大気ニュートリノ
樋口 格
東京大学宇宙線研究所
＠ニュートリノ研究会

内容• 大気ニュートリノについて• SKにおける大気ニュートリノの結果
1. 2 flavor analysis (太陽効果を含む)
2. L/E analysis
3. τ appearance• Neutrino 2006 presentation
1. MINOS
2. SNO• summary大気ニュートリノp

天頂角 θDownward（L=10~100 km）
πDetectorμe

νμνμνeUpward（L= up to 13000 km）

大気に降り注ぐ宇宙線(主に陽子)が大気と衝突してニュートリノを生成する。
それを検出器で捕まえる

天頂角分布(Honda et al.)
700

200

600

175-2-1-1

Integrated neutrino flux (m sec sr )期待されるニュートリノフラックス30

νμ+νμνμ–ντ oscillation (best fit)
null oscillationMlti-GeV μ-like

251505002012540010015300752005010010νe+νe5250.3-0.5 GeV

0-100.9-1.5 GeV

10-103.0-5.0 GeV

10-101cosΘ
UpDown

大気ニュートリノの天頂角分布はエネルギーの高いところ(数GeV以上)で上下対称になることが期待される（ニュートリノ振動が無い場合）

Data set
• Super-K I+II(全データ)
SK-I (1489days) + SK-II (804days)• MINOS
418 live days (contained vertex events)
842 live days (ν induced μ events)• SNO
149 days exposure

Super-Kamiokande
1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

SK-Iaccident

SK-II reconstruction SK-III• 50kton cylindrical water
Cherenkov detector(22.5kt fiducial vol.)• 1000m underground(2700m water equiv.)

SK-I

SK-II

• optically separated into
ID and OD

PMT enclosure :Acrylic (front) andFiberglass (back)

11146

Num. of inner detector PMTs

5182

40 %

Photocathod coverage

19 %SK-III physics run will start in July 2006.

観測される大気ニュートリノ事象
各サンプルでのニュートリノエネルギー

イベントカテゴリー
1000

Fully Contained

750(contained vertex)

500

Partially Contained(Eν ~10GeV)
Stopping μ (Eν ~10GeV)
Through-going μ (Eν ~100GeV)(neutrino induced muon events)

FCμ-like

Events / 1000 days(Eν ~1GeV)FC νμFC νe
PC νμ250 e-like

PC0150

UpwardUp-Stop νμthrough-going
Up-Thru νμ μ

10050

Upwardstopping μ

0 -2-11010

11010Eν (GeV)

2103104105

SK-I + SK-II combined analysis(data binning)

Sub-GeV

Multi-GeV

PlepCC νe

CC νμUP throughshowering

FCFCFCFCPC
PC1ring mring 1ring mring stop thru
e-like e-like μ-like μ-likeUP throughnon-showering

UPstop38 event type andmomentum binsx10 zenith bins
Æ 380 binsSince various detector related systematic errors are different,
we do not combine the SK-I and SK-II bins.
380 bins for SK-I + 380 bins for SK-II Æ 760 bins in total

SK-I + SK-II combined analysis(systematic errors)
neutrino flux (14)neutrino interaction (12)solar activity (1)event selection
and reconstruction (21)

Identical for SK-I and SK-II

Regarded as independent
between SK-I and SK-II

The total number of systematic errors is :Flux (14) + Interaction (12) + SK-I (22) + SK-II (22) = 70

