Lecture 3/4
The neutrino oscillation industry
Solar Neutrinos
SuperK : Solar neutrino-gram
Light from the solar core
takes a million years to reach
the surface
Fusion processes generate
electron neutrinos which take
2s to leave
Solar neutrinos are a direct
probe of the solar core
Roughly 4.0 x 1010 solar e
per cm2 per second on earth
Solar neutrino
generation
Solar Neutrino Flux
As predicted by Bahcall's
Solar model
The Solar Neutrino
Problem - Homestake
SSM
Homestake sensitive to
8
B and 7Be electron neutrinos
E > 800 keV
Observe 1/3 of the expected
number of solar neutrinos
1 SNU = 1 interaction per
1036 atoms per second
(Super)Kamiokande
1987 – Kamiokande : 1000 phototubes, 5000 tons of water
1997 – SuperKamiokande : 11000 PMT, 50000 tons of water
SuperK can only observe
the 8B flux (> 5 MeV)
Data
=0.451±0.017
SSM
Confirmation that
it wasn't just the radioChemical experiments
SuperK only sensitive to e
Experimental summary
Atmospheric neutrinos
High energy cosmic rays interact in the upper atmosphere
producing showers of mesons (mostly pions)
Neutrinos produced by
Expect
N ( νμ + νμ )
≈2
N (ν e + ν e )
At higher energies, the muons
can reach the ground before
decaying so ratio increases
 /e Data
R=
 /e MC
R ~ 0.6 - 0.7
The Atmospheric
Neutrino Anomaly
Neutrino Flavour Oscillations
Mixing
CKM
Mechanism

u
d'
,
L
c
s'
L
d '=d cos  c s sin  c
s '=−d sin  c s cos c
In the quark sector, the flavour eigenstates (those states
which couple to the W/Z) are not identical to the mass
eigenstates (those states which are solutions of the
Dirac equation)
Weak
states
 
 
0.97 0.23 0.003 d
d'
s ' = 0.23 0.97 0.04 s
0.008 0.04 0.99 b
b'
Mass
states
Mixing
CKM
Mechanism

u
d'
,
L
c
s'
L
d '=d cos  c s sin  c
s '=−d sin  c s cos c
In the quark sector, the flavour eigenstates (those states
which couple to the W/Z) are not identical to the mass
eigenstates (those states which are solutions of the
Dirac equation)
Weak
states
Unitary mixing matrix
 
e
1
  =U  2

3
Mass
states
Neutrino Oscillations
*
i
Amp     ∝ ∑i U Prop  i U  i
If we can't resolve the individual mass states then
the amplitude involves a coherent superposition of i states
Prob     =  −4 ∑ i j ℜU* i U i U j U* j sin2  m2ij
L

4E
L
2 ∑ i j ℑU U i U j U  sin m

2E
*
i
*
j
2
ij
If mij2 = 0 then neutrinos don't oscillate
Oscillation depends on |m2| - absolute masses, or mass
patterns cannot be determined.
If there is no mixing (If Ui = 0) neutrinos don't oscillate
One can detect flavour change in 2 ways : start with 
and look for appearance) or start with and see if any
disappears (disappearance)
Flavour change oscillates with L/E. L and E are chosen by
the experimenter to maximise sensitivity to a given m2
Flavour change doesn't alter total neutrino flux – it just
redistributes it amongst different flavours (unitarity)
Two flavour oscillations
  


=U
1
⇒U=
2
cos 
sin 
−sin  cos 

L
P    =   −4 ∑ i j U i U i U j U j sin  m

4E
2
2
ij
P() : Appearance Probability
P() : Survival Probability
L
P    =−4U 1 U 1 U 2 U 2 sin  m

4E
2
2
2
2 L km
.=sin 2 sin 1.27 m eV 

EGeV
2
(changing to useful units)
2
ij
Survival Probability
L
E
≪ m 2
L
E
L
~ m2
E
≫ m2
L/E
2
2
P   0    x =1−sin 2
 sin 1.27  m
2
 L /km
 E /GeV 

