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Three Flavor Oscillations of Atmospheric Neutrinos in Super Kamiokande
Roger Wendell, Duke University 20090403
Tokai, J-PARC
Outline
Super – Kamiokande Neutrino Oscillations
Incorporating three actvive flavors Signatures of θ
13
Pure ProbabilitiesEffects of Reconstruction
Oscillation FittingFits in θ
13 for SK-I, SK-II and SK-I+ SK-II
Results Conclude
Introduction
Neutrinos are included in the Standard Model, but are massless. However, there is now a lot of compelling evidence to suggest that in fact, neutrinos are massive
We want to constrain the last unknown mixing angle in neutrino oscillation physics by searching for evidence of electron neutrino appearance in atmospheric neutrinos
Much of this evidence comes in the form of neutrino oscillation experiments which have constrained several of the parameters governing the behavior of neutrinos.
50 kiloton Water Cherenkov Detector
11,146 Photomultiplier TubesInner Detector (ID):
22.5 kt fiducial volume
Under Mt. Ikenoyama, western Japan,at depth of 2700 m.w.e
In operation since 1996
Outer Detector (OD):Cylindrical Shell ~ 2m
1885 PMTs
Super-Kamiokande
Phases of Super-KamiokandeOn November 12th 2001 a PMT imploded creating a shock wave that destroyed ~60% of PMTs
The run period prior to July 2001 is termed SK-I (1489 days) Detector was rebuilt from 2001 - 2003
Half as many PMTs were installed in the IDID are covered in a fiber reinforced plastic (FRP) shell with an acrylic windowAll damaged OD tubes were replaced
Data taken from 2003 – 2005 in this configuration is known as SK-II (804 days) Both run periods are used in this talk
...fully reconstructed and took data from June 2006 ~ August 2008
The ν news at SuperK
Electronic upgrade complete Fall 2008,Now running as SK-IV
Atmospheric Neutrinos
Neutrinos produced in the decay products of cosmic ray interactions with air nuclei
p N air
e e
Two νµ's and one ν
e
Flux is isotropic about the EarthLarge variation in ν path lengths - 15 ~ 1.5 x 104 km
Large variation in energy 100 MeV – 1 TeV
Very useful for studying neutrino oscillations....
Two Types of Rings
e-likee-like µ-like
Electrons have low mass and multiply scatter and may produce e+e- pairsCollection of Cherenkov light produces a diffuse ring pattern ⇒ e-like
Muons are more massive and pass relatively undeflected Produce Cherenkov rings with well defined edges ⇒ µ-like
Neutrino Oscillations
Super-K data is well described by standard two flavor νµ disappearance
What about sub-leading oscillation effects?
High Energy Atmospheric Neutrinos at Super-K
Deficit seen in µ-like events coming from below the detector (long baselines ) Electron-like event rate is consistent with expectation
disappearance
Cosine Zenith Angle
Upward-going Downward-going
(preliminary)
P =sin2 2sin2 1.27m2LE [ eV
2 kmGeV ] m2
≡m22−m1
2
Energy [ GeV ]
Co
sin
e Z
enit
h A
ng
le
νµ → ν
τ
Long Pathlengths
Short Pathlengths
⇒ data well described by dominant two-flavor νµ
→ ν
τ oscillations with
maximal mixing
Two-flavor Result: sin22θ = 1.0 , ∆m2 = 2.1 x 10-3 eV2
Two Flavor Oscillations at Super-K
What about sub-leading effects?.....
(preliminary)
Three Active Flavors• s
ij ≡ sin θ
ij and c
ij ≡ cos θ
ij
With three ν flavors there are3 Mixing angles : θ
12 , θ
23 , θ
13
3 Mass states : m1, m
2, m
3
2 Mass differences : ∆m2
12 , ∆m2
31
1 cp violating phase: δcp
If all of these angles are non-zero it becomes possible to measure CP-violation in leptons...