2 flavor analysis
Zenith Angle Distributions (SK-I + SK-II)
SK-I + SK-II
400

Sub-GeV e-likeP < 400 MeV/c400

Sub-GeV μ-likeP < 400 MeV/c200300

1502002001000-1
Number of Events

SK-I + SK-II300

100

400

00.5

1Sub-GeV e-likeP > 400 MeV/c

300

0-1600300

multi-ring e-like

-0.5

00.5

1

Sub-GeV μ-likeP > 400 MeV/c0-1-0.5

00.5

1300

20

10-1-0.5

00.5

1Multi-GeV μ-like

Multi-GeV e-like

0-120020015015015010010010050500-1-0.50cosΘ

0.5

10-100.5

1PC through

100

100
0.5-0.5200

20000-1eliminary40

400-0.5Pr

100

PC stop2000-1

multi-ring μ-like

200

50

100-0.5

νμ–ντ oscillation (best fit)
null oscillation SK-I + SK-II

-0.5

00.5

1

Upward stopping μ

50
-0.5

0cosΘ

0.5

10-1
600

-0.5

00.5

1

Upward through-going
non-showering μ150

400

100

20050

Upward through-goingshowering μ

0-1 -0.8 -0.6 -0.4 -0.2 00-1 -0.8 -0.6 -0.4 -0.2 00-1 -0.8 -0.6 -0.4 -0.2 0cosΘ

cosΘ

cosΘ

Result from SK-I + SK-II data
SK-I + SK-II

2015

χ2 - χ2minBest Fit: Δm2 = 2.5 x 10-3 eV2
sin2 2θ = 1.00
χ2 = 839.7 / 755 dof (18%)

1052Δm (eV )10SK-I + SK-II-2

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

02102102Δm(eV )SK-I+ SK-II-2

20

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

Pr0.8

0.92sin 2θe1liminary

1.9 x 10-3 eV2 < Δm2 < 3.1 x 10-3 eV2
sin2 2θ > 0.93

at 90% CLχ2 - χ2min

0.7

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

15-310-3

10500.8

0.9

SK-I : 1489 days
SK-II : 804 days

1sin22θ

1.1

1.2

太陽効果 νμ Æ νe Oscillation effects
O. L. G. Peres and A. Yu. Smirnov,
hep-ph/0309312

P2 : 2ν transition prob. νe Æ νμ , τin matter

P(νe Æ νe)driven by Δm212= 1 – P2P(νe Æ νμ) = P(νμ Æ νe) = cos2 θ23 P2P(νe Æ ντ) = P(ντ Æ νe) = sin2 θ23 P2

ν2c223 : s223
s212 :ν1νec212Δm212

νμ ντνe decrease rate by νe oscillation : 1 – P(νe Æ νe) = P2
νe increase rate by νμ oscillation : r P(νμ Æ νe)= r cos2 θ23 P2

r = Φ0(νμ) / Φ0(νe) ~ 2 (for low energy ν)

if cos2 θ23 = 0.5 (sin2 θ23 = 0.5) νe increase ~ νe decrease
if cos2 θ23 > 0.5 (sin2 θ23 < 0.5) νe increase > νe decrease
if cos2 θ23 < 0.5 (sin2 θ23 > 0.5) νe increase < νe decreaseSolar term effect to atmospheric
neutrinosDue to the LMA solution,
atmospheric neutrinos should
also oscillate by (θ12 , Δm212).

00.9cosΘνdriven by Δm2

0.8

-0.4
-0.6

0.4
0.3

-0.8

= 0.5

= 0.6

sin2 θ13 = 00.2

120.1
-1 -1
10

sin2 θ23 = 0.4

sin2 2θ12=0.83
0.7Δm212=8.3x10-3
0.6(eV2)
0.5-0.2

P2 : 2ν transition prob. νe Æ νμ , τin matter

101Eν (GeV)10

νe flux (osc.)νe flux (no osc.)

1010

Discrimination between θ23<π/4and >π/4 might be possible
by studying low energy
atmospheric νe and νμ events.

Result of sin2 θ23 determination (SKI+II combined)

20.96

102

χ -χ minχ2 – χ2min distribution as a functionof sin2 θ23 where the other oscillation
parameters are chosen to minimize χ2

90.99

1.00

0.99

0.96

sin2 2θ23

Solar terms off :The 1-2 parameters(Δm212 , sin2 θ12)
are fixed at zero.

87
65

best-fit : sin2 θ23 = 0.50

43

Pr

2
1
00.3

χ2sol from Solar-ν+KamLAND
results are added in each(Δm212 , sin2 θ12) point.

