Kern- und Teilchenphysik SS2012KT2012 Johannes Blümer IKP in KCETA Oszillationsmuster 7 13....

IKP in KCETAKT2012 Johannes BlümerKIT – Universität des Landes Baden-Württemberg undnationales Forschungszentrum in der Helmholtz-Gemeinschaft

KIT-Centrum Elementarteilchen- und Astroteilchenphysik KCETA

www.kit.eduKIT – Universität des Landes Baden-Württemberg undnationales Forschungszentrum in der Helmholtz-Gemeinschaft

KIT-Centrum Elementarteilchen- und Astroteilchenphysik KCETA

www.kit.edu

Kern- und Teilchenphysik SS2012

Johannes BlümerVorlesung-Website

1

http://www.auger.de/~rulrich/lehre/kerneteilchen2012/index.html%23vorlesung

http://www.auger.de/~rulrich/lehre/kerneteilchen2012/index.html%23vorlesung

Schwache Wechselwirkung...Neutrinoquellen im UniversumNeutrino-Oszillationen

solare...Reaktor...atmosphärische...Beschreibung

absolute NeutrinomasseDirac- oder Majorana-Masse?Betazerfall0vßß-Zerfallandere Methoden

Von W- und Z-Bosonen zum Standardmodell

IKP in KCETAKT2012 Johannes Blümer

v20 3. Juli 2012 Neutrino-Oszillationen und -Masse

2

Erinnerung an v19

heute

KT2012 Johannes Blümer IKP in KCETA

Neutrinoquellen

3

Kernreaktoren

Beschleuniger

Luftschauer

Erdkruste

Sonne

Supernovae

kosmische Beschleuniger

Urknall

✔

✔

✔

gerade so ✔

✔

✔ 1987a

? noch nicht

✔indirekt

[Georg Raffelt]


Das Solare Neutrino-Problem und die Lösung

4

SonnenSonnen--Neutrinos: Neutrinos: expexp. Raten & SSM. Raten & SSM

Theorie: Experimenterelat. Fehler


Neutrino-Oszillationen

5

Quelle Nachweis

EnergienFlüsseArten

NachweiseffizienzEnergieauflösung

L = 10 m … 10.000 km

µ Propagation der Massenzustände

≈µ_≈

Oszillationen

bei der Quelle mussbekannt sein:

Flavourzustand Flavourzustand

Emission Nachweis

_

_

_

ν-Oszillationen

QM-Betrachtung von v-Oszillationen: Boris Kayser, hep-ph/0104147, 16 Apr2001

[Drexlin]


Neutrino-Mischungsmatrix

6

1. & 2. Generation|| 22

21

212 mmm


22

223 mmm e

1

2


321

213 mmm

leptonische Mischungsmatrix:Pontecorvo-Maki-Nakagawa-Sakata

U = unitäre 3 × 3 Mischungsmatrix

3

2

1

321

321

321

UUUUUUUUU

µµµ

eee

µ

e


Oszillationsmuster

7

13. Neutrino mixing 9

Eν in MeV

Pee

= 1 - sin22θ sin2 (∆m2L/4Eν)

baseline = 180 KmP

ee

0 5 10 150.0

0.2

0.4

0.6

0.8

1.0

Figure 13.1: The νe (ν̄e) survival probability P (νe → νe) = P (ν̄e → ν̄e),Eq. (13.30), as a function of the neutrino energy for L = 180 km, ∆m2 =7.0 × 10−5 eV2 and sin2 2θ = 0.84 (from Ref. 62).

CPT invariance implies: A(l′l)CP = −A

(ll′)CP , A

(l′l)T = P (ν̄l′ → ν̄l) − P (ν̄l → ν̄l′) = A

(l′l)CP . It

follows further directly from Eq. (13.13) and Eq. (13.14) that

A(l′l)CP = 4

∑

j>k

Im(

Ul′j U∗lj Ulk U∗

l′k

)

sin∆m2

jk

2pL , l, l′ = e, µ, τ . (13.17)

Eq. (13.2) and Eq. (13.13) - Eq. (13.14) imply that P (νl → νl′) and P (ν̄l → ν̄l′) donot depend on the Majorana CP violation phases in the neutrino mixing matrix U [40].Thus, the experiments investigating the νl → νl′ and ν̄l → ν̄l′ oscillations, l, l′ = e, µ, τ ,cannot provide information on the nature - Dirac or Majorana, of massive neutrinos.The same conclusions hold also when the νl → νl′ and ν̄l → ν̄l′ oscillations take place inmatter [54]. In the case of νl ↔ νl′ and ν̄l ↔ ν̄l′ oscillations in vacuum, only the Diracphase(s) in U can cause CP violating effects leading to P (νl → νl′) %= P (ν̄l → ν̄l′), l %= l′.

In the case of 3-neutrino mixing all different Im(Ul′jU∗ljUlkU∗

l′k) %= 0, l′ %= l = e, µ, τ ,j %= k = 1, 2, 3, coincide up to a sign as a consequence of the unitarity of U . Thereforeone has [55]:

A(µe)CP = −A

(τe)CP = A

(τµ)CP =

4 JCP

(

sin∆m2

32

2pL + sin

∆m221

2pL + sin

∆m213

2pL

)

, (13.18)

whereJCP = Im

(

Uµ3 U∗e3 Ue2 U∗

µ2

)

, (13.19)

June 18, 2012 16:19

[RPP]

KT2012 Johannes Blümer IKP in KCETA8

40 13. Neutrino mixing

Cl 95%

Ga 95%

νµ↔ν

τ

νe↔ν

X

100

10–3

∆m

2 [

eV2]

10–12

10–9

10–6

102 100 10–2 10–4

tan2θ

CHOOZ

Bugey

CHORUS NOMAD

CHORUS

KA

RM

EN

2

νe↔ν

τ

NOMAD

νe↔ν

µ

CDHSW

NOMAD

KamLAND95%

SNO 95%

Super-K 95%

all solar 95%

http://hitoshi.berkeley.edu/neutrino

SuperK 90/99%

All limits are at 90%CL

unless otherwise noted

LSND 90/99%

MiniBooNE

K2KMINOS

Figure 13.9: The regions of squared-mass splitting and mixing angle favored orexcluded by various experiments based on two-flavor neutrino oscillation analyses.The figure was contributed by H. Murayama (University of California, Berkeley, andIPMU, University of Tokyo). References to the data used in the figure can be foundat http://hitoshi.berkeley.edu/neutrino.

June 18, 2012 16:19

40 13. Neutrino mixing

Cl 95%

Ga 95%

νµ↔ν

τ

νe↔ν

X

100

10–3

∆m

2 [

eV2]

10–12

10–9

10–6

102 100 10–2 10–4

tan2θ

CHOOZ

Bugey

CHORUS NOMAD

CHORUS

KA

RM

EN

2

νe↔ν

τ

NOMAD

νe↔ν

µ

CDHSW

NOMAD

KamLAND95%

SNO 95%

Super-K 95%

all solar 95%

http://hitoshi.berkeley.edu/neutrino

SuperK 90/99%

All limits are at 90%CL

unless otherwise noted

LSND 90/99%

MiniBooNE

K2KMINOS

Figure 13.9: The regions of squared-mass splitting and mixing angle favored orexcluded by various experiments based on two-flavor neutrino oscillation analyses.The figure was contributed by H. Murayama (University of California, Berkeley, andIPMU, University of Tokyo). References to the data used in the figure can be foundat http://hitoshi.berkeley.edu/neutrino.

June 18, 2012 16:19


P (νµ(e) → νe(µ)) ∼= 2 |Uµ3|2 |Ue3|2(

1 − cos∆m2

31

2pL

)

=|Uµ3|2

1 − |Ue3|2P 2ν

(

|Ue3|2, m231

)

, (13.23)

Table 13.1: Sensitivity of different oscillation experiments.