Three Flavour Oscillation
The three flavour case is more complicated, but no different
  
e
1
U e1
U e2
U e3
  =U  2 ⇔U= U  1 U  2 U 3

3
U  1 U  2 U 3

U is the Pontecorvo-Maskawa-Nakayama-Sakata (PMNS) matrix
L
Prob     =  −4 ∑ i j ℜU U i U j U  sin  m

4E
*
*
2 L
2 ∑ i j ℑU i U i U j U j  sin mij

2E
*
i
*
j
2
2
ij
Oscillation parameters
)(
)(
U e1 U e2 U e3
c 12 s 12 0
c 13
0 s 13 e i δ 1 0
0 1 0 0
iα
U= U μ 1 U μ 2 U μ 3 = −s 12 c12 0
0
c
s
0
1 0
0
23
23 0 e
U τ1 U τ2 U τ3
0 0 1 −s13 ei δ 0 c13 0 −s 23 c 23 0 0 e iβ
(
)(
)( )
2 independent m2
L
Prob     =  −4 ∑ i j ℜU U i U j U  sin  m

4E
*
*
2 L
2 ∑ i j ℑU i U i U j U j  sin mij

2E
*
i
*
j
2
2
ij
Oscillation parameters
)(
)(
U e1 U e2 U e3
c 12 s 12 0 c 13
0 s 13 e i δ 1 0
0 1 0 0
iα
U= U μ 1 U μ 2 U μ 3 = −s 12 c12 0
0
c
s
0
1
0
0
23
23 0 e
U τ1 U τ2 U τ3
0
0 1 −s13 ei δ 0 c13 0 −s 23 c 23 0 0 e iβ
(
)(
)( )
Three angles
L
Prob     =  −4 ∑ i j ℜU U i U j U  sin  m

4E
*
*
2 L
2 ∑ i j ℑU i U i U j U j  sin mij

2E
*
i
*
j
2
2
ij
Oscillation parameters
)(
)(
U e1 U e2 U e3
c 12 s 12 0
c 13
0 s 13 e
U= U μ 1 U μ 2 U μ 3 = −s 12 c12 0
0
1 0
U τ1 U τ2 U τ3
0 0 1 −s13 ei δ 0 c13
(
iδ
)(
1 0
0 1 0 0
0 c 23 s 23 0 e i α 0
0 −s 23 c 23 0 0 e iβ
)( )
CP violating phase
L
Prob     = −4 ∑ i j ℜU U i U j U  sin  m

