Upload
others
View
3
Download
0
Embed Size (px)
Citation preview
Three Flavor Oscillations of Atmospheric Neutrinos in Super Kamiokande
Roger Wendell 20080409
Virginia Tech.
Outline
Super – Kamiokande Neutrino Oscillations Signatures of θ
13
Oscillation Fitting Results
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 neutrino oscillation experimentswhich 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
SuperKamiokande
Phases of SuperKamiokandeOn November 12th 2001 a PMT imploded creating a shock wave that destroyed thousands of PMTs
The run period prior to July 2001 is termed SKI (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 topped with an acrylic windowThe OD was completely rebuilt
Data taken from 2003 – 2005 in this configuration is known as SKII (804 days)
...fully reconstructed and taking data since June 2006!
The ν news at SuperK
θ
Detection With Cherenkov Radiation
cos=1n
Charged particles traveling faster than the speed of light in a medium emit light, known as Cherenkov radiation
electromagnetic analogue of a sonic boom A cone of light is formed with opening angle
photons
Light is projected onto the SuperK 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, Spin1/2, lepton Undergo weak interactions
Only three light active neutrinos (LEP) One neutrino flavor for each charged lepton
Determined by lepton accompanying reactionν
ε , ν
µ , ν
τ
νl
p
l
CC reactions can occur if there is enough energy to produce l
Charged current quasielastic ( CCQE )
ν
l + n p + l
νl + p n + l+
Neutral current ( NC )
νx + n(p) n(p) + ν
x
Charged current quasielastic ( CC1π )
ν
l + n p +π+ l
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
elikeelike µlike
Electrons have low mass and multiply scatter and may produce e+e pairsCollection of Cherenkov light produces a diffuse ring pattern elike
Muons are more massive and pass relatively undeflected Produce Cherenkov rings with well defined edges µlike
Neutrino Oscillations
Neutrino Oscillations
Neutrino mass eigenstates ,νi , 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 α and being β after traveling L with energy E:
U= cos sin− sin cos
P =sin2 2sin2 1.27m2 LE [ eV 2 km
GeV ] m2≡m22 − m1
2
Nonzero ifU is not diagonal , ie θ m
i
mi m
j
Amplitude ~ sin2 2θ , Frequency ~ ∆ m2
Large range of L/E is useful Atmospheric ν
Look for appearance of β or disappearance of α
High Energy Atmospheric Neutrinos at SuperK
Deficit seen in µlike events coming from below the detector (long baselines ) Elike event rate is consistent with expectation
Cosine Zenith Angle Cosine Zenith Angle
disappearance
Energy [ GeV ]
Cosi
ne Z
enith
Ang
le
νµ ∄
ντ
Long Pathlengths
Short Pathlengths
data well described by dominant twoflavor νµ ν
τ oscillations with maximal mixing
Twoflavor Result: sin22θ = 1.0 , ∆m2 = 2.5 x 103 eV2
Two Flavor Oscillations at SuperK
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 : ∆m212
, ∆m231
1 cp violating phase: δcp
If all of these angles are nonzero it becomes possible to measure CPviolation in
leptons...
Atmospheric Solar
Each piece of the mixing matrix (MNS matrix) is a rotation 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
Solar :
∆m2
127.6 x 105 eV2 [ 7.3 , 8.1 ] x 105 eV2 KamLAND, SNO, SuperK
sin2 θ12
0.32 [ 0.23, 0.37 ] Atmospheric :
| ∆m231
| 2.4 x 103 eV2 [ 2.1 , 2.7 ] x 103 eV2 K2K, SuperK, Minos
sin2 θ23
0.50 [ 0.38, 0.63 ] Other :
sin2 θ13
0.007 [ 0.00, 0.033] CHOOZ δ
cp ???
Parameter BestFit 2 σ C.L. Contributing Experiments
Normal Hierarchy
∆m2sol
∆m2atm
mν
ν3
ν2
ν1
Inverted Hierarchy
ν3
ν2
ν1
∆m2atm
∆m2sol
OR ?
