1. Neutrino oscillations/mixing
P Spring 2003 L15
Neutrino oscillations/mixing
Richard Kass
The derivation of neutrino oscillations is very similar to the derivation of “strangeness” oscillations (Lec. 7) and B meson oscillations.
To make the derivation “simple” assume that CP is conserved, there are only 2 types of neutrinos and both neutrinos are stable (t1 = t2 = ¥).
At t=0 we have an electron (ne) and muon (nm) neutrino which are both mixtures of n1 and n2.
ne(t=0) º ne= n1cosq+n2sinq nm(t=0) º nm= -n1sinq+n2cosq
Since we don’t know (beforehand) how “mixed” the neutrinos are we use q to describe the mixture. Note: for the kaon case we assumed equal amounts of K1 and K2 or q=45 degrees.
The mass eigenstates (n1 and n2) propagate through space with energy E1 and E2 according to:
We are interested in the case where the neutrinos are relativistic (E>>m) and therefore:
Assuming the same energy (and E= p) for both neutrino components we can write:
The probability of observing a ne at x (=ct) given that a nm was produced at t=0 is:
P(nm® ne)=|< ne|nm(t)> |2
M&S

2. Neutrino Oscillations/Mixing
P Spring 2003 L15
Richard Kass
Neutrino Oscillations/Mixing
If we measure mass in eV, x in meters, and E in MeV we can write the above as:
The probability of observing a nm at x given that a nm was produced at t=0 is:
P(nm® nm)=|< nm|nm(t)> |2
In order to have neutrino oscillations:
at least one neutrino must have mass
the neutrinos must mix
Since the oscillation depends on Dm2 the mass of the neutrinos
must be determined from “other” experiments:
n energy endpoint experiments
double b-decay experiments

3. The SuperKamiokande Experiment
P Spring 2003 L15
The SuperKamiokande Experiment
Richard Kass
Original purpose was to search for proton decay: p®e+p0 (baryon # violation).
Found lepton number violation instead!
Use water as target and detector medium
Need lots of protons to get neutrino interactions.
Size: Cylinder of 41.4m (Height) x 39.3m (Diameter)
Weight: 50,000 tons of pure water
Need to identify e-’s and, m’s, p0’s (use Cerenkov radiation)
Reject unwanted backgrounds (cosmic rays, natural radiation)
103m underground at the Mozumi mine
of the Kamioka Mining&Smelting Co Kamioka-cho, Japan

4. Atmospheric Neutrinos
P Spring 2003 L15
Atmospheric Neutrinos
Richard Kass
Atmospheric neutrinos are the end
product of high energy collisions of
cosmic rays (mostly protons) with
the nuclei in our upper atmosphere.
Neutrinos are mostly the result of
pion decay (and subsequent muon
decay) but kaons also contribute to
neutrino production.
From the figure on the right we (naively) expect for the number of muon and electron induced interactions:
The experiments cannot distinguish
the charge of the lepton produced in the
neutrino interaction.
The efficiency for detecting muons is usually very different than the efficiency for
detecting electrons so the measured R is not 2.

5. Atmospheric Neutrino Oscillation Results from SuperK
P Spring 2003 L15
Richard Kass
Atmospheric Neutrino Oscillation Results from SuperK
Measure the number of ne and nm interactions in SuperK as a function of neutrino path length in the earth’s atmosphere. n
Neutrinos are produced by
cosmic ray interactions in
earths atmosphere.
superK
Phys. Rev. Lett. 86(2001)
earth
Phys. Rev. Lett. 81 (1998) 
atmosphere n
The nm‘s are
“disappearing”!
2002 Nobel Prize
M. Koshiba

6. Atmospheric Neutrino Oscillation Results from SuperK
P Spring 2003 L15
Richard Kass
Atmospheric Neutrino Oscillation Results from SuperK
SuperK does not actually see an “oscillation”.
For example use the solution with:
Dm2 = 2.2x10-3 eV2 assume <En>=103 MeV
losc = (p/1.27)(<En>/Dm2) = (p/1.27)(103/2.2x10-3) = 1.1x106 m
SuperK sees too few muon neutrinos.
The number of expected muon neutrino interactions is calculated using a detailed simulation of the detector and takes into account detection efficiency as a function of energy and angle (atmospheric path length and detector path length).
Scenario #1: No oscillations (or equal muon and electron neutrino oscillations neÛnm)
number of muon and electron neutrino interactions independent of L/E.
Scenario #2: muon neutrino oscillates into electron neutrino (nm®ne)
excess number of electron neutrino interactions Vs. L/E
depletion of muon neutrino interactions Vs. L/E
Scenario #3: muon neutrino oscillates into tau neutrino (nm®nt)
SuperK has low detection efficiency for nt interactions
constant number of electron neutrino interactions Vs. L/E
Scenario #4: muon neutrino oscillates into a neutrino (nm®nS) that doesn’t interact
Scenario #5: Combination of 3&4 or something else??