4E
*
*
2 L
2 ∑ i j ℑU i U i U j U j  sin mij

2E
*
i
*
j
2
2
ij
Oscillation parameters
)(
)(
U e1 U e2 U e3
c 12 s 12 0
c 13
0 s 13 e
U= U μ 1 U μ 2 U μ 3 = −s 12 c12 0
0
1 0
U τ1 U τ2 U τ3
0 0 1 −s13 ei δ 0 c13
(
iδ
)(
1 0
0 1 0 0
0 c 23 s 23 0 e i α 0
0 −s 23 c 23 0 0 e iβ
)( )
Extra Majorana phases
The extra Majorana matrix does not affect
flavour oscillation processes.....so is usually dropped.
However it will affect the interpretation of
neutrinoless double beta decay results
Explaining the solar data
Testing the oscillation
hypothesis
Solar neutrino problem
ne from sun would change to n or n . However these have
too little energy to interact via the charged current, and all
the detectors are only sensitive to charge current interactions.
Non-ne component would effectively disappear, reducing
the apparent ne flux.
Proof : Neutral current event rate shouldn't change.
Sudbury Neutrino
Observatory
1000 tonnes of D20
6500 tons of H20
Viewed by 10,000 PMTS
In a salt mine 2km underground
in Sudbury, Canada
SNO
e
e+
e+0.15*(
SNO Results
5.3 appearance of  in a e beam
Roughly 70% of e oscillates away
Naively...
First instinct is to assume that neutrinos leave the sun as e
and oscillate on their way to the earth. Assuming this
8
2
L∼10 km , E ν< 10 MeV → Δ m ∼3×10
−10
eV
2
Naively...
First instinct is to assume that neutrinos leave the sun as e
and oscillate on their way to the earth. Assuming this
8
2
−10
-5
L∼10 km , E ν< 10 MeV → Δ m ∼3×10
eV
7 x 10 eV
22
Naively...
First instinct is to assume that neutrinos leave the sun as e
and oscillate on their way to the earth. Assuming this
8
2
−10
-5
L∼10 km , E ν< 10 MeV → Δ m ∼3×10
7 x 10 eV
eV
2
Oscillations come from phase difference between mass
states. In a vacuum the phase diff comes from free particle
Hamiltonian. In a material there are interaction potentials
as well
2 2
2 2
∂ψ
∂ψ
−ℏ ∂ ψ
−ℏ ∂ ψ
−i ℏ
=E ψ=
→−i ℏ
=( E+ V ) ψ=
2
∂t
2m ∂ x
∂t
2 m ∂ x2
2
2
E − p =m
2
vac
2
2
→ ( E+ V ) − p =m
2
mat
→ m mat ≈ √ m + 2 E V
2
vac
c.f. effective mass of an electron in a semiconductor or light in glass
Oscillations in Matter
Electrons exist in standard matter –  do not. Electron
neutrinos travelling in matter can experience an extra charged
current interaction that other flavours cannot.
V W= 2 GF Ne
Interaction
Potential
V Z=−
2
F
 e,  ,  
e
2
Δ
m
2
2
M L
P(ν e → ν e )=1−sin (2 θ M )sin (
)
4E
2 G
Oscillation probability modified by
matter effects
 m2M = m2V  sin2 2 cos 2− 2
sin2 2 
2
sin 2  M = 2
2
sin 2cos 2 − 
=
2 2 GF N e E
 m2V
Nn
Implications
2
sin 2 
2
sin 2 M =
2
sin 2cos 2− 
2
=
2  2 GF N e E
m
2
Vac
If m2Vac = 0 or matter is very dense, = ∞ and m = 0
Similarly, if =0, then M = 0
If there is no matter, then  = 0 and we have vacuum
mixing
At a particular electron density, dependent on m2,
ζ=
2 √ 2 GF N e E
Δ m2
=cos2 θ ⇒ sin2 2 θ M =1
Even if the vacuum mixing angle is tiny, there is a density
for which the matter mixing is large
Mass heirarchy
2
sin 2 
2
sin 2 M =
sin2 2cos 2− 2
2 2 GF N e E
=
 m2V
If mass of 1 < mass of 2, m2=m12-m22<0
ζ=−
2 √ 2 GF N e E
2
∣Δ m ∣
2
sin 2 θ
2
→ sin 2 θ M =
2
2
sin 2 θ+ (cos2 θ+ ∣ζ∣)
Positive definite – no resonance
If mass of 1 > mass of 2, m2=m12-m22>0
ζ=
2 √ 2 GF N e E
2
∣Δ m ∣
2
sin 2 θ
2
→ sin 2 θ M =
2
2
sin 2 θ+ (cos2θ−∣ζ∣)
Mixing matrix
)(
)(
U e1 U e2 U e3
c 12 s 12 0
c 13
0 s13 e
U= U μ 1 U μ 2 U μ 3 = −s 12 c 12 0
0
1
0
U τ 1 U τ2 U τ 3
0
0 1 −s 13 e i δ 0 c 13
(
Solar sector
o
o
 e  =32.5 ±2.4
 m212=7.9×10−5 eV 2
iδ
)(
1 0
0
0 c 23 s 23
0 −s 23 c 23
)
Explaining the atmospheric
data
Cosmic Labs
cos zenith = 1.0
15km
L
E
~
10 km
1000 MeV
13000 km
L
E ~
10000 km
1000 MeV
2
⇒  m 0.00001eV
2
cos zenith = -1.0
2
⇒  m 0.01eV
2
Atmospheric
results
Prediction for e rate agrees
with data.
 disappear at large baseline
consistent with →
Don't detect  as
Upcoming
-below  mass threshold
-SuperK is awful at  detection
Downgoing
2
atmos
∣ m
∣≈0.0025 eV
sin2 2  atmos ≈1.0
1 2
1− sin 2 
2
2
Accelerator Cross-check
Δ m 2atmos≈3×10−3 eV 2 → L / E≈400 kmGeV −1
L=250 km→ E ν≈0.6 GeV
Beam events tagged using GPS at both near and far
detector sites
Disappearance Experiments
m2
Φ ν (@ FD )
P( ν α → ν α ) →
Φ ν (@ ND)
 : Neutrino Flux
Use Near Detector to measure (@ND)
T2K verification
T2K Disappearance
2
# events observed
Δ
m
L
2
2
=P( νμ → ν μ )=1−sin (2θ )sin (
)
# events expected
4E
(best fit)
−3
2
eV
∣Δ m223∣=(2.51±0.1)×10
sin2 ( θ23 )=0.514+0.055
−0.056 →θ23 =45.8±3.2
Mixing matrix
)(
)(
U e1 U e2 U e3
c 12 s 12 0
c 13
0 s13 e
U= U μ 1 U μ 2 U μ 3 = −s 12 c 12 0
0
1
0
U τ 1 U τ2 U τ 3
0
0 1 −s 13 e i δ 0 c 13
(
o
θ eμ=33.7 ±1.1
2
12
−5
Δ m =+(7.54±0.24 )×10 eV
)(
1 0
0
0 c 23 s 23
0 −s 23 c 23
Atmospheric sector
  
