Studies of Neutrino Oscillations withand without Mass using Super-K

Wei Wang, Boston University
Neutrino Workshop, Kashiwa, Feb 20, 2007

Preaching Buddhism to Buddha
Teaching Grandmas
to Suck Eggs●●

Ban-Men Nong-Fu

Syaka ni Seppou
Feb 20, 2007

Massive and Massless Neutrino Osc

2

An Era of Discovery in Neutrino Physics



 


cos sin  m=
The Standard “Blame”
 −sin  cos  m

a

b

2

2
2 m L P    =1−sin 2sin
4E
Feb 20, 2007



Massive and Massless Neutrino Osc

3

Outline

Atmospheric neutrinos, Super-K experiment and eventsStandard νμ-ντ oscillation analysis using zenith distributions



Sterile neutrino as a alternative to tau neutrino





➔

νμ-ντ mixing vs νμ-νs mixing➔

An admixture analysis

Neutrino oscillations induced by the violations of Lorentz(LIV) invariance and CPT (CPTV) symmetry➔

Fit LIV and CPTV induced oscillation against Super-K data➔

Allowed limits of LIV and CPTV

Summary and conclusions

Feb 20, 2007

Massive and Massless Neutrino Osc

4Atmospheric Neutrinos●

A large uncertainty on the absolute flux●

Good knowledge on flavor ratio●

Up-down symmetricWell predicted ratio
Up-down symmetryAbs flux: ~20% uncertainty

Feb 20, 2007

Massive and Massless Neutrino Osc

5Super-Kamiokande Collaboration●

140 collaborators from 35 institutes of 5 countries

Feb 20, 2007

Massive and Massless Neutrino Osc

6

Super-Kamiokande Experiment●

A 50 kt water Cherenkov detector
Inner detector and outer detector opticallyseparated➔ ID: 25in PMTs; gaps filled by black sheet➔ OD: 8in PMTs with wavelength shifters,
wall covered by reflective Tyvek➔●

Operating periods
SK-I: 1996 – 2001
✔ 1489 days livetime✔ ~40% ID coveragethis➔ SK-II: 2003 – 2005
analysis✔ 804 days livetime✔ Half ID tubes (acrylic&FRP)~20% coverage➔ SK-III: since Summer 2006
✔ ID tubes (acrylic&FRP)
fully recovered➔

Feb 20, 2007

Massive and Massless Neutrino Osc

7

Super-K Neutrino Events●●

Neutrino interaction→ charged particles→ Cherenkov radiation→ recorded by PMTs
Neutrino event categories–

Fully contained–

Partially contained
μ-like ring–Feb 20, 2007

e-like ring

Upward going μMassive and Massless Neutrino Osc

8Event Reconstruction●●●●

Vertex finding
Ring recognition
PID (e-/μ-like)

FC Single Ring Events

Momentum reconstruction
Sub-GeVCCνe: 88.0%

CCνμ: 94.5%

Multi-GeVCCνe: 82.6%

Feb 20, 2007

Massive and Massless Neutrino Osc

CCνμ: 99.4%

9

Number of events

Five Decades of EnergyEν(GeV)Feb 20, 2007

Fully
Contained

~1GeV

FC
Multi-Ring~3GeV

PC STOP

~5GeV

PC
THRU

~10GeVUPμSTOP~10GeVUPμTHRU~100GeVUPμSHOWER~1TeV

Massive and Massless Neutrino Osc

10Four Decades of Pathlengths

Long baseline experiments

Large ranges of L and E➔

Various matter densities➔⇒ great advantages forstudying exotic phenomena
Feb 20, 2007