Source Type of ν E[MeV] L[km] min(∆m2)[eV2]

Reactor νe ∼ 1 1 ∼ 10−3

Reactor νe ∼ 1 100 ∼ 10−5

Accelerator νµ, νµ ∼ 103 1 ∼ 1Accelerator νµ, νµ ∼ 103 1000 ∼ 10−3

Atmospheric ν’s νµ,e, νµ,e ∼ 103 104 ∼ 10−4

Sun νe ∼ 1 1.5 × 108 ∼ 10−11

and P (ν̄µ(e) → ν̄e(µ)) = P (νµ(e) → νe(µ)). Here P 2ν(

|Ue3|2, m231

)

is the probability of

the 2-neutrino transition νe → (s23νµ + c23ντ ) due to ∆m231 and a mixing with angle θ13,

where

sin2 θ13 = |Ue3|2, s223 ≡ sin2 θ23 =

|Uµ3|2

1 − |Ue3|2,

c223 ≡ cos2 θ23 =|Uτ3|2

1 − |Ue3|2. (13.24)

Eq. (13.22) describes with a relatively high precision the oscillations of reactor ν̄e on adistance L ∼ 1 km in the case of 3-neutrino mixing. It was used in the analysis of thedata of the Chooz [58], Double Chooz [59], Daya Bay [26] and RENO [27] experiments.Eq. (13.20) with n = 3 and l = l′ = µ describes with a relatively good precision the effectsof oscillations of the accelerator νµ, seen in the K2K [19] and MINOS [20,21] experiments.The νµ → ντ oscillations, which the OPERA experiment [60,61] is aiming to detect,can be described by Eq. (13.20) with n = 3 and l = µ, l′ = τ . Finally, the probabilityEq. (13.23) describes with a good precision the νµ → νe and ν̄µ → ν̄e oscillations underthe conditions of the K2K experiment.

In certain cases the dimensions of the neutrino source, ∆L, are not negligible incomparison with the oscillation length. Similarly, when analyzing neutrino oscillationdata one has to include the energy resolution of the detector, ∆E, etc. in the analysis.As can be shown [39], if 2π∆L/Lv

jk & 1, and/or 2π(L/Lvjk)(∆E/E) & 1, the oscillating

terms in the neutrino oscillation probabilities will be strongly suppressed. In this case (aswell as in the case of sufficiently large separation of the νj and νk wave packets at the

June 18, 2012 16:19

[RPP]


KamLand

9

KAMioka Liquid scintillator Anti-Neutrino Detector

arX

iv:0

801.

4589

v3 [

hep-

ex]

25 Ju

n 20

08

Precision Measurement of Neutrino Oscillation Parameters with KamLAND

S. Abe,1 T. Ebihara,1 S. Enomoto,1 K. Furuno,1 Y. Gando,1 K. Ichimura,1 H. Ikeda,1 K. Inoue,1 Y. Kibe,1 Y. Kishimoto,1M. Koga,1 A. Kozlov,1 Y. Minekawa,1 T. Mitsui,1 K. Nakajima,1, ∗ K. Nakajima,1 K. Nakamura,1 M. Nakamura,1

K. Owada,1 I. Shimizu,1 Y. Shimizu,1 J. Shirai,1 F. Suekane,1 A. Suzuki,1 Y. Takemoto,1 K. Tamae,1 A. Terashima,1H. Watanabe,1 E. Yonezawa,1 S. Yoshida,1 J. Busenitz,2 T. Classen,2 C. Grant,2 G. Keefer,2 D.S. Leonard,2

D. McKee,2 A. Piepke,2 M.P. Decowski,3 J.A. Detwiler,3 S.J. Freedman,3 B.K. Fujikawa,3 F. Gray,3, † E. Guardincerri,3L. Hsu,3, ‡ R. Kadel,3 C. Lendvai,3 K.-B. Luk,3 H. Murayama,3 T. O’Donnell,3 H.M. Steiner,3 L.A. Winslow,3

D.A. Dwyer,4 C. Jillings,4, § C. Mauger,4 R.D. McKeown,4 P. Vogel,4 C. Zhang,4 B.E. Berger,5 C.E. Lane,6J. Maricic,6 T. Miletic,6 M. Batygov,7 J.G. Learned,7 S. Matsuno,7 S. Pakvasa,7 J. Foster,8 G.A. Horton-Smith,8

A. Tang,8 S. Dazeley,9, ¶ K.E. Downum,10 G. Gratta,10 K. Tolich,10 W. Bugg,11 Y. Efremenko,11 Y. Kamyshkov,11

O. Perevozchikov,11 H.J. Karwowski,12 D.M. Markoff,12 W. Tornow,12 K.M. Heeger,13 F. Piquemal,14 and J.-S. Ricol14

(The KamLAND Collaboration)1Research Center for Neutrino Science, Tohoku University, Sendai 980-8578, Japan

2Department of Physics and Astronomy, University of Alabama, Tuscaloosa, Alabama 35487, USA3Physics Department, University of California, Berkeley and

Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA4W. K. Kellogg Radiation Laboratory, California Institute of Technology, Pasadena, California 91125, USA

5Department of Physics, Colorado State University, Fort Collins, Colorado 80523, USA6Physics Department, Drexel University, Philadelphia, Pennsylvania 19104, USA

7Department of Physics and Astronomy, University of Hawaii at Manoa, Honolulu, Hawaii 96822, USA8Department of Physics, Kansas State University, Manhattan, Kansas 66506, USA

9Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803, USA10Physics Department, Stanford University, Stanford, California 94305, USA

11Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA12Triangle Universities Nuclear Laboratory, Durham, North Carolina 27708, USA and

Physics Departments at Duke University, North Carolina Central University, and the University of North Carolina at Chapel Hill13Department of Physics, University of Wisconsin, Madison, Wisconsin 53706, USA

14CEN Bordeaux-Gradignan, IN2P3-CNRS and University Bordeaux I, F-33175 Gradignan Cedex, France(Dated: June 25, 2008)

The KamLAND experiment has determined a precise value for the neutrino oscillation parameter ∆m221 and

stringent constraints on θ12. The exposure to nuclear reactor anti-neutrinos is increased almost fourfold over pre-vious results to 2.44×1032 proton-yr due to longer livetime and an enlarged fiducial volume. An undistorted re-actor νe energy spectrum is now rejected at >5σ. Analysis of the reactor spectrum above the inverse beta decayenergy treshold, and including geo-neutrinos, gives a best-fit at ∆m2

21 = 7.58+0.14−0.13(stat)+0.15

−0.15(syst)×10−5 eV2

and tan2 θ12 = 0.56+0.10−0.07(stat)+0.10

−0.06(syst). Local ∆χ2-minima at higher and lower ∆m221 are disfavored at

>4σ. Combining with solar neutrino data, we obtain ∆m221 = 7.59+0.21

−0.21 × 10−5 eV2 and tan2 θ12 = 0.47+0.06−0.05 .

PACS numbers: 14.60.Pq, 26.65.+t, 28.50.Hw, 91.35.-x

Experiments studying atmospheric, solar, reactor and ac-celerator neutrinos provide compelling evidence for neutrinomass and oscillation. The Kamioka Liquid scintillator Anti-Neutrino Detector (KamLAND) investigates neutrino oscil-lation parameters by observing electron anti-neutrinos (νe)emitted from distant nuclear reactors. Previously, KamLANDannounced the first evidence of νe disappearance [1], fol-lowed by direct evidence for neutrino oscillation by observingdistortion of the reactor νe energy spectrum [2]. More re-cently, KamLAND showed the first indication of geologicallyproduced anti-neutrinos (geo-neutrinos) from radioactive de-cay in the Earth [3], possibly a unique tool for geology.

This Letter presents a precise measurement of ∆m221 and

new constraints on θ12 based on data collected from March9, 2002 to May 12, 2007, including data used earlier [1, 2].We have enlarged the fiducial volume radius from 5.5 m to

6 m and collected significantly more data; the total exposureis 2.44×1032 proton-yr (2881 ton-yr). We have expanded theanalysis to the full reactor νe energy spectrum and reducedthe systematic uncertainties in the number of target protonsand the background. We now observe almost two completeoscillation cycles in the νe spectrum and extract more precisevalues of the oscillation parameters.

KamLAND is at the site of the former Kamiokande experi-ment at a depth of ∼2700 m water equivalent. The heart of thedetector is 1 kton of highly purified liquid scintillator (LS) en-closed in an EVOH/nylon balloon suspended in purified min-eral oil. The LS consists of 80% dodecane, 20% pseudoc-umene and 1.36± 0.03 g/l of PPO [4]. The anti-neutrino de-tector is inside an 18-m-diameter stainless steel sphere. Anarray of 1879 50-cm-diameter photomultiplier tubes (PMTs)is mounted on the inner surface of the sphere. 554 of these are

2

TABLE I: Estimated systematic uncertainties relevant for the neu-trino oscillation parameters∆m2

21 and θ12.