Atmospheric Solar
Pieces of the mixing matrix (MNS matrix) are rotations among two states Oscillation probabilities in vacuum can be written in a closed form and
maintain an L/E type dependence in each mass splitting
Current Experimental Knowledge ( Maltoni - arXiv:0812.3161 )
Solar :
∆m2
127.6 x 10-5 eV2 [ 7.0 , 8.3 ] x 10-5 eV2 KamLAND, SNO...
sin2 θ12
0.30 [ 0.23, 0.37 ] Atmospheric :
| ∆m2
31 | 2.4 x 10-3 eV2 [ 2.07, 2.75 ] x 10-3 eV2
Super-K, MINOS..
sin2 θ23
0.50 [ 0.36, 0.67 ] Other :
sin2 θ13
0.01 [ 0.00, 0.056] Chooz δ
cp ???
Parameter Best-Fit 3 σ C.L. Experiments
Normal Hierarchy
∆m2
sol
∆m2
atmmn
n3
n2n1
Inverted Hierarchy
n3
n2n1
∆m2
atm
∆m2
solOR ?
Matter Effects Neutrinos traveling through matter are subject to additional scattering
amplitudes:
Z0 exchange flavor blind, no net effect
W± ExchangeOnly ν
e
⇒ Effective potential added to the hamiltonian
⇒ Alters νe → ν
α oscillations....
neutrino
anti-neutrino
Matter Effects (2)
neutrinoanti-neutrino
( ∆m2 > 0 )
Density [g/cm3]
sin
2 2θ M
P e = sin2 2M sin2 1.27M2 LE
Resonance depends on sign of ∆m2 and whether neutrino or anti-neutrino Exists for a given set of oscillation parameters at some density Ideas carry over well to three neutrino flavors
Leads to a resonance condition
For two flavors: replace vacuum variables with “matter” variables
“Matter” variables
neutrino
anti-neutrino
PREM ModelThisAnalysis
Extend νµ→ν
τ oscillations to include ν
µ→ν
e
Three flavor oscillation probabilities in matter cannot be written in a simple form
But constant density evolution is solvable Same resonant features are present
Under the normal hierarchy: ν's and notν's Under the inverted hierarchy:ν's and not ν's Magnitude of the effect is regulated by θ
13
sin2θ13
= 0
sin2θ13
= 0 sin2θ
13 = 0.01
sin2θ
13 = 0.03
Energy [ GeV ]
Co
sin
e Z
enit
h A
ng
le
Radius [ km ]
Den
sity
[g
/cm
3 ]Three-Flavors and Matter Effect in the Earth
⇒ Use these properties to look for non-zero θ13
and test the hierarchy
Pure Oscillation Probabilities At the Chooz limitν
µ → ν
τ ν
µ → ν
e
At the Chooz limitMay be a noticeable effect on ν
µ → ν
τ
probability in the matter resonance regionEffect on ν
µ→ ν
e probability can be quite large
However, generation and subsequent disappearance are competing processes
sin2θ13
= 0.04
Energy [ GeV ] Energy [ GeV ]
Co
sin
e Z
enit
h A
ng
le
Co
sin
e Z
enit
h A
ng
le
2f: νµ → ν
τ
Consider the excess of events after three-flavor oscillations relative to two-flavors
Alternating bands of excess and deficits in the νµ's
Resonance region clearly visible in νe's
Look for high energy e-like events in the Super-K data Detector resolution effects have not been considered so far....