Solar sector : ν  νe
o
iδ
2
θμ τ =41.4o ±2.0 o
2
−3
2
Δ m23=∣(2.43±0.06)×10 ∣ eV
)
So how big is 13?
)(
)(
U e1 U e2 U e3
c 12 s 12 0 c 13
0 s13 e
U= U μ 1 U μ 2 U μ 3 = −s 12 c 12 0
0
1 0
iδ
U τ 1 U τ2 U τ 3
0
0 1 −s 13 e 0 c 13
(
iδ
)(
1 0
0
0 c 23 s 23
0 −s 23 c 23
)
Is it zero ? This would be bad news since the CP violating phase
always appears in the PMNS matrix together with 13.
Zero 13 would make any CP violation in the light neutrino sector
unobservable in principle.
Better try to measure it......
How do we measure 13?
  e oscillations with atmospheric L/E
2
2
2
P   e =sin 2  13 sin  23 sin 1.27 m
2
23
L
E

e appearance in a  beam – ideal for accelerator experiments
e  x disappearance oscillations with atmospheric L/E
L
p(ν e →ν x ) = P (νe → ν x )=1−sin (2 θ 13)sin (1.27 Δ m
)
E
C^ P^
2
e disappearance – ideal for reactor experiments
2
2
23
13 from reactors
oscillations
due to 13
sin2213 = 0.090 ± 0.008
T2K Results
e events observed in SuperK
Allowed region for (13)
2
sin (2θ 13)=0.14±0.036
o
θ 13≈10.9
3-Neutrino Mixing
 
i
c 13
0 s 13 e
1 0
0
U PMNS = 0 c 23 s 23
0
1
0
0 −s 23 c 23 −s 13 ei  0 c13
Atmospheric sector
   
o
θ e μ=45.0 ±2.4
−3
o
o
Δ m =|2.4×10 | eV
2
23
13 Sector
e → 
Solar sector
o
θ13 =10.6 ±0.3
2
 
c 12 s12 0
−s 12 c 12 0
0
0 1
 e  
o
θ eμ =32.5 ±2.4
o
Δ m223=|2.4×10−3| eV 2 Δ m2 =+7.5×10−5 eV 2
12
Summary of Current Knowledge
13 : how much e is in 3
e