Searching for θ13
Look for the appearance of νe against the main disappearance of ν
µ
Matter Effects Neutrinos traveling through matter are subject to additional scattering amplitudes:
Z0 exchange flavor blind, no net effect
WExchangeOnly ν
e
Effective potential added to the hamiltonian
Alters νe ν
α oscillations....
neutrino
antineutrino
Matter Effects (2)
neutrinoantineutrino ( ∆m2 > 0 )
Density [g/cm3]si
n2 2θ M
P e = sin2 2M sin2 1.27M2 LE
Resonance depends on sign of ∆m2 and whether neutrino or antineutrino There exists a resonance region for a set of oscillation parameters for 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
antineutrino
ThreeFlavors and Matter Effect in the Earth
PREM ModelHere
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 in constant density evolution is solvable Same resonant features are present
Under the normal hierarchy: ν's and not ν's Under the inverted hierarchy: ν's and not ν's Magnitude of the effect is regulated by θ
13
Use these properties to look for nonzero θ13
and test the hierarchy
sin2θ13
= 0
sin2θ13
= 0 sin2θ
13 = 0.01
sin2θ
13 = 0.03
Energy [ GeV ]
Cosi
ne Z
enith
Ang
le
Radius [ km ]
Dens
it y [g
/cm
3 ]
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 ] Energy [ GeV ]
Cosi
ne Z
enith
Ang
le
Cosi
ne Z
enith
Ang
le
Consider the excess of events after threeflavor oscillations relative to twoflavorsAlternating bands of excess and deficits in the ν
µ's
Resonance region clearly visible in νe's
Look for high energy elike events in the SuperK data Detector resolution effects have not been considered so far....
Energy [ GeV ]Energy [ GeV ] Energy [ GeV ]
After Incorporating the ν FluxesCo
sine
Zen
ith A
ngle
Cosi
ne Z
enith
Ang
le
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
Main signal For the inverted hierarchy there is only an 8% excess in the resonance Muon event samples have a much lower effect 4% in just a few bins
Evis
[ log GeV ]Evis
[ log GeV ]
Cosi
ne Z
enith
Ang
le
Cosi
ne Z
enith
Ang
le
Relative excess θ13
=CHOOZ / θ13
= 0 MultiRing elike
MultiRing elike Bin Contents
Total σ
νµ
Above ~2 GeV CC 1π production and DIS are important CCQE still present
Look at high energy singlering and multiring elike events for signs of θ13
What to look for?
Matter resonance
νe
CC QuasielasticCC Single πDeep InelasticNC Single πNC Elastic
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
construct a multiGeV multiring elike data sample using a likelihood method:SKI 75% pure, SKII 73% pure
Oscillation Fitting
Analysis Structure
Oscillation Space Over 3 oscillation parametersSolar oscillations are neglected 5% effect on the main resonance Fits to SKI, SKII and SKI+SKII Fits to MC for both hierarchies
sin2θ13
sin2θ23
∆m2Systematic Uncertainties
66 sources of uncertainty, 26 common between SKI and SKII ν flux uncertainties (13) ν interaction uncertainties (13) Event reduction uncertainties (7 SKI + 7 SKII ) Event reconstruction uncertainties (13 SKI + 13 SKII )
Look for evidence of nonzero 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 differentiating
Fast fitting methodEquivalent to fitting using a covariance method
sin2θ13
sin2θ23
∆m2 ∆m2
sin2θ13
sin2θ13
sin2θ23
sin2θ23
∆m2
Drawing Contours from a 3dimensional χ2 surface
Easier to visualize in twodimensionsso “project” χ2 surface onto each 2variable planeminimize over the 3rd variable
Results : Normal Hierarchy
SKI Contours: 320 Bins 99% C.L. 90% C.L.