Energy [ GeV ] Energy [ GeV ]
After Incorporating the ν FluxesC
os
ine
Zen
ith
An
gle
Relative excess θ13
=Chooz / θ13
= 0 νµ
Relative excess θ13
=Chooz / θ13
= 0 νe
The Reconstructed bins
Matter resonance is visible but now represents only a 20% excess Fortunately, the bins in the resonance area are well populated For the inverted hierarchy there is only an 8% excess in the resonance µ-like samples(not shown) show a lower effect ± 4% in just a few bins
Evis
[ log MeV ]Evis
[ log MeV ]
Relative excess θ13
=Chooz / θ13
= 0
Multi-Ring e-like
Multi-Ring e-like Bin Contents
Co
sin
e Z
enit
h A
ng
le
Co
sin
e Z
enit
h A
ng
le
High Energy ν's
High energy ν interactions often produce multiple charged particleslook for events with multiple rings
At such high energies though it becomes difficult to tell what is νe and ν
µ
left image is νµ (background) and right is ν
e (signal)
Other aspects of the data can be used to determine the difference
multi-GeV multi-ring e-like data sample using a likelihood method:
Likelihood: Multi-ring e-like sample
Likelihoods for 5 energy bins in 4 variables,(applied to multi-ring events)Most Energetic Ring's PID and momentum fractionNumber of decay elections and maximum distance to them
Background to this sample is νµ or NC-π production
Resulting sample signal purity: SK-I 75% , SK-II 73%
Signal: CC νe
BG: CC νµ
/ NC - π
Analysis Structure
Oscillation Space Over 3 oscillation parametersSolar oscillations are neglected -- ≤ 5% effect on the main resonance
Computationally intensive to use all 5 Fits to SK-I, SK-II and SK-I+SK-II Fits to MC for both hierarchies
sin2θ13
sin2θ23
∆m2
Systematic Uncertainties90 sources of uncertainty, 32 common between SK-I and SK-II
ν flux uncertainties (18) ν interaction uncertainties (14) Event reduction uncertainties (10 SK-I + 10 SK-II ) Event reconstruction uncertainties (19 SK-I + 19 SK-II )
Look for evidence of non-zero θ13
and the mass hierarchy by comparing
data with several oscillation models
About the Fitting Method
Fit is done using the “Pull” method of systematic uncertaintyMC expectation is adjusted directly during the fit to minimize χ2
Adjustment is controlled by εε is constrained by penalty term
χ2 is based on a poisson likelihood n indexes bins and i indexes systematic errors
χ2 is minimized over εi by inverting a matrix equation obtained by
differentiatingFast fitting methodEquivalent to fitting using a covariance method
sin2θ13
sin2θ23
∆m2 ∆m2
sin2θ13
sin2θ13
sin2θ23
sin2θ23
∆m2
Drawing Contours from a 3-dimensional χ2 surface
Easier to visualize in two-dimensionsso “project” χ2 surface onto each 2-variable planeminimize over the 3rd variable
Normal Hierarchy: Chooz Limit
99% C.L. 90% C.L.
Chooz Exclusion
SK-II SK-I +SK-II
Chooz Exclusion
SK-I
Chooz Exclusion
Best fit point for SK-I+SK-II agrees with the recent Two-Flavor result All contours enter the Chooz exclusion region SK-II and SK-I+SK-II have smaller contours than their expected sensitivity
(preliminary)∆m2 = 2.1 x 10-3 eV2
sin2 θ23
= 0.5
sin2 θ13
= 0.00
χ2 = 841 / 745
∆m2 = 2.6 x 10-3 eV2
sin2 θ23
= 0.5
sin2 θ13
= 0.00
χ2 = 413 / 347
∆m2 = 2.6 x 10-3 eV2
sin2 θ23
= 0.5
sin2 θ13
= 0.00
χ2 = 413 / 347
SK-I + SK-II
99% C.L. 90% C.L.
SK-I + SK-IISensitivity
Normal
Sensitivity computed as average contour of 1000 Toy MC sets generated at the best fit of the two-flavor analysis and randomly fluctuated Data's contour is roughly half of the sensitivity in terms of its extent in
the θ13
direction
(preliminary)
Contour Overlay at 90% C.L.
SK-I
SK-II
SK-I + SK-II 90% C.L.
SK-I
SK-II
Size of the SK-I + SK-II contour is dominated by the small size of SK-II However, SK-II has roughly half of the statistics of SK-I
Why is its θ13
contour so small?