Massive and Massless Neutrino Osc

11

Atmospheric Neutrino Observations
SubGeV e-like

MultiGeV e-like

Multiring MultiGeV
CC e-likeobservation

Number of Events

Null oscillation
prediction

SubGeV μ-like

MultiGeV μ-like

Multiring μ-like

PC Stopping

PC through-going

Up stopping μNonshowering μ

Showering μcosθFeb 20, 2007

Massive and Massless Neutrino Osc

12

Data Analysis: Binning
2

FC
1ring
e-likeFCm-ringe-likeCC νμFC
FC1ring mringμ-like μ-like

PC
stop





PC
thru

Showering μ
Non-Showering μ

Multi-GeV

logPleporlogEvisCC νe2
2 m LP    =1−sin 2 sin
4E

Sub-GeVUp stopping μ

e-like events forflux normalization

Feb 20, 2007

μ-like events foroscillation signal

In total, for SK-I and SK-II,
2×38 energy bins
×10 zenith bins = 760 bins

Massive and Massless Neutrino Osc

13

Data Analysis: Pull Method
obs

N

M

2

j
2
exp
obs
obs
 =∑ 2 N i − N i −N i ln exp  ∑  
Nii=1
j =1  j
Ni

Data bins: likelihood ratio Systematic uncertainties: Gaussian{

Predicted events
based on ν flux

N

exp0
i

N

exp
i

nosc

=P survival model x with parameters x  N i
M=1 ∑ f i  j  N i
j =1

j

exp0

Expected number of events
without considering systematics
Expected number of events

Plug in different models and find the minimum chi-squares
1. Minimize wrt systemic terms➢ Solving a linear equation set
2. Minimize wrt model parameters➢ searching on a grid in parameter space)Feb 20, 2007

Massive and Massless Neutrino Osc

14

Combining SK-I and SK-II
Data bins are considered as independent observations●

Systematic uncertainties●

Atm neutrino flux (14)Identical for SK-I and SK-II➔

Neutrino interaction (12)Solar activity (1)Independent for SK-I and SK-II➔➔

Data selection andevent reconstruction (21)In total, 70 systematic uncertainties in SK-I and SK-II combined analysis

Feb 20, 2007

Massive and Massless Neutrino Osc

15

Zenith Distributions of νμ-ντ Oscillation
SubGeV e-like

MultiGeV e-like

Multiring MultiGeV
CC e-likeobservation
null oscillation

Number of Events

νμ-ντ

SubGeV μ-like

MultiGeV μ-like

Multiring μ-like

PC Stopping

PC through-going

Up stopping μNonshowering μ

Showering μcosθFeb 20, 2007

Massive and Massless Neutrino Osc

16

Standard Mixing Parameters  
68% C.L.
90% C.L.
99% C.L.

Feb 20, 2007

Massive and Massless Neutrino Osc2

sin 2 =12
−32
 m =2.5×10 eV
2 / dof =839.7/ 755
p−value=18 %17Must It Be Tau Neutrino?

●●

LEP experiments:
Z decay cross section
indicates there are only
three neutrino flavors:Nν=2.992±0.020

If only three flavors of neutrinos, it must be tau neutrino➢➢

νμ-νe oscillation does not explain the Super-K observation
Chooz and Palo Verde experiments⇒ NO 
e  
 x oscillation at the scale of Δm2~10-3eV2

Feb 20, 2007

Massive and Massless Neutrino Osc

18

Sterile Neutrinos Are Possible●

Sterile neutrino (νs: no electric, strong or weak charge) is not
charged under Standard Model → a potential candidate of
atmospheric neutrino oscillation➢

Some theoretical models do predict the existence of sterile neutrinos

e.g. right-handed neutrino to explain neutrino mass
➢ Some observation are in favor of the existence of sterile neutrinos
✔

✔

✔

➔

Sterile neutrino helps to solve the LSND anomaly
Sterile neutrino helps to solve the nuclear synthesis problem during thesupernova R-process

Compare νμ-ντ oscillation and νμ-νs oscillation

Feb 20, 2007

Massive and Massless Neutrino Osc

19

Signatures of Sterile Neutrinos
Based on the definition of sterile neutrino:νs: no interaction