Detector-related (%) Reactor-related (%)∆m2

21 Energy scale 1.9 νe-spectra [7] 0.6

Event rate

Fiducial volume 1.8 νe-spectra 2.4Energy threshold 1.5 Reactor power 2.1Efficiency 0.6 Fuel composition 1.0Cross section 0.2 Long-lived nuclei 0.3

reused from the Kamiokande experiment, while the remain-ing 1325 are a faster version masked to 17 inches. A 3.2-ktoncylindrical water-Cherenkov outer detector (OD), surroundingthe containment sphere, provides shielding and operates as anactive cosmic-ray veto detector.Electron anti-neutrinos are detected via inverse β-decay,

νe +p → e++n, with a 1.8MeV threshold. The prompt scin-tillation light from the e+ gives a measure of the νe energy,Eνe

" Ep + En + 0.8MeV, where Ep is the prompt eventenergy including the positron kinetic and annihilation energy,and En is the average neutron recoil energy, O(10 keV). Themean neutron capture time is 207.5± 2.8µs. More than 99%capture on free protons, producing a 2.2MeV γ ray.KamLAND is surrounded by 55 Japanese nuclear power

reactor units, each an isotropic νe source. The reactor oper-ation records, including thermal power generation, fuel bur-nup, and exchange and enrichment logs, are provided bya consortium of Japanese electric power companies. Thisinformation, combined with publicly available world re-actor data, is used to calculate the instantaneous fissionrates using a reactor model [5]. Only four isotopes con-tribute significantly to the νe spectra; the ratios of the fis-sion yields averaged over the entire data taking period are:235U : 238U : 239Pu : 241Pu= 0.570:0.078: 0.295: 0.057. Theemitted νe energy spectrum is calculated using the νe spectrainferred from Ref. [6], while the spectral uncertainty is eval-uated from Ref. [7]. We also include contributions from thelong-lived fission daughters 90Sr, 106Ru, and 144Ce [8].We recently commissioned an “off-axis” calibration sys-

tem capable of positioning radioactive sources away from thecentral vertical axis of the detector. The measurements in-dicate that the vertex reconstruction systematic deviations areradius- and zenith-angle-dependent, but smaller than 3 cm andindependent of azimuthal angle. The fiducial volume (FV) isknown to 1.6% uncertainty up to 5.5m using the off-axis cal-ibration system. The position distribution of the β-decays ofmuon-induced 12B/12N confirms this with 4.0% uncertaintyby comparing the number of events inside 5.5m to the num-ber produced in the full LS volume. The 12B/12N event ratiois used to establish the uncertainty between 5.5m and 6m,resulting in a combined 6-m-radius FV uncertainty of 1.8%.Off-axis calibration measurements and numerous central-

axis deployments of 60Co, 68Ge, 203Hg, 65Zn, 241Am9Be,137Cs and 210Po13C radioactive sources established the event

reconstruction performance. The vertex reconstruction res-olution is ∼12 cm/

√

E(MeV) and the energy resolution is6.5%/

√

E(MeV). The scintillator response is corrected forthe non-linear effects from quenching and Cherenkov lightproduction. The systematic variation of the energy recon-struction over the data-set give an absolute energy-scale un-certainty of 1.4%; the distortion of the energy scale resultsin a 1.9% uncertainty on ∆m2

21, while the uncertainty at theanalysis threshold gives a 1.5% uncertainty on the event rate.Table I summarizes the systematic uncertainties. The totaluncertainty on ∆m2

21 is 2.0%, while the uncertainty on theexpected event rate, which primarily affects θ12, is 4.1%.For the analysis we require 0.9MeV< Ep < 8.5MeV. The

delayed energy, Ed, must satisfy 1.8MeV< Ed < 2.6MeVor 4.0MeV< Ed < 5.8MeV, corresponding to the neutron-capture γ energies for p and 12C, respectively. The timedifference (∆T ) and distance (∆R) between the promptevent and delayed neutron capture are selected to be 0.5µs<∆T < 1000µs and∆R < 2m. The prompt and delayed radialdistance from the detector center (Rp, Rd) must be <6m.Accidental coincidences increase near the balloon surface

(R= 6.5m), reducing the signal-to-background ratio. Weuse constraints on event characteristics to suppress acciden-tal backgrounds while maintaining high efficiency. We con-struct a probability density function (PDF) for accidental co-incidence events, facc(Ep, Ed, ∆R, ∆T, Rp, Rd), by pairingevents in a 10-ms-to-20-s delayed-coincidence window. APDF for the νe signal, fνe

(Ep, Ed, ∆R, ∆T, Rp, Rd), is con-structed from a Monte Carlo simulation of the prompt anddelayed events using the measured neutron capture time anddetector response. For the Ep distribution in fνe

, we choosean oscillation-free reactor spectrum including a contributionfrom geo-neutrinos estimated from Ref. [9]. A discriminatorvalue, L = fνe

fνe+facc

, is calculated for each candidate pairthat passes the earlier cuts. We establish a selection valueLcut

i in Ep bins of 0.1MeV, where Lcuti is the value of L at

which the figure-of-merit, Si√Si+Bi

is maximal. Si is the num-ber of Monte Carlo signal events in the ith energy bin withL > Lcut

i . Bi is calculated similarly using the accidentalcoincidence event pairs. The choice of the Ep distribution infνe

affects only the discrimination power of the procedure;substituting the oscillation-free reactor spectrum by an oscil-lated spectrum with the parameters from Ref. [2] changes ouroscillation parameter results by less than 0.2σ. The selectionefficiency ε(Ep) is estimated from the fraction of selected co-incidence events relative to the total generated in R< 6m inthe simulation, see Fig. 1(top).The dominant background is caused by 13C(α,n)16O reac-

tions from α-decay of 210Po, a daughter of 222Rn introducedinto the LS during construction. We estimate that there are(5.56± 0.22)× 109 210Po α-decays. The 13C(α,n)16O re-action results in neutrons with energies up to 7.3MeV, butmost of the scintillation energy spectrum is quenched be-low 2.7MeV. In addition, 12C(n,n′)12C∗, and the 1st and 2ndexcited states of 16O produce signals in coincidence with

2

TABLE I: Estimated systematic uncertainties relevant for the neu-trino oscillation parameters∆m2

21 and θ12.

Detector-related (%) Reactor-related (%)∆m2

21 Energy scale 1.9 νe-spectra [7] 0.6

Event rate

Fiducial volume 1.8 νe-spectra 2.4Energy threshold 1.5 Reactor power 2.1Efficiency 0.6 Fuel composition 1.0Cross section 0.2 Long-lived nuclei 0.3

reused from the Kamiokande experiment, while the remain-ing 1325 are a faster version masked to 17 inches. A 3.2-ktoncylindrical water-Cherenkov outer detector (OD), surroundingthe containment sphere, provides shielding and operates as anactive cosmic-ray veto detector.Electron anti-neutrinos are detected via inverse β-decay,

νe +p → e++n, with a 1.8MeV threshold. The prompt scin-tillation light from the e+ gives a measure of the νe energy,Eνe

" Ep + En + 0.8MeV, where Ep is the prompt eventenergy including the positron kinetic and annihilation energy,and En is the average neutron recoil energy, O(10 keV). Themean neutron capture time is 207.5± 2.8µs. More than 99%capture on free protons, producing a 2.2MeV γ ray.KamLAND is surrounded by 55 Japanese nuclear power

reactor units, each an isotropic νe source. The reactor oper-ation records, including thermal power generation, fuel bur-nup, and exchange and enrichment logs, are provided bya consortium of Japanese electric power companies. Thisinformation, combined with publicly available world re-actor data, is used to calculate the instantaneous fissionrates using a reactor model [5]. Only four isotopes con-tribute significantly to the νe spectra; the ratios of the fis-sion yields averaged over the entire data taking period are:235U : 238U : 239Pu : 241Pu= 0.570:0.078: 0.295: 0.057. Theemitted νe energy spectrum is calculated using the νe spectrainferred from Ref. [6], while the spectral uncertainty is eval-uated from Ref. [7]. We also include contributions from thelong-lived fission daughters 90Sr, 106Ru, and 144Ce [8].We recently commissioned an “off-axis” calibration sys-

tem capable of positioning radioactive sources away from thecentral vertical axis of the detector. The measurements in-dicate that the vertex reconstruction systematic deviations areradius- and zenith-angle-dependent, but smaller than 3 cm andindependent of azimuthal angle. The fiducial volume (FV) isknown to 1.6% uncertainty up to 5.5m using the off-axis cal-ibration system. The position distribution of the β-decays ofmuon-induced 12B/12N confirms this with 4.0% uncertaintyby comparing the number of events inside 5.5m to the num-ber produced in the full LS volume. The 12B/12N event ratiois used to establish the uncertainty between 5.5m and 6m,resulting in a combined 6-m-radius FV uncertainty of 1.8%.Off-axis calibration measurements and numerous central-

axis deployments of 60Co, 68Ge, 203Hg, 65Zn, 241Am9Be,137Cs and 210Po13C radioactive sources established the event

reconstruction performance. The vertex reconstruction res-olution is ∼12 cm/

√

E(MeV) and the energy resolution is6.5%/

√

E(MeV). The scintillator response is corrected forthe non-linear effects from quenching and Cherenkov lightproduction. The systematic variation of the energy recon-struction over the data-set give an absolute energy-scale un-certainty of 1.4%; the distortion of the energy scale resultsin a 1.9% uncertainty on ∆m2