Atmospheric variables fit in the same place as twoflavor result Extent of atmospheric contours is consistent
∆m2 = 2.5 x 103 eV2
sin2 θ23
= 0.5
sin2 θ13
= 0.00
χ2 = 317.4 / 318 dof
This FitSKI Normal
∆m2
sin2θ23sin2θ23sin2θ13
sin2 θ 13
∆m2
(Preliminary)
∆m2 = 2.8 x 103 eV2
sin2 θ23
= 0.5
sin2 θ13
= 0.00
χ2 = 289.6 / 268 dof
This FitSKII Normal
SKII Contours: 270 Bins
Range of ∆m2 is larger than SKI ∆m2 best fit point is higher than SKI Extent of θ
13 contour slightly smaller than SKI
99% C.L. 90% C.L.∆m
2
sin2θ23sin2θ23sin2θ13
sin2 θ 13
∆m2
(Preliminary)
∆m2 = 2.6 x 103 eV2
sin2 θ23
= 0.5
sin2 θ13
= 0.00
χ2 = 602.7 / 587 dof
This FitSKI+SKII Normal
SKI+SKII Contours: 320 Bins SKI 270 Bins SKII
Common to SKI alone Range of ∆m2 and ∆m2 best fit point are consistent
Extent of θ13
contour smaller than SKI alone
99% C.L. 90% C.L.∆m
2
sin2θ23sin2θ23sin2θ13
sin2 θ 13
∆m2
(Preliminary)
SKI+SKII SKI+SKII
CHOOZ Exclusion
SKI + SKII : Sensitivity and CHOOZ
Combined θ13
contour is smaller than sensitivity 90% C.L . is right on the border of the CHOOZ limit
99% C.L. 90% C.L.
Sensitivity Data
(Preliminary) (Preliminary)
500 Toy MC generated at the best fit point Larger Contours and Smaller Contours in the Toy MC Extent same as data in 98 / 500
Data has a larger extent than ~20% of the toy MC
Toy MC SKI + SKII : Extent of θ13
Contour ( 320 Bins )
0.2
Data
20%
Sensitivity
SKI + SKII result is consistent with statistical fluctuations
57%
sin2θ13
SKII
SKI
So why is the θ13
contour so small ?
SKI and SKII allowed regions do not overlap completely
SKI
SKII
SKI + SKII 90%
90% C.L. cut ~ 4.6
Results : Inverted Hierarchy
Similar to Normal Hierarchy case though θ13
contour is not as strongly constrained
∆m2 = 2.6 x 103 eV2
sin2 θ23
= 0.5
sin2 θ13
= 0.00
χ2 = 602.7 / 587 dof
This FitSKI Inverted
SKI+SKII Contours: 320 Bins SKI 270 Bins SKII Inverted Hierarchy 99% C.L. 90% C.L.
∆m2
sin2θ23sin2θ23sin2θ13
sin2 θ 13
∆m2
(Preliminary)
Conclusions
Fits for SKI, SKII, and SKI + SKII performed SKI Atmospheric variables are consistent with previous twoflavor analyses SKII results are consistent with SKI
Slightly larger/shifted Atmospheric variablesSlightly smaller θ
13
SKI + SKII results
Atmospheric contours are consistent with other data sets and slightly improved over SKI aloneθ
13 contour is smaller than either SKI or SKII alone
and smaller than the CHOOZ limitToy MC studies indicate that the contour is 20% likely and the smallness is consistent with statistical fluctuations Inverted Hierarchy fits are similar
All fits are consistent with θ13
= 0No preference in the data for either mass hierarchy
Measuring θ13
is the goal of the next generation of ν oscillation experiments
The Future of θ13
ν's from reactors
T2KNOνA
T2KNOνA
Double CHOOZ Daya Bay
ν beamline experiments
SuperK Taking data as SKIII Improvements to reconstruction algorithms and MC Gd in SuperK?
Improved measurement of θ13
!!
Supplements
Fitting Scheme
Data and MC are binned SKI (1489 days data and 100 yr. MC ) SKII ( 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 SKI, SKII and SKI+SKII Fits to MC for both hierarchies
Look for evidence of nonzero θ13
and the mass hierarchy by comparing data with several oscillation models
Gadolinium Studies The SuperKamiokande collaboration is considering adding 0.2% gadolinium trichloride to the experiment
~100% of n captures occur on Gd at this concentration
Currently investigating tag antineutrino events? benefits/detriments Gd brings to other physics topics
Muon Gd Gammas
l+
Gd γ
γγ
υ
n
p
Rings are MC Truth
Gadolinium Studies: Good Stuff
neutron distance from Vertex (m) Time [µs]
main event window
Gd Captures
Gd capture events are well separated in space and time from the main event vertex distinguish from decay electrons
Characteristic 8 MeV Gamma cascade, can possibly be handled by low energy reconstruction tools
94% that start in F.V. stop in F .V.