Difference between νμ-ντ oscillation and νμ-νs oscillation:
1. Inside the detector: less neutral current events
2. During the propagation: Matter EffectFeb 20, 2007

Massive and Massless Neutrino Osc

20

1. NC Events at Super-K●●●

Multi-ring events: neutral pions are the NC signature at SK
Brightest ring e-like: to remove CC νμ events
Evis>400MeV: low energy events do not point well

Feb 20, 2007

400MeV<Evis<1330MeV

Evis>1330MeV

CCνμ: 18%CCνμ: 31%

NC: 37%

NC: 24%Massive and Massless Neutrino Osc

21

2. Matter Effect●If two neutrino flavors interact differently in matter
2
M

m L
P osc =sin 2  M sin
4E
2

●

2

{

2

sin 2 2

sin 2  M =

2

2

2

2 E  V /  m −cos 2  sin 2  m M = m  2 E  V / m −cos 2  sin 2 22νμ-νs: νμ and νs interact with matter differently⇒ matter effect ⇒ oscillation is suppressed

2

2

2

n
 V =∓  2 G F
2Survival probability of νμ crossing Earth: Δm2=2.5x10-3eV2, sin22θ=1

νμ-νs

1

0.5

0
Feb 20, 2007

Massive and Massless Neutrino Osc

Survival Probability

νμ-ντ

22

Tau Neutrino vs Sterile Neutrino  
2

sin 2 =0.9952−32 m =2.5×10 eV
2 / dof =971.2/853
p−value=7.3 %68% C.L.
90% C.L.
99% C.L.

  s2

sin 2 =12
−32
 m =3.5×10 eV
2 / dof =1023.6/853
p−value=0.6 %68% C.L.
90% C.L.
99% C.L.

P-values calculated using toy MC method.
●Feb 20, 2007

Exclusion Level: 7.2σ
Massive and Massless Neutrino Osc

23

Comparison of Zenith Distributions
NC SubGeV

χ2 Breakdown

NC MultiGeV

χ (Standard)χ2 (Sterile)
Difference2

Number of Events

SubGeV e-like

MultiGeV e-like

Multiring MultiGeV
CC e-like

Data bins
952.9
990.7
37.8

Systematics
18.3
32.9
14.6

observation
null oscillation

νμ-ντ
νμ-νs
SubGeV μ-like

MultiGeV μ-like

Multiring μ-like

PC Stopping

PC through-going

Up stopping μNonshowering μ

Showering μcosθFeb 20, 2007

Massive and Massless Neutrino Osc24

Δχ2 Contribution Breakdown
Single Ring SubGeV e-like

0.8

Single Ring MultiGeV e-like-2.1

Multi-Ring MultiGeV CC e-like

0.8

Single Ring SubGeV μ-like-1.3

Single Ring MultiGeV μ-like-2

Multi-Ring μ-like

3.8

NC-Enhanced SubGeV

5

NC-Enhanced MultiGeV

1.2

PC Stopping μ

2.9

PC Through-Going μ

12.3

Upward Stopping μ

7.2

Upward NonShowering μ

11.2

Upward Showering μ

-1.5

TOTAL

37.8

Feb 20, 2007

∆χ2=14.
6●

The right energies andbaselines of those events givethe strongest matter effects

Massive and Massless Neutrino Osc

25

An Admixture Case●

Admixtures are model dependent●

This analysis is base on Fogli et al PRD 63(053008), 2001–

A 2+2 mass hierarchy model–

Constructing two superposition states of νs and ντ → two flavor mixing
ATM
LSND

Sterile Neutrino Portion

Solar

 

 

1
cos sin  =
2 −sin  cos sFeb 20, 2007

Massive and Massless Neutrino Osc

26

Admixture Allowance

68% C.L.
90% C.L.
99% C.L.