(
0.8 0.5 −0.15
U MNSP = −0.4 0.7
0.6
0.4 −0.5 0.7
)
Some elements only
known to 10-30%
Very very different from
the quark CKM matrix
A bonfire of anomalies
The fly in the ointment
The LSND experiment was the first accelerator experiment
to report a positive appearance signal
+
+
    
+
e  e 
↳

e
E : 20-55 MeV
baseline : 30m
L/E  1.0
+
e p e n
20-60 MeV
n p  d
1280 PMTs
167 t liquid scintillator
2.2 MeV
LSND Result (1997)
87.9 ± 22.4 ± 6 excess events
from  → e
3.3 evidence for
oscillations
m2 = 1.2 eV2
LSND Result (1997)
87.9 ± 22.4 ± 6 excess events
from  → e
Δm
Δm
2
solar
2
atmos
3.3 evidence for
−5oscillations
2
∼8×10 eV
−3
∼2.5×10 eV
2
??
2
Δ m ∼1eV
fourth neutrino ?
2
m2 = 1.2 eV2
MiniBooNE
Ran from 2002 to 2014 at Fermilab
Average neutrino energy ≈ 1 GeV
L/E the same as LSND
Same technology as LSND
Different energy = different event types = different
systematics
LSND L/E Region
2013 analysis
No excess of e events in
signal region (E>450 MeV)
Unknown excess of events
at low energy (where NC
/0 would be)
The Gallium Anomaly
We've discussed the Homestake
experiment which studied the reaction
37
37
­
 e Cl  Ar e
A couple of experiments (SAGE and
GALLEX) also studied
71
71
ν e + Ga→ Ge+ e
-
In early 2000's the response of
the Gallex experiment (remember
that?) was being tested using
radioactive sources.
Sources emitted e which were then
observed using the standard Ge
signature
2
L/ E≈0.1 m/ 0.1 MeV →Δ m ≈1 eV
2
(or is it our understanding of the
inverse beta decay cross section?)
Reactor Anomaly
Over the years there have been lots of reactor experiments who
measured the electron antineutrino flux from reactors and found
that observed rates matched expected rates.
In 2011, new techniques in modelling nuclear reactions led to a
re-evaluation of the expected electron antineutrino flux. The new
estimate was about 6% higher than the old.
Suddenly all the experiments now observed a general deficit of
electron antineutrinos being emitted from reactors
Could this be (i) the new flux estimate is just a bit dodgy or (ii) we
have short baseline neutrino oscillations to a sterile state?
Reactor Anomaly
2
2
Deficit consistent with a sterile
state
with
m

1.5
eV
Decaying sterile
neutrinos?
Lorentz violation?
Extra dimensions?
CPT Violation?
Experimental
problems?
3+1 sterile?
3+2 ?
3+n ?
No bleedin' idea
Wait for more data
Summary of sterile hints
There are odd hints, each at the level of 2-3 , that they may be
at least one other light sterile state floating around with
m2  1 eV2. This is not very easy to fit into the standard model.
It is very hard to find an oscillation model, including steriles, which
is consistent with all of the data
Current “best model” is a 3+1 model but it doesn't fit very well and
it could all be a conspiracy of
systematic uncertainties
Many new experiments being proposed
to search for signs of steriles in
neutrino oscillations
Δ m2sterile =1 eV 2
Δm
2
sol
2
Δ m atmos
Story is certainly not over.....watch this
space
To Infinity and Beyond!
The next 20 years
Measurement
23
13
Method
 Disapp. T2K, NovA
e Appear. T2K, NovA
Anti-e
Sgn(m232)
CP
Experiments
Why?
Is it maximal?
Equal to 0? Can't
measure CP if it is
Reactor
When
2009
2012
2012
Disapp.
e / anti-e Next Gen
Unification, GUT
Neutrino Factory Lepton asymmetry
2020
2035?
Current Experiments
Next generation of
experiments
DUSEL Underground
Neutrino Experiment (DUNE)
Hyper-Kamiokande
1300 km
MW beams
multi-kton far detectors
SK (to scale'ish)
Dune / HK Comparison
DUNE
Hyper-K
T2K
Beam Energy
3 GeV
0.7 GeV
0.7 GeV
Baseline (L)
800 km
295 km
295 km
Beam Power
1.2 MW
0.75 MW
0.3 MW
Type of Beam
Wideband
Off-axis
Off-axis
Mass of far
detector
70 kton
560 kton
22.5 kton
Technology
Liquid Ar TPC
Running
from
2025
Water Cerenkov Water Cerenkov
2025(30)
The Future – Mass Heirarchy
CP violation and
Mass Heirarchy
Measuring CP is the ultimate goal of neutrino oscillation
experiments. How? CP is a complex phase.
L
Prob     =  −4 ∑ i j ℜU U i U j U  sin  m