Is the C.L. Cut value correct?Checking the critical values using the Feldman-Cousins (FC) method shows that the 90% C.L. Value of 4.6 is close to the FC value near and beyond the data's contour
SK-I + SK-II 90% c.l. (cut 4.6)
First Checks
Systematic Errors?Increasing systematic errors like background contamination in the high evergy e-like samples by a factor of two does not significantly expand the contour
Signal Sample: Multi-GeV e-like
In these bins the effect of non-zero θ13
is apparent and strong
However, the data lies consistently below the MC expectation, a disparity that is aggravated as θ
13 becomes larger
This provides a strong portion of the constraint SK-I does not show such disparities in this sample
MC @ Best Fit MC @ Best Fit + CHOOZData
Cosine Zenith Angle Cosine Zenith Angle
(preliminary)
Do these bins provide a real constraint? : Remove them and refit
sensitivity
SK-II 90% full data Set SK-II 90% with bins removed
Without these bins the size of the contour balloons out towards the expected sensitivity and the constraint on θ
13 is relaxed
(The best fit point is the same in both cases θ13
= 0)
In this case the SK-I contour would provide the dominant constraint on the SK-I+SK-II result
SK-I + SK-II: Inverted Hierarchy
99% C.L. 90% C.L.
This Fit∆m2 = 2.1 x 10-3 eV2
sin2 θ23
= 0.5
sin2 θ13
= 0.00
χ2 = 841 / 745
SK-I + SK-II
(preliminary)
Inverted Hierarchy: Chooz Limit
99% C.L. 90% C.L.
CHOOZ Exclusion
SK-II SK-I +SK-II
CHOOZ Exclusion
SK-I
All contours enter the Chooz exclusion region SK-II and SK-I+SK-II have smaller contours than the expected sensitivity
the reason is the same as in the normal hierarchy case
CHOOZ Exclusion
(preliminary)
Conclusions
Fits for SK-I, SK-II, and SK-I + SK-II performed SK-I Atmospheric variables are consistent with two-flavor analysis SK-II results are consistent with SK-I
Slightly larger/shifted Atmospheric variablesSmaller θ
13
Results from discrepancies between Data and MC in a few bins
SK-I + SK-II results
Atmospheric contours are consistent with other data sets and slightly improved over SK-I aloneθ
13 contour is smaller than either SK-I or SK-II alone
Inverted Hierarchy fits are similar
All fits are consistent with θ13
= 0
No preference in the data for either mass hierarchy
Measuring θ13
is a goal of the next generation oscillation experiments
The Future of θ13
ν's from reactors
T2KNOνA
Double Chooz Daya Bay
ν beamline experiments
Super-K Taking data as SK-IV Improvements to reconstruction algorithms and MC Gd in Super-K?
Improved measurement of θ
13...
Neutrino Oscillations Neutrino mass eigenstates , | ν
i ⟩ , under which they propagate, are
different than their eigenstates of the weak interaction, | να ⟩
For two flavors α and β, U is a rotation, parameterized by a `mixing angle`, θ
∣ ⟩=∑iU i
∗ ∣i ⟩
Probability of starting as a and being b after traveling L with energy E:
U= cos sin
− sin cos
P =sin2 2sin2 1.27m2LE [ eV
2 kmGeV ] m2
≡m22−m1
2
Non-zero ifU is not diagonal , ie θ ≠ 0m
i ≠ 0
mi ≠ m
j
Amplitude ~ sin2 2θ , Frequency ~ ∆ m2
Large range of L/E is useful ⇒ Atmospheric νLook for appearance of β or disappearance of α
SK-I: Normal Hierarchy
99% C.L. 90% C.L.
This Fit∆m2 = 2.2 x 10-3 eV2
sin2 θ23
= 0.52
sin2 θ13
= 0.01
χ2 = 429 / 397
SK-I
(preliminary)
SK-II: Normal Hierarchy
99% C.L. 90% C.L.
This Fit∆m2 = 2.6 x 10-3 eV2
sin2 θ23
= 0.5
sin2 θ13
= 0.00
χ2 = 413 / 347
SK-II
(preliminary)
SK-I + SK-II: Normal Hierarchy
99% C.L. 90% C.L.
∆m2 = 2.1 x 10-3 eV2
sin2 θ23
= 0.5
sin2 θ13
= 0.00
χ2 = 841 / 745
SK-I + SK-II
(preliminary)
Total s
νµ
Above ~2 GeV CC 1-π production and DIS are important CCQE still present
⇒ Look at high energy single-ring and multi-ring e-like events for signs of θ
13
What to look for?