21, while the uncertainty at theanalysis threshold gives a 1.5% uncertainty on the event rate.Table I summarizes the systematic uncertainties. The totaluncertainty on ∆m2

21 is 2.0%, while the uncertainty on theexpected event rate, which primarily affects θ12, is 4.1%.For the analysis we require 0.9MeV< Ep < 8.5MeV. The

delayed energy, Ed, must satisfy 1.8MeV< Ed < 2.6MeVor 4.0MeV< Ed < 5.8MeV, corresponding to the neutron-capture γ energies for p and 12C, respectively. The timedifference (∆T ) and distance (∆R) between the promptevent and delayed neutron capture are selected to be 0.5µs<∆T < 1000µs and∆R < 2m. The prompt and delayed radialdistance from the detector center (Rp, Rd) must be <6m.Accidental coincidences increase near the balloon surface

(R= 6.5m), reducing the signal-to-background ratio. Weuse constraints on event characteristics to suppress acciden-tal backgrounds while maintaining high efficiency. We con-struct a probability density function (PDF) for accidental co-incidence events, facc(Ep, Ed, ∆R, ∆T, Rp, Rd), by pairingevents in a 10-ms-to-20-s delayed-coincidence window. APDF for the νe signal, fνe

(Ep, Ed, ∆R, ∆T, Rp, Rd), is con-structed from a Monte Carlo simulation of the prompt anddelayed events using the measured neutron capture time anddetector response. For the Ep distribution in fνe

, we choosean oscillation-free reactor spectrum including a contributionfrom geo-neutrinos estimated from Ref. [9]. A discriminatorvalue, L = fνe

fνe+facc

, is calculated for each candidate pairthat passes the earlier cuts. We establish a selection valueLcut

i in Ep bins of 0.1MeV, where Lcuti is the value of L at

which the figure-of-merit, Si√Si+Bi

is maximal. Si is the num-ber of Monte Carlo signal events in the ith energy bin withL > Lcut

i . Bi is calculated similarly using the accidentalcoincidence event pairs. The choice of the Ep distribution infνe

affects only the discrimination power of the procedure;substituting the oscillation-free reactor spectrum by an oscil-lated spectrum with the parameters from Ref. [2] changes ouroscillation parameter results by less than 0.2σ. The selectionefficiency ε(Ep) is estimated from the fraction of selected co-incidence events relative to the total generated in R< 6m inthe simulation, see Fig. 1(top).The dominant background is caused by 13C(α,n)16O reac-

tions from α-decay of 210Po, a daughter of 222Rn introducedinto the LS during construction. We estimate that there are(5.56± 0.22)× 109 210Po α-decays. The 13C(α,n)16O re-action results in neutrons with energies up to 7.3MeV, butmost of the scintillation energy spectrum is quenched be-low 2.7MeV. In addition, 12C(n,n′)12C∗, and the 1st and 2ndexcited states of 16O produce signals in coincidence with

[Kamland web]

Pee = 1� sin22✓sin2(�m2 L

E)


Kamland Daten: ve-Verschwinden

10

Ratio of the background and geo-neutrino subtracted anti-neutrino spectrum to the expectation for no-oscillation as a function of L/E. L is the effective baseline taken as a flux-weighted average (L=180km). The histogram and curve show the expectation accounting for the distances to the individual reactors, time-dependent flux variations and efficiencies. The figure shows the behavior expected from neutrino oscillation, where the electron anti-neutrino survival probability is:

Phys. Rev. Lett. 100, 221803 (2008)

Erinnerung an die zu erwartenden Energiespektren von Neutrinos aus Spaltreaktionen...


E)



10

3

TABLE II: Estimated backgrounds after selection efficiencies.

Background ContributionAccidentals 80.5± 0.19Li/8He 13.6± 1.0Fast neutron & Atmospheric ν <9.013C(α,n)16Ogs, np → np 157.2± 17.313C(α,n)16Ogs, 12C(n,n′)12C∗ (4.4 MeV γ) 6.1± 0.713C(α,n)16O 1st exc. state (6.05 MeV e+e−) 15.2± 3.513C(α,n)16O 2nd exc. state (6.13 MeV γ) 3.5± 0.2Total 276.1± 23.5

the scattered neutron but the cross sections are not knownprecisely. A 210Po13C source was employed to study the13C(α,n)16O reaction and tune a simulation using the crosssections from Ref. [10, 11]. We find that the cross sections forthe excited 16O states from Ref. [10] agree with the 210Po13Cdata after scaling the 1st excited state by 0.6; the 2nd excitedstate requires no scaling. For the ground-state we use the crosssection from Ref. [11] and scale by 1.05. Including the 210Podecay-rate, we assign an uncertainty of 11% for the ground-state and 20% for the excited states. Accounting for ε(Ep),there should be 182.0± 21.7 13C(α,n)16O events in the data.

To mitigate background arising from the cosmogenic betadelayed-neutron emitters 9Li and 8He, we apply a 2 s vetowithin a 3-m-radius cylinder around well-identified muontracks passing through the LS. For muons that either deposita large amount of energy or cannot be tracked, we apply a 2 sveto of the full detector. We estimate that 13.6± 1.0 eventsfrom 9Li/8He decays remain by fitting the time distribution ofidentified 9Li/8He since the prior muons. Spallation-producedneutrons are suppressed with a 2 ms full-volume veto after adetected muon. Some neutrons are produced by muons thatare undetected by the OD or miss the OD but interact in thenearby rock. These neutrons can scatter and capture in the LS,mimicking the νe signal. We also expect background eventsfrom atmospheric neutrinos. The energy spectrum of thesebackgrounds is assumed to be flat to at least 30 MeV based ona simulation following [12]. The atmospheric ν spectrum [13]and interactions were modeled using NUANCE [14]. We ex-pect fewer than 9 neutron and atmospheric ν events in thedata-set. We observe 15 events in the energy range 8.5 –30 MeV, consistent with the limit reported previously [15].

The accidental coincidence background above 0.9 MeV ismeasured with a 10-ms-to-20-s delayed-coincidence windowto be 80.5± 0.1 events. Other backgrounds from (γ,n) inter-actions and spontaneous fission are negligible.

Anti-neutrinos produced in the decay chains of 232Th and238U in the Earth’s interior are limited to prompt ener-gies below 2.6 MeV. The expected geo-neutrino flux at theKamLAND location is estimated with a geological referencemodel [9], which assumes a radiogenic heat production rateof 16 TW from the U and Th-decay chains. The calculated νe

fluxes for U and Th-decay, including a suppression factor of

(MeV)pE

0

50

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250

0 1 2 3 4 5 6 7 8

KamLAND datano oscillationbest-fit osci.accidental

O16,n)αC(13

eνbest-fit Geo best-fit osci. + BG

eν+ best-fit Geo

406080

100Selection efficiency

Even

ts / 0

.425

MeV

Effic

ienc

y (%

)

FIG. 1: Prompt event energy spectrum of νe candidate events.All histograms corresponding to reactor spectra and expected back-grounds incorporate the energy-dependent selection efficiency (toppanel). The shaded background and geo-neutrino histograms are cu-mulative. Statistical uncertainties are shown for the data; the band onthe blue histogram indicates the event rate systematic uncertainty.

0.57 due to neutrino oscillation, are 2.24×106 cm−2s−1 (56.6events) and 1.90×106 cm−2s−1 (13.1 events), respectively.