7. The Solar Neutrino Problem
P Spring 2003 L15
The Solar Neutrino Problem
Richard Kass
The sun only produces electron neutrinos (ne)!
M&S
Since 1968 R.Davis and collaborators have been measuring the cross section of:
ne + 37Cl ® e- + 37Ar
Their measured rate is significantly lower than what is expected from the
“standard solar model”
Measured: 2.55±0.17±0.18 SNU
Calculated: 7.3±2.3 SNU
SNU=standard solar unit
SNU=1 capture/s/1036 target atoms
Data from the
Homestake Gold
Mine (South Dakota)
2002 Nobel Prize
R. Davis
There is a long list of other experiments have verified this “problem”.
Too few neutrinos from the sun!

8. The Solar Neutrino Energy Spectrum
P Spring 2003 L15
Richard Kass
The Solar Neutrino Energy Spectrum
Figure by J. Bahcall
Homestake:
Chlorine
ne + 37Cl ® e- + 37Ar
SAGE/GALLEX:
Gallium
ne + 71Ga ® e- + 71Ge
SuperK:
nX + e- ® nX + e-
nmt + e- ® 1/6(ne + e-)

9. The Solar Neutrino Problem
P Spring 2003 L15
Richard Kass
The Solar Neutrino Problem

10. The SNO Detector Located in a mine in Sudbury Canada
P Spring 2003 L15
The SNO Detector
Richard Kass
Located in a mine in Sudbury Canada
Uses “Heavy” water (D2O)
Detects Cerenkov light like SuperK
SNO=Sudbury Neutrino Observatory
Nucl. Inst. and Meth. A449, p172 (2000)

11. Why Use “Heavy” Water? The quantities can be compared with the
P Spring 2003 L15
Why Use “Heavy” Water?
Richard Kass
Charged Current interaction (CC): ne + d ® e- + p + p (ne + n ® e- + p )
Deuterium has neutrons!
Only electron neutrinos can cause this reaction
Neutral Current Interactions (NC): nemt + d ® nemt+ n + p
D2O has twice as many nucleons as H2O
all neutrino flavors contribute equally
energy threshold for NC reaction is 2.2 MeV
Elastic Scattering interactions (ES): nemt + e- ® nemt + e-
mostly electron neutrinos (NC and CC)
Neutrons are captured by deuterium and produce 6.25 MeV g
SuperK only
has protons!
SNO measures several quantities (fCC, fNC, fES) and from
them calculates the flux of muon and tau neutrinos (fm+ft):
The quantities can
be compared with the
standard solar model.
They also measure the total 8B solar neutrino flux
into NC events and compare it with the prediction of the SSM.

12. Results from SNO neutral current results: Fssm = 5.05 Fsno = 5.09
P Spring 2003 L15
Results from SNO
Richard Kass
neutral current results:
Fssm = 5.05
+1.01
-0.81
+0.44
-0.43
+0.46
-0.43
Fsno = 5.09
Best fit to data gives:
Flux of 8B solar neutrinos
Fmt=0 if no oscillations.
“SSM”=Standard Solar Model
Strong evidence for Neutrino Flavor Mixing at 5.3s (5.5s if include SuperK).
Total active neutrino flux agrees with standard solar model predictions.
Believe that the mixing occurs in the sun (“MSW effect”)

13. The Mikheyev Smirnov Wolfenstein Effect
P Spring 2003 L15
Richard Kass
The Mikheyev Smirnov Wolfenstein Effect
Neutrino oscillations can be enhanced by traveling through matter.
Origin of enhancement is very similar to a “birefringent” medium where different
polarizations of light have different indexes of refraction. When polarized light passes
through a birefringent medium the relative phase of each polarization component
evolves differently and the plane of polarization rotates.
The neutrino “index of refraction” depends on its scattering amplitude with matter:
sun is made of protons, neutrons, electrons ®up/down quarks, electrons
All neutrinos can interact through neutral currents equally.
Only electron neutrino can interact through CC scattering: ne+ e- ® ne + e-
The “refractive index” seen by electron neutrinos is different than the one seen
by muon and tau neutrinos.
The MSW effect gives for the probability of an electron neutrino produced at t=0
to be detected as a muon neutrino:
The MSW effect is
very similar to
“K-short regeneration”
M&S
Here Ne is the electron density.
For travel through vacuum Ne=0 and the MSW result reduces to our previous result.

14. P Spring 2003 L15
The MSW Effect
Richard Kass
There are only a few allowed regions in (q, Dm2) space that are compatible with
MSW effect:
LMA= Large Mixing Angle region favored.
SNO Day and Night Energy Spectra Alone
Combining All Experimental
and Solar Model information
From A. Hamer, APS Talk, 4/2002