SK 2km
Gadolinium Studies: Good Stuff (2)
Light from Gd captures is isotropic
Gd Capture Gammas Electrons
Possible to distinguish Gd events from other low energy light sources
Gadolinium Studies: Difficult Stuff
Tagged by Gd (31%) Tagged by Gd (44%)
Background neutrino events at T2K's 2km detector
Because of high energies, even neutrino events can create neutrons
Large number of neutrons, well separated in time may cause overlaps
Additional studies are underway...
Contours generally larger Best fit is the same as normal hierarchy
∆m2 = 2.5 x 103 eV2
sin2 θ23
= 0.5
sin2 θ13
= 0.00
χ2 = 317.2 / 318 dof
This FitSKI Inverted
SKI Contours: 320 Bins SKI Inverted Hierarchy
sin2θ13sin2θ23sin2θ13
99% C.L. 90% C.L.∆m
2
sin2 θ 23
∆m2
Slightly larger contours than Normal Hierarchy∆m2 = 2.8 x 103 eV2
sin2 θ23
= 0.5
sin2 θ13
= 0.00
χ2 = 289.6 / 268 dof
This FitSKI Inverted
SKII Contours: 270 Bins SKII Inverted Hierarchy
sin2θ13sin2θ23sin2θ13
99% C.L. 90% C.L.∆m
2
sin2 θ 23
∆m2
Binning
Multiring multiGeV elike
MultiGeV elike
SubGeV elike
Multiring multiGeV µlike
MultiGeV µlike
SubGeV µlike
PC Stopping
PC Throughgoing
Upward Stopping µ
Upward Throughgoing µ
Log
P
SKI 32 x 10 = 320 bins SKII 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
) χ2min
+ 4.6
99 % C.L. : χ2( x, y, zmin
) χ2min
+ 9.2 The third variable in each of the twovariable 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 crosssection 10%
% Change in red is f in
Coefficients are computed using the MCDuring fitting the MC expectation is adjusted by the error parameters, ε
MultiGeV Multiring Elike Sample
Select and enrich a MultiGeV Multiring elike sample using a likelihood method Probability density functions are built from 4 variables If MultiRing, FC, Most Energetic ring elike, and likelihood selection (w/oscillations):
SKI ~75 % pure signal SKII ~73 % pure signal
Background Signal: CC νe
Event Types at SuperK
Fully Contained Partially Contained Upward Stopping µ Upward Throughgoing µ
These categories are divided into elike and µlike subsamples
10 event samples in total
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 µlike samples
Relative excess θ13
=CHOOZ / θ13
= 0 PC Throughgoing
PC Throughgoing Bin Contents
Now looking at reconstructed binning
Evis
[ log GeV ]Evis
[ log GeV ]
Cosi
ne Z
enith
Ang
le
Cosi
ne Z
enith
Ang
le
Total σ
CC Single π CC Quasielastic
Deep Inelastic Scattering
νµ
Above ~2 GeV CC 1π production and DIS become important CCQE still present
Look at high energy singlering and multiring elike events for signs of θ13
What to look for?
Matter resonance
νe
CC QuasielasticCC Single πDeep InelasticNC Single πNC Elastic
SKI SKII
Up / Down Ratio Single Ring Elike Events
N.B. the scale is different between the plots
DataMC at Best FitMC at Best Fit w/ CHOOZ Limit
Looking for clues as to why SKI +SKII θ13
contour is smaller than SKI
SKI SKII
Up / Down Ratio Multi Ring Elike Events
N.B. the scale is different between the plots
DataMC at Best FitMC at Best Fit w/ CHOOZ Limit
The excess in the SKII bins does not seem statistically significant May explain small improvement seen with SKII over SKI
SKI Best Fit Distribution
DataOsc. MCUnOsc. MC
SubGeV elike low SubGeV elike high SubGeV µlike low SubGeV µlike high
MultiGeV elike MultiGeV µlike MultiRing µlike MultiRing elike
Up Through µ Up Stop µ PC Stop PC Through