With no νe disappearance, we expect 2179± 89 (syst)events from reactors. The backgrounds in the reactor energyregion listed in Table II sum to 276.1± 23.5; we also expectgeo-neutrinos. We observe 1609 events.

Figure 1 shows the prompt energy spectrum of selectedνe events and the fitted backgrounds. The unbinned data isassessed with a maximum likelihood fit to two-flavor neu-trino oscillation (with θ13 = 0), simultaneously fitting the geo-neutrino contribution. The method incorporates the abso-lute time of the event and accounts for time variations inthe reactor flux. Earth-matter oscillation effects are included.The best-fit is shown in Fig. 1. The joint confidence in-tervals give ∆m2

21 = 7.58+0.14−0.13(stat)+0.15

−0.15(syst) × 10−5 eV2

and tan2 θ12 = 0.56+0.10−0.07(stat)+0.10

−0.06(syst) for tan2 θ12<1. Ascaled reactor spectrum with no distortion from neutrino os-cillation is excluded at more than 5σ. An independent anal-ysis using cuts similar to Ref. [2] gives ∆m2

21 = 7.66+0.22−0.20 ×

10−5 eV2 and tan2 θ12 = 0.52+0.16−0.10.

The allowed contours in the neutrino oscillation parame-ter space, including ∆χ2-profiles, are shown in Fig. 2. Onlythe so-called LMA-I region remains, while other regions pre-viously allowed by KamLAND at ∼2.2σ are disfavored atmore than 4σ. For three-neutrino oscillation, the data givethe same result for ∆m2

21, but a slightly larger uncertainty onθ12. Incorporating the results of SNO [16] and solar flux ex-periments [17] in a two-neutrino analysis with KamLAND as-suming CPT invariance, gives ∆m2

21 = 7.59+0.21−0.21 × 10−5 eV2

and tan2 θ12 = 0.47+0.06−0.05.

To determine the number of geo-neutrinos, we fit the nor-malization of the νe energy spectrum from the U and Th-decay chains simultaneously with the neutrino oscillation pa-


Phys. Rev. Lett. 100, 221803 (2008)

Erinnerung an die zu erwartenden Energiespektren von Neutrinos aus Spaltreaktionen...


E)



10

3

TABLE II: Estimated backgrounds after selection efficiencies.

Background ContributionAccidentals 80.5± 0.19Li/8He 13.6± 1.0Fast neutron & Atmospheric ν <9.013C(α,n)16Ogs, np → np 157.2± 17.313C(α,n)16Ogs, 12C(n,n′)12C∗ (4.4 MeV γ) 6.1± 0.713C(α,n)16O 1st exc. state (6.05 MeV e+e−) 15.2± 3.513C(α,n)16O 2nd exc. state (6.13 MeV γ) 3.5± 0.2Total 276.1± 23.5

the scattered neutron but the cross sections are not knownprecisely. A 210Po13C source was employed to study the13C(α,n)16O reaction and tune a simulation using the crosssections from Ref. [10, 11]. We find that the cross sections forthe excited 16O states from Ref. [10] agree with the 210Po13Cdata after scaling the 1st excited state by 0.6; the 2nd excitedstate requires no scaling. For the ground-state we use the crosssection from Ref. [11] and scale by 1.05. Including the 210Podecay-rate, we assign an uncertainty of 11% for the ground-state and 20% for the excited states. Accounting for ε(Ep),there should be 182.0± 21.7 13C(α,n)16O events in the data.

To mitigate background arising from the cosmogenic betadelayed-neutron emitters 9Li and 8He, we apply a 2 s vetowithin a 3-m-radius cylinder around well-identified muontracks passing through the LS. For muons that either deposita large amount of energy or cannot be tracked, we apply a 2 sveto of the full detector. We estimate that 13.6± 1.0 eventsfrom 9Li/8He decays remain by fitting the time distribution ofidentified 9Li/8He since the prior muons. Spallation-producedneutrons are suppressed with a 2 ms full-volume veto after adetected muon. Some neutrons are produced by muons thatare undetected by the OD or miss the OD but interact in thenearby rock. These neutrons can scatter and capture in the LS,mimicking the νe signal. We also expect background eventsfrom atmospheric neutrinos. The energy spectrum of thesebackgrounds is assumed to be flat to at least 30 MeV based ona simulation following [12]. The atmospheric ν spectrum [13]and interactions were modeled using NUANCE [14]. We ex-pect fewer than 9 neutron and atmospheric ν events in thedata-set. We observe 15 events in the energy range 8.5 –30 MeV, consistent with the limit reported previously [15].

The accidental coincidence background above 0.9 MeV ismeasured with a 10-ms-to-20-s delayed-coincidence windowto be 80.5± 0.1 events. Other backgrounds from (γ,n) inter-actions and spontaneous fission are negligible.

Anti-neutrinos produced in the decay chains of 232Th and238U in the Earth’s interior are limited to prompt ener-gies below 2.6 MeV. The expected geo-neutrino flux at theKamLAND location is estimated with a geological referencemodel [9], which assumes a radiogenic heat production rateof 16 TW from the U and Th-decay chains. The calculated νe

fluxes for U and Th-decay, including a suppression factor of

(MeV)pE

0

50

100

150

200

250

0 1 2 3 4 5 6 7 8

KamLAND datano oscillationbest-fit osci.accidental

O16,n)αC(13

eνbest-fit Geo best-fit osci. + BG

eν+ best-fit Geo

406080

100Selection efficiency

Even

ts / 0

.425

MeV

Effic

ienc

y (%

)

FIG. 1: Prompt event energy spectrum of νe candidate events.All histograms corresponding to reactor spectra and expected back-grounds incorporate the energy-dependent selection efficiency (toppanel). The shaded background and geo-neutrino histograms are cu-mulative. Statistical uncertainties are shown for the data; the band onthe blue histogram indicates the event rate systematic uncertainty.

0.57 due to neutrino oscillation, are 2.24×106 cm−2s−1 (56.6events) and 1.90×106 cm−2s−1 (13.1 events), respectively.

With no νe disappearance, we expect 2179± 89 (syst)events from reactors. The backgrounds in the reactor energyregion listed in Table II sum to 276.1± 23.5; we also expectgeo-neutrinos. We observe 1609 events.

Figure 1 shows the prompt energy spectrum of selectedνe events and the fitted backgrounds. The unbinned data isassessed with a maximum likelihood fit to two-flavor neu-trino oscillation (with θ13 = 0), simultaneously fitting the geo-neutrino contribution. The method incorporates the abso-lute time of the event and accounts for time variations inthe reactor flux. Earth-matter oscillation effects are included.The best-fit is shown in Fig. 1. The joint confidence in-tervals give ∆m2

21 = 7.58+0.14−0.13(stat)+0.15

−0.15(syst) × 10−5 eV2

and tan2 θ12 = 0.56+0.10−0.07(stat)+0.10

−0.06(syst) for tan2 θ12<1. Ascaled reactor spectrum with no distortion from neutrino os-cillation is excluded at more than 5σ. An independent anal-ysis using cuts similar to Ref. [2] gives ∆m2

21 = 7.66+0.22−0.20 ×

10−5 eV2 and tan2 θ12 = 0.52+0.16−0.10.

The allowed contours in the neutrino oscillation parame-ter space, including ∆χ2-profiles, are shown in Fig. 2. Onlythe so-called LMA-I region remains, while other regions pre-viously allowed by KamLAND at ∼2.2σ are disfavored atmore than 4σ. For three-neutrino oscillation, the data givethe same result for ∆m2

21, but a slightly larger uncertainty onθ12. Incorporating the results of SNO [16] and solar flux ex-periments [17] in a two-neutrino analysis with KamLAND as-suming CPT invariance, gives ∆m2

21 = 7.59+0.21−0.21 × 10−5 eV2

and tan2 θ12 = 0.47+0.06−0.05.