Feb 20, 2007

Massive and Massless Neutrino Osc

Allowed sterile
neutrino admixture
limit at 90% C.L.:
sin2ξ< 23%●

27

Why Violations of Lorentz and CPT?
→ The other side of the story: neutrino oscillation without mass●●

Recall: mass eigenstate mixing→ E i = pcm2i /2 p → neutrino oscillation
Violations of Lorentz invariance and CPT symmetry→ modified dispersion relation→ different energies for the same momentum→ neutrino oscillation→ Important fundamental symmetries: are they broken at some highenergy level? (predicted by some Quantum Gravity theories)●✔

Feb 20, 2007

Not practical to reach ~MP yet→ Seek for small effects at low energy→ Neutrino oscillation (interferometry) provides a promising groundSK neutrino energy and pathlength coverage has great advantages forthis study

Massive and Massless Neutrino Osc

28

Minimal Standard Model Extension●

Minimal Standard Model Extension, Kostelecky et al,
hep-ph/0403088
i– L mSME = 2 c AB   L A  D L B  D L A  L B −a AB  L A  L B










– The first term only violates Lorentz invariance (LIV);
the second term violates both CPT (CPTV) and Lorentz invariance●Two rotationally invariant cases of LIV and CPTV
(only time components are considered)–

Coleman and Glashow, PRD 59(116008), 1999●–

Barger et al, PRL 85(5055), 2000●

Feb 20, 2007

LIV-induced oscillation
CPTV-induced oscillation

Massive and Massless Neutrino Osc

29

Oscillations Induced by LIV and CPTV●

Rotationally invariant cases: keeping only temporalcomponents
–

0 0
0
0


Hint=−c00

L

∂
L
∂
L

LB 
AB
A
B
A
●

●

The eigenstates by diagonalizing (rotating by θv) cAB
are defined as “maximum attainable velocity” eigenstates
Modified dispersion relation: E i = p c− p c i22⇒ P osc=sin 2 v sin c
–

TT

TT

L E, c ≡c A −c B0
Hint=a00
L

LB
AB A

2

2

⇒ P osc=sin 2 a sin ± a L,  a≡a A−a B●

Feb 20, 2007

Neutrino oscillation does depend on energy

Massive and Massless Neutrino Osc

30

Lorentz Invariance Violation22

Try a more general form: P    =1−sin 2 v sin  L / E●

LxE oscillation isstrongly disfavored–●

68% C.L.
90% C.L.
99% C.L.



L/E is within the 1stσ–●Excluded at ~14σ

1.16+0.14/-0.21

A natural question:
what is the scale
LIV might appear?

LxE
Feb 20, 2007

Massive and Massless Neutrino Osc

31

LIV as a Sub-Dominant Effect●Considering LIV as a sub-dominant effect●

Assuming best-fit parameter values for the standard oscillation●P   =1−sin2 2 sin2 


{



●

2

1 E / E c  sin 2 v
tan 2 =
 E / E c 2 cos 2 v

=1.27   m 2 L / E 2 ±4 c TT sin 2 v L E4 c TT L E 2
E c=

Feb 20, 2007

m
2c

2

●

TT

Massive and Massless Neutrino Osc

cTT: the difference of
maximum attainablevelocities
θv: mixing angle
between two different
maximal attainablevelocity eigenstates“+/-”: the 0/π phasedifference between themass mixing matrix
and the maximum
attainable velocity
mixing matrix
32Limits on LIV
=0●

Δφ=0: cTT<1.2x10-24 at 90% C.L.
–●

sin2θv=-0.12; cTT=0.05x10-23Δφ=π: cTT<1.3x10-24 at 90% C.L.
–Feb 20, 2007

68% C.L.
90% C.L.
99% C.L.