Matter resonance
νe
CC Quasi-elasticCC Single πDeep InelasticNC Single πNC Elastic
θ
Detection With Cherenkov Radiation
cos=1n
Charged particles traveling faster than the speed of light in a medium emit Cherenkov radiation A cone of light is formed with opening
angle
photons
Light is projected onto the Super-K PMTs as a ring
(n is refractive index, β is the particle velocity)
θmax
= 42° in water
Charge and time information from the PMTs is used to reconstruct a vertex, direction and momentum of the particle
About Neutrinos
Neutral, Spin-1/2, lepton Undergo weak interactions
Only three light active neutrinos (LEP) One neutrino flavor for each charged
leptonDetermined by lepton accompanying reaction
νε , ν
µ , ν
τ
νl
p
l
CC reactions can occur if there is enough energy to produce l
Charged current quasi-elastic ( CCQE )
ν
l + n → p + l
νl + p → n + l+
Neutral current ( NC )
νx + n(p) → n(p) + ν
x
Charged current quasi-elastic ( CC1π )
ν
l + n → p +π+ l
Signal Sample: Multi-ring multi-GeV e-like
In this sample the data is generally in better agreementOnly one bin noticeably contributes to the SK-I contour
Cosine Zenith Angle Cosine Zenith Angle
MC @ Best Fit MC @ Best Fit + CHOOZData
99% C.L. 90% C.L.
SK-I + SK-II, SK-I syst + 2 σ, SK-II syst – 2 σ
Effect of Systematic Errors
SK-I + SK-II
Change systematic errors on the high-energy e-like samples two be twice their normal value and refit
Only a minor change
Fitting Scheme
Data and MC are binned SK-I (1489 days data and 100 yr. MC ) SK-II ( 804 days data and 60 yr. MC )
The MC is oscillated at each point on a grid in an oscillation space Data is then fit to the oscillated MC at each point
“Fit” is achieved when the χ2 is minimized The MC point returning the smallest χ2 is deemed the “best fit” point Contours are then drawn expressing the level of agreement between the
data and MC at all of the oscillation points relative the “best fit” point.
Fits to SK-I, SK-II and SK-I+SK-II Fits to MC for both hierarchies
Look for evidence of non-zero θ13
and the mass hierarchy by comparing
data with several oscillation models
Binning
Multi-ring multi-GeV e-like
Multi-GeV e-like
Sub-GeV e-like
Multi-ring multi-GeV µ-like
Multi-GeV µ-like
Sub-GeV µ-like
PC Stopping
PC Through-going
Upward Stopping µ
Upward Through-going µ
Lo
g P
SK-I 32 x 10 = 320 bins SK-II 27 x 10 = 270 bins
Binning is different due to differences in livetimes
= 10 Zenith angle bins
About the Contour Plots:
Contours are not a simple projection Contours are drawn around all points that satisfy
90 % C.L. : χ2( x, y, zmin
) ≤ χ2
min + 4.6
99 % C.L. : χ2( x, y, zmin
) ≤ χ2
min + 9.2
The third variable in each of the two-variable plots has been minimized at each (x,y) pair in the space
x
y
z y
x
Systematic Uncertainties
A Bin A Bin at + 1 σ ~ 10% more CCQE events
Systematics are taken to have a linear effect on the contents of the bins A given systematic may affect only a subset of a bin's events Example:
CCQE ν interaction cross-section 10%
% Change in red is f i
n
Coefficients are computed using the MCDuring fitting the MC expectation is adjusted by the error parameters, ε
PC Sample is composed of mostly νµ
Regions of excess and deficit presentConfined to a few binsMagnitude of the difference is smallLower bin populations
Similar effect in other µ-like samples
Relative excess θ13
=CHOOZ / θ13
= 0
PC Through-going
PC Through-going Bin Contents
Now looking at reconstructed binning
Evis
[ log GeV ]Evis
[ log GeV ]
Co
sin
e Z
enit
h A
ng
le
Co
sin
e Z
enit
h A
ng
le
Event Types at Super-K
Fully Contained Partially Contained Upward Stopping µ Upward Through-going µ
These categories are divided into e-like and m-like subsamples
10 event samples in total
Feldman-Cousins Critical values : 400 Toy MC
Generated at: sin2 θ13
= 0.092
Critical value is slightly lower than the usual cut at 4.6 Both methods exclude this point
2 D.o.F cut 90% C.L. ∆χ2 = 4.612 D.o.F cut 99% C.L. ∆χ2 = 9.2
Feldman-Cousins Map: Constrain to ∆m2 x sin2 θ13
plane
When restricted to the plane, the distribution of critical values is consistent with the usual 2 D.o.F cut on ∆χ2 . But its not clear that the prescription for this analysis' plots is truly 2
D.o.F
Testing Coverage with Feldman-Cousins
Objective is to determine whether or not the contours that have been drawn have proper coverage Currently the contours are drawn
using a cut on ∆χ2 for 2 D.o.F ∆χ2 = 4.61 at 90% C.L. ∆χ2 = 9.2 at 99% C.L.
