an anti-neutrino, the 37Cl becomes 37Ar, which is radioactive with a half-life of 35 days. The 37Ar is then isolated and detected.
Chlorine 37 + neutrino => electron + Argon 71
The number of Argon atoms detected gives the number of neutrino. The site is 3km underground, located in Homestake golden mine, South Dakota.

20. Solar neutrino experiment (2)-- the GALLAX
Located in Abruzzo, Italy, the detector consists of 12.2 tons of watered Gallium. The experiment principle is similar to that of HOMESTAKE: when hit by a neutrino, 71Ga becomes 71Ge, a radioactive isotope with a half-life of days. The whole set of 71Ga and the eventual 71Ge atoms are filtered through a chemical system allowing to isolate with great efficiency and great purity the Germanium atoms, which are then counted to give the number of neutrino interactions.
Gallium 71 + neutrino => electron + Germanium 71

21. Solar neutrino experiments (3)-- the Super Kamiokande
The Super-Kamiokande detector is a 50,000 ton tank of water, located approximately 1 km underground. The water in the tank acts as both the target for neutrinos, and the detecting medium for the by-products of neutrino interactions.
The inside surface of the tank is lined with 11, cm diameter light collectors called "photo-multiplier tubes". In addition to the inner detector, which is used for physics studies, an additional layer of water called the outer detector is also instrumented light sensors to detect any charged particles entering the central volume, and to shield it by absorbing any neutrons produced in the nearby rock.
In addition to the light collectors and water, a forest of electronics, computers, calibration devices, and water purification equipment is installed in or near the detector cavity.

22. Detecting principle behind Super K
Super Kamiokande exploits a different detection principle: the Cherenkov radiation.
Each PMT is sensitive to illumination by a single photon of light. It measures the total amount of light reaching it, as well as the time of arrival; allowing one to reconstruct the energy and starting position, respectively, of any particles passing through the water.
The collective effect of the over 11,000 PMTs measurement allows one to reconstruct the distinctive ring pattern, revealing the direction of the incident particle.
Finally, from the ring pattern - most notably whether it has the sharp edges characteristic of a muon, or the fuzzy, blurred edges characteristic of an electron, one can reliably distinguish muon-neutrino and electron-neutrino interactions. 
Charged particles (and only charged particles) traversing the water with a velocity greater than 75% of the speed of light radiate light in a conical pattern around the direction of the track, as at left. Bluish Cherenkov light is transmitted through the highly-pure water of the tank, and eventually falls on the inner wall of the detector, which is covered with photo-multiplier tubes (PMT's).
In addition to the light collectors and water, a forest of electronics, computers,
calibration devices, and water purification equipment is installed in or near the detector cavity.
a light level of a single photon is approximately the same as the light visible on Earth from a candle at the distance of the moon!
As shown above, when charged particles traverse the water with a velocity greater than 75% of the speed of light, a radiated cone of light centering the trajectory of the particle is observed.

23. Solar neutrino experiment (4) -- the SNO
The Sudbury Neutrino Observatory (SNO) is a detector built 6800 feet under ground, in INCO's Creighton mine near Sudbury, Ontario. Similar to SuperK, SNO contains an array of 9600 photomultiplier tubes and is also a Cherenkov detector. Unlike SuperK, the target of SNO is heavy-water. It uses 1000 tons of heavy water, contained in a 12 meter diameter acrylic vessel. The detector is immersed in light (normal) water within a 30 meter barrel-shaped cavity (the size of a 10 story building!) excavated from Norite rock.
The heavy water is on loan from Atomic Energy of Canada Limited (AECL).
Located in the deepest part of the mine, the overburden of rock shields the detector from cosmic rays. The detector laboratory is extremely clean to reduce background signals from radioactive elements present in the mine dust which would otherwise hide the very weak signal from neutrinos.
From the neutrino flux and shape of the energy spectrum SNO will be able to determine how strongly the neutrino flavours mix together, and determine information about the neutrino masses. SNO started collecting the first data in April 1999, and this will be a very exciting time for neutrino physics.
With the heavy water, the SNO can detect all three flavors of neutrinos. So the SNO detector will be able to observe separately the number of electron neutrinos and the number of all neutrinos. This allows a determination of the probability for these flavor oscillations to occur.

24. Uniqueness of SNO

25. Conflicts between experiments and theory

26. Neutrino oscillation – a “solution”
Neutrinos produced at the sun is solely e. On their way to earth, however, they “oscillate” to  or .