68% C.L.
90% C.L.
99% C.L.

sin2θv=-0.02; cTT=0.06x10-23

●

=

Limits from other experiments–

Cosmic ray spectrum:~10-15(γ), ~10-23(p)–Nuclear magnetic resonancefrequencies:~10-21(e), ~10-30(n)Massive and Massless Neutrino Osc

33

An ad hoc CPT Violation Test●

Simple assumption: neutrinos
and antineutrinos could havedifferent mass squared
splittings222

P    /    =1−sin 2 sin


●

●







2



 m / m L
4E

Question: is this allowed bySK?



68% C.L.
90% C.L.
99% C.L.

Best-fit:{sin 2 =1
 m2 =3.7×10−3 eV 2
2
−3
2
m
 =1.5×10 eVSuper-K best-fit is far away from the LSND scale→ then, what is the limit on CPTV?
Feb 20, 2007

Massive and Massless Neutrino Osc

34

Limit on CPT Violation●●0−a AB L A  LB ⇒  aL oscillation


●

2

2
2 m
± a  L
As a sub-dominant effect ⇒ P   =1−sin 2  sin 
4EAssuming maximal mixing for the mass eigenstates
68% C.L.
90% C.L.
99% C.L.

• At 90% C.L.: Δa< 1.05x10-23 GeV• Limits from other experiments
Barger et al, PRL 85(5055), 2000–

g-2: ~10-23 GeV

 : ~0.44×10– K −K0

Feb 20, 2007

Massive and Massless Neutrino Osc

0

−18

GeV

35

Summary and Conclusions●●●

Neutrino oscillations can happen with or without massνμ-ντ oscillation is compared with 2 kinds of alternatives:
massive neutrino oscillation and massless neutrino oscillation–

Mass-induced νμ-νs oscillation: excluded at 7.2σ–

Oscillations induced by two isotropic cases of LIV and CPTV are notable to explain Super-K atmospheric observation

Atmospheric neutrino data provide valuable constraints on thescales of new physics beyond the Standard Model–

An admixture 23% of νs is allowed at 90% C.L. (2+2 mass hierarchy)–

LIV and CPTV limits are set by considering them as sub-dominant
effects:

Feb 20, 2007●

cTT~10-24 at 90% C.L.

●

Δa~10-23 GeV at 90% C.L.
Massive and Massless Neutrino Osc

36

Line Average Approximation
Earth Density Profile

Oscillation in uniform matter• A well-defined phase

expression• A well-defined amplitude
expression
Line Average

1. Integrate the density
along the path
2. Take the averageFeb 20, 2007

Massive and Massless Neutrino Osc

37

Matter Effect Reconsidered
2
M

m L
P osc =sin 2  M sin
4E
2

2

{

2

sin 2 2

sin 2  M =

2

2

2

2 E  V /  m −cos 2  sin 2  m M = m  2 E  V / m −cos 2  sin 2 
2

2

2

2

2

Osc Prob using Line Average Density
Exact Zone

Good approximationfor oscillation cycles
2➔ Δm
L/4E > 2π ?
M
●

–

YES:
osc prob = sin22θM/2–

NO:
propagate thru Earth→ exact osc prob

Average Zone

Feb 20, 2007

Massive and Massless Neutrino Osc

38

Tau Event Searching●

Expected: 79±28(sys)●Found:–

Likelihood:
145±48(stat)+15/-38(sys)–

Neural Network:
152±47(stat)+17/-29(sys)

No tau events assumption is
disfavored by ~2.4σ

Feb 20, 2007

Massive and Massless Neutrino Osc

39

Testing MaVaN•Neutrinos gain mass only in highdensity matter (not in air or vacuum) m2  m2•Best Fit:

 

0

–χ2MaVaN = 194.4/178 d.o.f(sin22θ, Δm2) = (1.00, 2.19x10-3 eV2)

–χ2Standard = 174.97/178 d.o.f(sin22θ, Δm2) = (1.00, 2.11x10-3 eV2)

•Excluded at 4.4σ level

 

2
2 
Under study:  m  m
0

Feb 20, 2007

nStandard 2-flavor oscillations
MaVaN oscillations

Massive and Massless Neutrino Osc

40