4E
*
*
2 L
2 ∑ i j ℑU i U i U j U j  sin mij

2E
*
i
*
j
2
2
ij
= 0 if 
CP violation can only take place in appearance experiments
Look for
P   e ≠P    e 
In all it's naked glory
P      e  e = P1P 2P 3P4
2
2
2
P 1=sin  23 sin 2  13
 
 13
2 B +sin 
L
B -+
2
2
2
2
P 2 =cos  23 sin 2 12
 
 12
2 A
sin  L
A
2
13
23>45 or 23<45
Sign(m232)

 23
 12  13
B-+
A
P 3= J cos  cos
L
sin  Lsin 
L
2
A B-+
2
2
 23
 12  13
B-+
A
P 4 =±J sin  sin 
L
 sin Lsin 
L
2
A B -+
2
2
 m2ij
 ij =
2E
A=  2 G F N e
B -+=∣ 13∓A∣
J =cos  13 sin2 12 sin 2  23 sin 2  13
Degeneracies
Experiments only measure at most two numbers; but
probability has three unknowns and parameters with errors.
Need more than
one measurement
at different L/E to
disentangle the
parameter space
Mass Heirarchy
measurements
As baseline grows,
matter effects increase
At distances of around
1000 km we can
unambiguously
identify the mass
heirarchy
Once we've done
that we need to
determine
CP phase
Heirarchy Measurement
m2
m1
Mass hierarchy in 0
decay
m3
2
2
2
Γ 0 ν ∝m ν =m1|U e1| + m2|U e 2| + m3|U e3|
e
In the inverted hierarchy : m3  m1  m2 , m132  m232
and m3 is the lightest mass state, so we can write
2
√
2
3
2
2
23
√
2
3
2
23
2
m 2 β =|U e1| m +Δ m +|U e 2| m + Δ m +|U e3| m
2
3
Setting m3 to zero (not a bad approximation) one can show that
m2 β > √ Δ m cos θ13
2
23
2
i.e for the inverted hierarchy, the decay rate, 0 would havea
lower limit.
Mass hierarchy & 0
decay
mν [eV ]
Current upper limit
e
IH
NH
m 3 [eV ]
Experimental
limit needs to
decrease by a factor
of 10
Limit scales with
mass and run time
Experiments
need to be 10 times
bigger and run 10
times longer
These are being
built now.
Mass Hierarchy
Determination
A number of different experiments, both accelerator
and 0 decay focused, are now trying to
determine the mass hierarchy.
Timescale : 10-15 years from now (although
good indications before hand – mass hierarchy is a
binary measurement, after all)
A way around the
degeneracies
e oscillation probability
Second
maximum
First
maximum
CP = 0
CP = 90
CP = 270
Osc. Prob. @ First Max
= f (δCP )
Osc. Prob. @ Second Max
E/L
Could study CPV using an experiment
sensitive
to both maxima using
only a wide-band neutrino
beam.
DUNE Sensitivity
5  significance for
sin CP  0 over
56% of CP space
20% precision at
CP = -90 degrees
Hint of CP?
Fitting full 3-flavour model to T2K e appearance data
suggests CP > 0 disfavoured (mild sensitivity to second
oscillation maximum)?
What do we really want
to do though?
We need to do this in the
neutrino sector
We can't do it only with
superbeams
Another problem...
To do these sort of measurements
Measure number of events at
Far Detector
Compare with expected number of
events
Number of events=σ Φ T ϵ
Cross
Section
Neutrino
Flux
Number of
Targets
Selection
Efficiency
15-100%
10-15%
1-2%
10%
Effect of Systematics
Example of state of the
data (pre-2007)
The data is impressively imprecise
−
  p   p
−