To determine the number of geo-neutrinos, we fit the nor-malization of the νe energy spectrum from the U and Th-decay chains simultaneously with the neutrino oscillation pa-


Phys. Rev. Lett. 100, 221803 (2008)


Atmosphärische Neutrinos

11

Atmosphärische Neutrinos Atmosphärische Neutrinos -- EinführungEinführung


Super-Kamiokande

12


e/µ-Identifizierung in Super-Kamiokande

14

6 IPMU News　No. 15　September　2011

oscillation is discovered, it gives evidence for non-zero neutrino mass. Fig. 3 shows the probability for a neutrino, which was initially QP , to remain QP as a function of the !ight distance. Here, the mass of the heavier neutrino state is assumed to be about 1/107 of the electron mass. If neutrino mass is heavier than this value, the period of oscillation is shorter, and vice versa. Therefore, we can "nd the heavier neutrino mass from the measurement of the rate of neutrino’s transmutation. In reference to Fig. 3, it should be noted that the “zero” survival probability is actually realized in a special case. Generally, the extent of QP disappearance is somewhere between a tiny level and complete disappearance. The effect of neutrino oscillation is maximized in the case of “zero” survival probability in Fig. 3. This is the easiest case to observe the neutrino oscillation.

Let us now think about combining Fig. 3 and the atmospheric neutrino before returning to the real experiment. Roughly speaking, neutrino interactions at energies around 1GeV are most frequently observed in atmospheric neutrino experiments. Looking at Fig. 3, it is clear that if the heavier neutrino state has about 1/107 of the electron mass, the QP survival probability becomes

0 after a QP traveled about 500 km, showing clear oscillation effects. If neutrinos produced in the upper atmosphere come from directly above, their distance of !ight to the detector is about 15 km on the average, so that neutrinos do not yet oscillate. Neutrinos coming from the opposite side of the earth, however, reach the detector after several times of oscillations because the earth’s diameter is about 12,800 km.

Though the Kamiokande results were very interesting, they were not necessarily accepted by many physicists. At that time, there were at least three detectors that could observe atmospheric neutrinos other than Kamiokande, but their observation results were not consistent. Because of this situation, we had to wait for the next generation neutrino detector, namely, Super-Kamiokande (SK) which would have overwhelming statistical accuracy.

As soon as the Super-Kamiokande experiment was commissioned in 1996, the observed atmospheric neutrino data greatly increased since its effective mass for observation was about 20 times that of

Atmospheric neutrino observations in SK and neutrino oscillations

Figure 2. Examples of (a) electron neutrino and (b) muon neutrino events observed in Super-Kamiokande. The sizes of the circles in this "gure show the observed light intensity. Also, the color of the circles shows the timing information of the observed light.

&ŝŐ͘�ϮĂ &ŝŐ͘�Ϯď

(a) (b)

[KAVLI IPMU Tokyo http://www.ipmu.jp/node/1148]

http://www.ipmu.jp/node/1148%5D

http://www.ipmu.jp/node/1148%5D


Super-K atm-v

15


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Figure 13.5: The zenith angle distributions for fully contained 1-ring e-likeand µ-like events with visible energy < 1.33 GeV (sub-GeV) and > 1.33 GeV(multi-GeV). For multi-GeV µ-like events, a combined distribution with partiallycontained (PC) events is shown. The dotted histograms show the non-oscillatedMonte Carlo events, and the solid histograms show the best-fit expectations forνµ ↔ ντ oscillations. (This figure is provided by the Super-Kamiokande Collab.)

hypothesis is disfavored at 2.4σ.

Although the SK-I atmospheric neutrino observations gave compelling evidencefor muon neutrino disappearance which is consistent with two-neutrino oscillationνµ ↔ ντ [131], the question may be asked whether the observed muon neutrinodisappearance is really due to neutrino oscillations. First, other exotic explanations suchas neutrino decay [132] and quantum decoherence [133] cannot be completely ruled outfrom the zenith-angle distributions alone. To confirm neutrino oscillation, characteristicsinusoidal behavior of the conversion probability as a function of neutrino energy E fora fixed distance L in the case of long-baseline neutrino oscillation experiments, or as afunction of L/E in the case of atmospheric neutrino experiments, should be observed. Byselecting events with high L/E resolution, evidence for the dip in the L/E distributionwas observed at the right place expected from the interpretation of the SK-I data in termsof νµ ↔ ντ oscillations [14], see Fig. 13.7. This dip cannot be explained by alternative

June 18, 2012 16:19

[RPP]


Neutrino-Oszillationen Gesamtschau

16

1. & 2. Generation2. & 3. Generation 1. & 3. Generation 1. & 2. Generationatmosphärische ´s Reaktorexperimente solare Neutrinos

long baseline Beschleuniger long baseline Beschleuniger Reaktorexperimente

: CP-Phase

e - x e – x_

e – x_

µ - eµ - x µ -

1000cossin0sincos

cos0sin010

sin0cos

cossin0sincos0001

1212

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i

i

e

eU

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sen-

diffe

renz

m

2

2. & 3. Generation 1. & 3. Generation 1. & 2. Generationm23

2 = 2.3 × 10-3 eV2 m132 = 2.3 × 10-3 eV2 m12

2 = 7.9 × 10-5 eV2

23 = (45 ± 4)° (maximal) 13 < 15° (sehr klein) 23 = (33.7±1.3)° (groß)

sin2 13 tan2 12tan2 23

10-4

m12

2

m

132

m

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10-3 10-3 Mischungs-winkel

0.1 1 10 0.1 1 0.1 1 [Drexlin 2010, siehe Update]


Theta-13

17

2

25China Institute of Atomic Energy, Beijing26Department of Physics, University of Houston, Houston, TX

27Shandong University, Jinan28School of Physics, Nankai University, Tianjin

29Department of Physics, University of Cincinnati, Cincinnati, OH30Dongguan Institute of Technology, Dongguan

31Department of Physics, University of California, Berkeley, CA32Department of Physics, The University of Hong Kong, Pokfulam, Hong Kong

33Charles University, Faculty of Mathematics and Physics, Prague34Sun Yat-Sen (Zhongshan) University, Guangzhou

35University of Science and Technology of China, Hefei36College of William and Mary, Williamsburg, VA

37China Guangdong Nuclear Power Group, Shenzhen38Iowa State University, Ames, IA

(Dated: April 3, 2012)

The Daya Bay Reactor Neutrino Experiment has measured a non-zero value for the neutrino mixing angle θ13with a significance of 5.2 standard deviations. Antineutrinos from six 2.9 GWth reactors were detected in sixantineutrino detectors deployed in two near (flux-weighted baseline 470 m and 576 m) and one far (1648 m)underground experimental halls. With a 43,000 ton-GWth-day livetime exposure in 55 days, 10416 (80376)electron antineutrino candidates were detected at the far hall (near halls). The ratio of the observed to expectednumber of antineutrinos at the far hall is R = 0.940 ± 0.011(stat) ± 0.004(syst). A rate-only analysis findssin2 2θ13 = 0.092 ± 0.016(stat)± 0.005(syst) in a three-neutrino framework.

PACS numbers: 14.60.Pq, 29.40.Mc, 28.50.Hw, 13.15.+gKeywords: neutrino oscillation, neutrino mixing, reactor, Daya Bay

It is well established that the flavor of a neutrino oscil-lates with time. Neutrino oscillations can be described by thethree mixing angles (θ12, θ23, and θ13) and a phase of thePontecorvo-Maki-Nakagawa-Sakata matrix, and two mass-squared differences (∆m2

32 and ∆m221) [1, 2]. Of these mix-

ing angles, θ13 is the least known. The CHOOZ experi-ment obtained a 90%-confidence-level upper limit of 0.17 forsin22θ13 [3]. Recently, results from T2K [4], MINOS [5] andDouble Chooz [6] have indicated that θ13 could be non-zero.In this paper, we present the observation of a non-zero valuefor θ13.For reactor-based experiments, an unambiguous determina-

tion of θ13 can be extracted via the survival probability of theelectron antineutrino νe at short distances from the reactors,

Psur ≈ 1− sin2 2θ13 sin2(1.267∆m2

31L/E) , (1)

where ∆m231 = ∆m2

32 ±∆m221, E is the νe energy in MeV

and L is the distance in meters between the νe source and thedetector (baseline).The near-far arrangement of antineutrino detectors (ADs),

as illustrated in Fig. 1, allows for a relative measurement bycomparing the observed νe rates at various baselines. Withfunctionally identical ADs, the relative rate is independent ofcorrelated uncertainties and uncorrelated reactor uncertaintiesare minimized.A detailed description of the Daya Bay experiment can be

found in [7, 8]. Here, only the apparatus relevant to this anal-ysis will be highlighted. The six pressurized water reactorsare grouped into three pairs with each pair referred to as anuclear power plant (NPP). The maximum thermal power ofeach reactor is 2.9 GWth. Three underground experimentalhalls (EHs) are connected with horizontal tunnels. Two ADs

are located in EH1 and one in EH2 (the near halls). ThreeADs are positioned near the oscillation maximum in the farhall, EH3. The vertical overburden in equivalent meters ofwater (m.w.e.), the simulated muon rate and average muonenergy, and average distance to the reactor pairs are listed inTable I.