27. Oscillation from SNO
Using all three reactions: charged current, neutral current and elastic scattering reactions, SNO collaboration is able to confirm that flavor transformation between e and () DO happen as neutrinos propagate from Sun to Earth.
Physical Review Letters, vol. 89, p (2002)

28. About neutrino oscillation
1) Neutrinos produced at the Sun are via nuclear reactions (e.g. beta decay) and are eigenstates of “flavors”.
2) When they propagate in space, however, they are eigenstates of energy. The corresonding Hamilton is simply (when m<<p):
3) When detected at Earth, which is through nuclear reactions (e.g. inverse beta decay) again, they must be eigenstates of “flavors”.
Two transformations must happen!

29. Some mathematics
1) At t= 0, assuming a  is produced. This can be expressed as a combination of 1 and 2 through,
2) After a period of time t of propagation, the 1 and 2 behave differently and the  evolves to,
3) The survival probability that this state is still a  is

30. Atmospheric ’s– the source
Atmospheric ’s are produced when cosmic rays (mostly protons) collide with atmospheric nuclei, giving secondary cosmic rays of  and K. These mesons will then decay, giving two types of neutrinos:  and e
                  
Reactions producing  and e :
  u + 
u  e +  + e
Experimentally, people look for deviation of R from 1, where R is
The number of  should be twice of that of e .

31.  and e as seen in SuperK
A typical  event
A typical e event.
Discerning  and e experimentally is easy.
Electron neutrino induced events have a fuzzy edged ring because electrons can generate more electromagnetic shower through brehmstrahlung and pair production. These electron-positron pairs will then generate many small overlapping rings.

32. Atmospheric ’s – the geometry
Neutrinos can come from all directions:
1) L = km for down-going events.
2) L = km for up-going events.
If there is neutrino oscillation, since the survival possibility depends on L, observation should show a  dependence.

33. Missing nm!
Data of e agree with expectation. No more, No less. NO  (e ) oscillate to/from e ( ).
 come from below shows a decrease of 50%.  oscillates to  (or sterile neutrino).

34. Oscillations between  and 

36. Why do we care if neutrinos are massive?
Candidate for dark matter : Scientists believe that the hadronic mater only makes up a small portion ~ 5% of the universe. Invisible material, so called dark matter, is inferred through gravitation effect. If neutrinos were massive, they would be good candidates to this dark matter, since they are copious~330 neutrinos/cm3.
Candidate for High Energy cosmic rays: Ultra high energy cosmic ray (>= 1020 eV) is detected at earth, with its origin and propagation mechanism still remains a mystery. A massive neutrino could be a very good candidate.
Since more than 20 years, a strange puzzle gives headaches to astrophysicists. Measurements of the orbital velocity of stars in many galaxies give unexpected results. The outer stars of galaxies are orbiting more rapidly than expected. Gravitation has been doubted and an hypothetical fifth force was invented... but nothing was able to give a simple explanation to those too high velocities. An other explanation is that some dark matter, invisible, is orbiting around and inside the galaxies, only detectable through its gravitational effects. If neutrinos were massive, they would be good candidates to this dark matter, since the theory says that they must be numerous in the universe: 330 neutrinos per cm3. A good candidate, but with the condition that its mass is neither too small nor to high. Since about 30 years, a phenomena, whose origin is still unknown and which is called "cosmic rays", keeps a mystery. The cosmic rays of high energy are particles coming from somewhere in the universe and producing a great shower of particles (pions, kaons, muons, electrons, neutrinos, photons...) when collisionnin with the atoms of our atmosphere. Some of those cosmic rays have been detected and it was found that they have more energy than an ace tennis ball, that is about 10 Joules, that means about 1020 eV. This is a lot of energy for only one particle. If the particle were a tennis ball, it would have an energy of 1046 eV, that is 1027 Joules. This is about 10 times the energy released by the whole sun each second. For now, no known cosmic phenomena is able to accelerate a particle to reach such energy. Some physicists think that those high energy cosmic particles could be neutrinos. But from where and how do they acquire such an energy? Mystery is still open.

37. References and further readings
Books:
Neutrino astrophysics, by John Bahcall
Neutrino Physics by K Zuber
Websites:
1) Super K homepage /
2) SNO homepage
3) Science magzine:
4) Scientific american:
5) John Bahcall’s homepage

38. Project Ideas A survey of next generation neutrino experiments
What? Why? How?
Implications of a massive neutrinos
a) cosmological
b) theoretical unification theory

39. Neutrinos family – a hierarchy
Leptons

40. Neutrinos from Supernova explosion

41. Another view of SNO Detector