 p  n 

  p   n 

Added complication that the final state pions can (i) scatter
(ii) be absorbed (iii) charge exchange within the nucleus
before being observed (iv) nucleons rescatter producing 
+
0
 n  p
Getting better
CC 0 differential xsec from
MINERvA
Phys.Lett. B749 (2015) 130-136
CC 0 differential Xsec from T2K
arXiv:1602.03652
Lot's of effort going into trying
to understand neutrino
interaction cross sections
But it's hard...
1. We are assuming that the initial target nucleon is just sitting still
before interaction. Actually in the nucleus it has some initial momentum
distribution.
The Fermi momentum modifies the scattering angles and momentum
spectra of the outgoing final state
2. The outgoing final state can interact with the target nucleus.
This nuclear re-interaction affects the outgoing nucleon momentum
direction and charge (through charge exchange interactions)
Theoretical uncertainties are large
At least 15%
If precise knowledge is needed for a particular target
(e.g. Water, hydrocarbon) then measurements
are needed
Last measurements taken in the '70s
Quasi-Elastic Scattering



+
W
n
p
Usually thought of as a
single nucleon knock-on
process
In the past has been used as
a “standard candle” to
normalise other cross
sections
Heavily studied in the 1970's
and 1980's and considered to
be “understood”
I. Very important for current oscillation experiments as it
contributes the most of the total cross section at a few
GeV
Quasi-Elastic Scattering



+
W
n
p
Usually though of as a
single nucleon knock-on
process
In the past has been used as
a “standard candle” to
normalise other cross
sections
Heavily studied in the 1970's
and 1980's and considered to
be “understood”
2
2
2( mN −E B ) E μ −( E B−2 mN E B + mμ )
II. Energy reconstruction is
E ν ;rec =
unbiased
assuming 2 body
2(m N −E B− Eμ +|pμ| cos θ μ)
kinematics
Extra processes
contribute : e.g.


W


p
p
+
n

+=

n

p
n
p
unobserved final
state proton
Meson Exchange Current
(MEC)
Effect on energy
reconstruction
CCQE single nucleon
Multinucleon
Martini et al, arxiv : 1211.1523
Summary
We measure events = flux*cross section
We don't generally have a handle on the flux to
better than 10% - there is a lot of work trying to
deal with this.
The other side of the coin, cross-sections, are even
more poorly known.
We need new, high-statistics, measurements of these
cross sections on multiple target materials and at
multiple energies.
Concluding Remarks
We have gone through a lot but I can easily fill another 15 hours of
lectures.
The neutrino is : light, neutral, left-handed (chiral) and almost left-handed
(helicity). It is generated purely in weak interactions (which is why it is
chiral). It is generated by many sources : the Big Bang, astrophysical
events, supernova, the sun, cosmic rays, radioactive decays, and
countless other sources. We can generate them in reactors and
accelerators. Their cross sections are tiny and we need big detectors
to look at them. They mix and oscillate.
They may be the reason that we are here at all.
But...what is their mass? Why is it so small? Why are the mixing
parameters so odd? What about these hints of a 1 eV sterile state?
Still lots of questions remain – watch this space.....