FIG. 1. Layout of the Daya Bay experiment. The dots representreactors, labeled as D1, D2, L1, L2, L3 and L4. Six ADs, AD1–AD6, are installed in three EHs.

As shown in Fig. 2, the ADs in each EH are shielded with>2.5 m of high-purity water against ambient radiation in alldirections. Each water pool is segmented into inner and outerwater shields (IWS and OWS) and instrumented with photo-multiplier tubes (PMTs) to function as Cherenkov-radiationdetectors whose data were used by offline software to removespallation neutrons and other cosmogenic backgrounds. The

3

Overburden Rµ Eµ D1,2 L1,2 L3,4EH1 250 1.27 57 364 857 1307EH2 265 0.95 58 1348 480 528EH3 860 0.056 137 1912 1540 1548

TABLE I. Vertical overburden (m.w.e.), muon rate Rµ (Hz/m2), andaverage muon energy Eµ (GeV) of the three EHs, and the distances(m) to the reactor pairs.

detection efficiency for long-track muons is >99.7% [7].The νe is detected via the inverse β-decay (IBD) reaction,

νe + p → e+ + n, in a Gadolinium-doped liquid scintillator(Gd-LS) [9, 10]. The coincidence of the prompt scintillationfrom the e+ and the delayed neutron capture on Gd providesa distinctive νe signature.Each AD consists of a cylindrical, 5-m diameter stainless

steel vessel (SSV) that houses two nested, UV-transparentacrylic cylindrical vessels. A 3.1-m diameter inner acrylicvessel (IAV) holds 20 t of Gd-LS (target). It is surrounded bya region with 20 t of liquid scintillator (LS) inside a 4-m diam-eter outer acrylic vessel (OAV). Between the SSV and OAV,37 t of mineral oil (MO) shields the LS and Gd-LS from ra-dioactivity. IBD interactions are detected by 192 HamamatsuR5912 PMTs. A black radial shield and specular reflectors areinstalled on the vertical detector walls and above and belowthe LS volume, respectively. Gd-LS and LS are prepared andfilled into ADs systematically to ensure all ADs are function-ally identical [7]. Three automated calibration units (ACUs)mounted on the SSV lid allow for remote deployment of anLED, a 68Ge source, and a combined source of 241Am-13Cand 60Co into the Gd-LS and LS liquid volumes along threevertical axes.

FIG. 2. Schematic diagram of the Daya Bay detectors.

The results are based on data taken from 24 December 2011to 17 February 2012. A blind analysis strategy was adopted,with the baselines, the thermal power histories of the cores,and the target masses of the ADs hidden until the analy-

ses were frozen. Triggers were formed from the number ofPMTs with signals above a ∼0.25 photoelectron (pe) thresh-old (NHIT) or the charge-sum of the over-threshold PMTs(ESUM). The AD triggers were NHIT > 45 or ESUM ! 65pe. The trigger rate per AD was < 280 Hz with a negligibletrigger inefficiency for IBD candidates. The data consist ofcharge and timing information for each PMT, and were accu-mulated independently for each detector. To remove system-atic effects due to reactor flux fluctuations, only data sets withall detectors in operation were used.The energy of each trigger in an AD was reconstructed

based on the total pe collected by the PMTs. The energycalibration constant, ∼163 pe/MeV for all ADs and stablethroughout the data collection period, was determined by set-ting the energy peak of the 60Co source deployed at eachAD center to 2.506 MeV. Vertex reconstruction was basedon center-of-charge (COC), defined as the charge-weighted-mean of the coordinates of all PMTs. The mapping fromCOCto vertex was done by analytic corrections determined usingdata collected with 60Co sources deployed at various pointswithin the AD. A vertex-dependent correction to energy(<10%) and a constant factor (0.988) were applied equally toall ADs to correct for geometrical effects and energy nonlin-earity between the 60Co and the neutron capture on Gd (nGd),determined by the 60Co and Am-C sources at the detector cen-ter. An independent energy calibration that utilized the peakof the nGd from spallation neutron to set the energy scale andtemplates derived from Monte Carlo simulations (MC) forvertex reconstruction, gave consistent performance [7]. Theenergy resolution was (7.5/

√

E(MeV)+0.9)% for all 6 ADs.IWS and OWS triggers with NHIT > 12 were classified

as ‘WS muon candidates’ or µWS. Events in an AD within±2 µs of a µWS with energy >20 MeV and >2.5 GeV wereclassified as muons (µAD) and showering muons (µsh), re-spectively, for vetoing purposes. An instrumental backgrounddue to spontaneous light emission from a PMT, denoted as aflasher, was rejected efficiently [7].IBD events were selected with the following criteria: 0.7<

Ep < 12.0 MeV, 6.0 < Ed < 12.0 MeV, 1 < ∆t < 200 µs,the prompt-delayed pair was vetoed by preceding muons iftd − tµWS

< 600 µs, td − tµAD< 1000 µs or td − tµsh

< 1s, and a multiplicity cut that requires no additional>0.7 MeVtrigger in the time range (tp − 200µs, td + 200µs), where Ep

(Ed) is the prompt (delayed) energy and ∆t = td − tp is thetime difference between the prompt and delayed signals. Sta-tistically consistent performance was achieved by an indepen-dent analysis that used different energy reconstruction, muonveto, and multiplicity cuts.The inefficiency of the muon veto for selecting IBD events

(1− εµ) was calculated by integrating the vetoed time of eachmuon with temporal overlaps taken into account. Inefficiencydue to the multiplicity selection (1 − εm) was calculated byconsidering the probability that a random signal occurred nearan IBD in time. The average values of εµ · εm are given foreach AD in Table II.We considered the following kinds of background: acciden-

3

Overburden Rµ Eµ D1,2 L1,2 L3,4EH1 250 1.27 57 364 857 1307EH2 265 0.95 58 1348 480 528EH3 860 0.056 137 1912 1540 1548

TABLE I. Vertical overburden (m.w.e.), muon rate Rµ (Hz/m2), andaverage muon energy Eµ (GeV) of the three EHs, and the distances(m) to the reactor pairs.

detection efficiency for long-track muons is >99.7% [7].The νe is detected via the inverse β-decay (IBD) reaction,

νe + p → e+ + n, in a Gadolinium-doped liquid scintillator(Gd-LS) [9, 10]. The coincidence of the prompt scintillationfrom the e+ and the delayed neutron capture on Gd providesa distinctive νe signature.Each AD consists of a cylindrical, 5-m diameter stainless

steel vessel (SSV) that houses two nested, UV-transparentacrylic cylindrical vessels. A 3.1-m diameter inner acrylicvessel (IAV) holds 20 t of Gd-LS (target). It is surrounded bya region with 20 t of liquid scintillator (LS) inside a 4-m diam-eter outer acrylic vessel (OAV). Between the SSV and OAV,37 t of mineral oil (MO) shields the LS and Gd-LS from ra-dioactivity. IBD interactions are detected by 192 HamamatsuR5912 PMTs. A black radial shield and specular reflectors areinstalled on the vertical detector walls and above and belowthe LS volume, respectively. Gd-LS and LS are prepared andfilled into ADs systematically to ensure all ADs are function-ally identical [7]. Three automated calibration units (ACUs)mounted on the SSV lid allow for remote deployment of anLED, a 68Ge source, and a combined source of 241Am-13Cand 60Co into the Gd-LS and LS liquid volumes along threevertical axes.

FIG. 2. Schematic diagram of the Daya Bay detectors.