0.40.5w/o 1-2 parameters
w/ 1-2 parameters

0.6elimin
ary0.72sin θ23

Solar terms on :The 1-2 parameters
are scanned.
best-fit : sin2 θ23 = 0.52
(sin2 2θ23 = 0.9984)

L/E analysis
Survive probability

Neutrino oscillation :PμμΔm2L2
2= 1 – sin 2θsin (1.27)EPμμ = (cos2θ + sin2θ x exp(– m L ))22τ E
1L
Pμμ = 1 – 2 sin22θ x (1 – exp(–γ0 ))E

Neutrino decay :Prob.( νμνμ )Neutrino decoherence :1The first dip can be observed

0.80.6

neutrino decay, decoherence は否定する事ができる。

0.40.20110102103104L/E (km/GeV)Tests for neutrino decay & decoherence

Best fit parametersΔm2=2.3x10-3,sin22θ=1.00
χ2min=83.9/83 d.o.f(sin22θ=1.03, χ2min=83.4/83 d.o.f)

2.0x10-3 < Δm2 < 2.8x10-3 eV20.93 < sin22θ
at 90% C.L.

χ2osc = 83.9/83 d.o.f
Decayχ2dcy = 107.1/83 d.o.f, Δχ2 = 23.2(4.8σ)
Decoherence χ2dec = 112.5/83 d.o.f, Δχ2 = 27.6(5.3σ)
Oscillation

SK-I
3.4σ
3.8σ

ντ appearanceνμ Æ ντ 振動τ neutrino event selection criteria:(1) Fiducial Volume: 2m from the ID PMTs (FC events)(2) Visible Energy (Evis) > 1.33 GeV (Multi-GeV events)(3) Most energetic ring is electron-like. (Showering events)
Approximately 90% of the backgrounds are rejected.

Likelihood or Neural Network analysis
These two statistical methods are employed independently.

ντ appearance
SK-I

Likelihood analysis:- Total τ excess: 138 ± 48(stat.) + (+14.8/-31.6)(sys.) ( 2.4 sigma)- Expected τ excess: 78.4 ± 26(sys.)
Neural Net analysis:- Total τ excess: 134± 48(stat.) + (+16.0/-27.2)(sys.) (2.4sigma)- Expected τ excess: 78.4 ± 27(sys.)

MINOS&SNO@Neutrino 2006

MINOSClasses of atmospheric ν events

Contained Vertex Analysis(0.9,1.3×10-3)

107 data events compared with 127±13 expected for no oscillations
Event direction measured by timing
77 events with a well measured direction, 49 downward going, 28 upward going
Rdataup/down /RMCup/down = 0.62 +0.19-0.14 (stat.) ±0.02(sys.)
An extended maximum likelihood analysis with Feldman-Cousins style error analysis yields theabove allowed regions

Neutrino induced μ Analysis
Upward going μ are produced by νinteractions in the surrounding rockμ direction determined by timing
Single hit timing resolution 2.3 ns
131 upward going μ selected

Soudan overburden is flat
Horizontal cosmic ray μ have totraverse a large column of rock andare absorbed.
Cut at a zenith angle of 0.05
10 extra neutrino induced μ not
selected by the timing cut

Combined Charge Analysis• Divide data into three categories
1. 1 < Pμ < 10 GeV/c (low)
2. 10 < Pμ < 150 GeV/c (high)
3. Poorly measure momentum
and charge sign (mostly highmomentum )Oscillation analysis•

Oscillation fit to the momentum
separated zenith angle distribution• Five systematic errors included
as nuisance parameters in the fit
Reconstruction
Cross sections• Oscillation analysis, best fit point
Δm2=7.9×10-4 eV2
sin22θ=1.0
χ2/ndf=5.7/7• No oscillations excluded at the87% confidence level

Charge Separated Analysis••Both νμ and νμ show a deficit
with respect to the prediction
Ratio consistent with 1.0 but
with a large uncertainty

SNO
1000t D2O

2094 m under groundSNO Atmospheric νz SNO is a very deep experimentz Cosmic μ are absorbed a longway above the horizontalz Neutrino induced μ from thesurrounding rock are visible well
above the horizonz See the transition region where
the oscillation dip is maximalz Data from the first 149 days
exposure is availablez Remaining data is still in ablinded analysis

summary• 全ての大気ニュートリノデータで２世代振動(νμ Æ ντ)に矛盾がない。
• SK:@90C.L.
1.9 × 10-3 eV2 < Δm2 < 3.1 × 10-3 eV2
sin22θ > 0.93
• 太陽効果(νμ Æ νe 振動) の有意な結果は見えていない。