Test with Feldman-Cousins MethodBut to save time, consider only a few representative points around the 90% C.L. drawn in the usual way
F.C. 90% Critical Value is computed using 400 Toy MC at each of 6 points (lines above)
Statistics are a little low, but saves computation timeFull F.C. method might entail 1000 Toy MC for each of the 80,000 points in the analysis
Feldman-Cousins Critical values : 400 Toy MC, minimized to plane
Generated at: sin2 θ13
=
0.07
Critical value is slightly higher than the usual cut at 4.6 Both methods include this point
2 D.o.F cut 90% C.L. ∆χ2 = 4.612 D.o.F cut 99% C.L. ∆χ2 = 9.2
Feldman-Cousins Critical values : 400 Toy MC, minimized to plane
Generated at: sin2 θ13
=
0.08
Critical value is slightly higher than the usual cut at 4.6 Both methods may exclude this point
even with Feldman-cousins, the size of the contour would only increase nominally
2 D.o.F cut 90% C.L. ∆χ2 = 4.612 D.o.F cut 99% C.L. ∆χ2 = 9.2
Feldman-Cousins Critical values : 400 Toy MC, minimized to plane
Generated at: sin2 θ13
=
0.10
Critical value is slightly higher than the usual cut at 4.6 Both methods exclude this point
2 D.o.F cut 90% C.L. ∆χ2 = 4.612 D.o.F cut 99% C.L. ∆χ2 = 9.2
Feldman-Cousins Critical values : 400 Toy MC, minimized to plane
Generated at: sin2 θ13
=
0.13
Critical value is the same as usual cut at Both methods exclude this point
2 D.o.F cut 90% C.L. ∆χ2 = 4.612 D.o.F cut 99% C.L. ∆χ2 = 9.2
Feldman-Cousins Map: Minimize to ∆m2 x sin2 θ13
plane
Feldman-Cousins critical values are near the usual 2 D.o.F cut at 4.6Size of the contour would not change appreciably even with a full F-C treatment
90% of 400 Toy MC generated at the Data's best fit point fall within 90% C.L of the sensitivity. ( 98.5% fall within its 99% C.L. )
Sensitivity 99% C.L.
Sensitivity 90% C.L.
SK-I + SK-II 90% c.l. (cut 4.6)
SK-I SK-II
Up / Down Ratio Single Ring E-like Events
Data
MC at Best FitMC at Best Fit w/ CHOOZ Limit
Looking for clues as to why SK-II θ13
contour is smaller than SK-I
SK-I SK-II
Up / Down Ratio Multi-Ring E-like Events
Data
MC at Best FitMC at Best Fit w/ CHOOZ Limit
99% C.L. 90% C.L.
SK-I + SK-II, SK-I syst + 2 σ, SK-II syst – 2 σ
Normal Bins : + Sensitivitites
SK-I + SK-II
Small effect seen in both χ2 methods