The results are based on data taken from 24 December 2011to 17 February 2012. A blind analysis strategy was adopted,with the baselines, the thermal power histories of the cores,and the target masses of the ADs hidden until the analy-

ses were frozen. Triggers were formed from the number ofPMTs with signals above a ∼0.25 photoelectron (pe) thresh-old (NHIT) or the charge-sum of the over-threshold PMTs(ESUM). The AD triggers were NHIT > 45 or ESUM ! 65pe. The trigger rate per AD was < 280 Hz with a negligibletrigger inefficiency for IBD candidates. The data consist ofcharge and timing information for each PMT, and were accu-mulated independently for each detector. To remove system-atic effects due to reactor flux fluctuations, only data sets withall detectors in operation were used.The energy of each trigger in an AD was reconstructed

based on the total pe collected by the PMTs. The energycalibration constant, ∼163 pe/MeV for all ADs and stablethroughout the data collection period, was determined by set-ting the energy peak of the 60Co source deployed at eachAD center to 2.506 MeV. Vertex reconstruction was basedon center-of-charge (COC), defined as the charge-weighted-mean of the coordinates of all PMTs. The mapping fromCOCto vertex was done by analytic corrections determined usingdata collected with 60Co sources deployed at various pointswithin the AD. A vertex-dependent correction to energy(<10%) and a constant factor (0.988) were applied equally toall ADs to correct for geometrical effects and energy nonlin-earity between the 60Co and the neutron capture on Gd (nGd),determined by the 60Co and Am-C sources at the detector cen-ter. An independent energy calibration that utilized the peakof the nGd from spallation neutron to set the energy scale andtemplates derived from Monte Carlo simulations (MC) forvertex reconstruction, gave consistent performance [7]. Theenergy resolution was (7.5/

√

E(MeV)+0.9)% for all 6 ADs.IWS and OWS triggers with NHIT > 12 were classified

as ‘WS muon candidates’ or µWS. Events in an AD within±2 µs of a µWS with energy >20 MeV and >2.5 GeV wereclassified as muons (µAD) and showering muons (µsh), re-spectively, for vetoing purposes. An instrumental backgrounddue to spontaneous light emission from a PMT, denoted as aflasher, was rejected efficiently [7].IBD events were selected with the following criteria: 0.7<

Ep < 12.0 MeV, 6.0 < Ed < 12.0 MeV, 1 < ∆t < 200 µs,the prompt-delayed pair was vetoed by preceding muons iftd − tµWS

< 600 µs, td − tµAD< 1000 µs or td − tµsh

< 1s, and a multiplicity cut that requires no additional>0.7 MeVtrigger in the time range (tp − 200µs, td + 200µs), where Ep

(Ed) is the prompt (delayed) energy and ∆t = td − tp is thetime difference between the prompt and delayed signals. Sta-tistically consistent performance was achieved by an indepen-dent analysis that used different energy reconstruction, muonveto, and multiplicity cuts.The inefficiency of the muon veto for selecting IBD events

(1− εµ) was calculated by integrating the vetoed time of eachmuon with temporal overlaps taken into account. Inefficiencydue to the multiplicity selection (1 − εm) was calculated byconsidering the probability that a random signal occurred nearan IBD in time. The average values of εµ · εm are given foreach AD in Table II.We considered the following kinds of background: acciden-

[Daya Bay arXiv: 1203.1669v2]


6

uncertainties were not included in the analysis; the absolutenormalization ε was determined from the fit to the data. Thebest-fit value is

sin2 2θ13 = 0.092± 0.016(stat)± 0.005(syst)

with a χ2/NDF of 4.26/4. All best estimates of pull parametersare within its one standard deviation based on the correspond-ing systematic uncertainties. The no-oscillation hypothesis isexcluded at 5.2 standard deviations.

The accidental backgrounds were uncorrelated while theAm-C and (alpha,n) backgrounds were correlated amongADs. The fast-neutron and 9Li/8He backgrounds were site-wide correlated. In the worst case where they were correlatedin the same hall and uncorrelated among different halls, wefound the best-fit value unchanged while the systematic un-certainty increased by 0.001.

Fig. 4 shows the measured numbers of events in each de-tector, relative to those expected assuming no oscillation. The6.0% rate deficit is obvious for EH3 in comparison with theother EHs, providing clear evidence of a non-zero θ13. Theoscillation survival probability at the best-fit values is givenby the smooth curve. The χ2 versus sin22θ13 is shown in theinset.

Weighted Baseline [km]0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

expe

cted

/ N

dete

cted

N

0.9

0.95

1

1.05

1.1

1.15

EH1 EH2

EH3

13θ22sin0 0.05 0.1 0.15

2 χ

05

101520253035

σ1

σ3

σ5

FIG. 4. Ratio of measured versus expected signal in each detector,assuming no oscillation. The error bar is the uncorrelated uncertaintyof each AD, including statistical, detector-related, and background-related uncertainties. The expected signal is corrected with the best-fit normalization parameter. Reactor and survey data were used tocompute the flux-weighted average baselines. The oscillation sur-vival probability at the best-fit value is given by the smooth curve.The AD4 and AD6 data points are displaced by -30 and +30 m forvisual clarity. The χ2 versus sin2 2θ13 is shown in the inset.

The observed νe spectrum in the far hall is compared toa prediction based on the near hall measurements in Fig. 5.The disagreement of the spectra provides further evidence ofneutrino oscillation. The ratio of the spectra is consistent withthe best-fit oscillation solution of sin2 2θ13 = 0.092 obtainedfrom the rate-only analysis [31].

Entri

es /

0.25

MeV

0

200

400

600

800 Far hall

Near halls (weighted)

Prompt energy (MeV)0 5 10

Far /

Nea

r (w

eigh

ted)

0.8

1

1.2No oscillationBest Fit

FIG. 5. Top: Measured prompt energy spectrum of the far hall (sumof three ADs) compared with the no-oscillation prediction from themeasurements of the two near halls. Spectra were background sub-tracted. Uncertainties are statistical only. Bottom: The ratio of mea-sured and predicted no-oscillation spectra. The red curve is the best-fit solution with sin2 2θ13 = 0.092 obtained from the rate-only anal-ysis. The dashed line is the no-oscillation prediction.

In summary, with a 43,000 ton-GWth-day livetime expo-sure, 10,416 reactor antineutrinos were observed at the farhall. Comparing with the prediction based on the near-hallmeasurements, a deficit of 6.0% was found. A rate-only anal-ysis yielded sin2 2θ13 = 0.092± 0.016(stat) ± 0.005(syst).The neutrino mixing angle θ13 is non-zero with a significanceof 5.2 standard deviations.

The Daya Bay experiment is supported in part by the Min-istry of Science and Technology of China, the United StatesDepartment of Energy, the Chinese Academy of Sciences, theNational Natural Science Foundation of China, the Guang-dong provincial government, the Shenzhen municipal govern-ment, the China Guangdong Nuclear Power Group, ShanghaiLaboratory for Particle Physics and Cosmology, the ResearchGrants Council of the Hong Kong Special Administrative Re-gion of China, University Development Fund of The Univer-sity of Hong Kong, the MOE program for Research of Ex-cellence at National Taiwan University, National Chiao-TungUniversity, and NSC fund support from Taiwan, the U.S. Na-tional Science Foundation, the Alfred P. Sloan Foundation, theMinistry of Education, Youth and Sports of the Czech Repub-lic, the Czech Science Foundation, and the Joint Institute ofNuclear Research in Dubna, Russia. We thank Yellow RiverEngineering Consulting Co., Ltd. and China railway 15th Bu-reau Group Co., Ltd. for building the underground laboratory.We are grateful for the ongoing cooperation from the ChinaGuangdong Nuclear Power Group and China Light & Power

6


sin2 2θ13 = 0.092± 0.016(stat)± 0.005(syst)





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sin2 2θ13 = 0.092 ± 0.016(stat) ± 0.005(syst) in a three-neutrino framework.


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sin2 2θ13 = 0.092± 0.016(stat)± 0.005(syst)





expe

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7

Company.

∗ Deceased.[1] B. Pontecorvo, Sov. Phys. JETP 6, 429 (1957) and 26, 984

(1968).[2] Z. Maki, M. Nakagawa, and S. Sakata, Prog. Theor. Phys. 28,

870 (1962).[3] M. Apollonio et al. (CHOOZ Collaboration), Phys. Lett. B466,

415 (1999); Eur. Phys. J. C27, 331 (2003).[4] K. Abe et al. (T2K Collaboration), Phys. Rev. Lett. 107, 041801

(2011).[5] P. Adamson et al. (MINOS Collaboration), Phys. Rev. Lett. 107,

181802 (2011).[6] Y. Abe et al. (Double Chooz Collaboration), arXiv:1112.6353

(2012).[7] F. P. An et al. (Daya Bay Collaboration), arXiv:1202.6181

(2012).[8] X. H. Guo et al. (Daya Bay Collaboration), Proposal of the

Daya Bay experiment, arXiv:hep-ex/0701029 (2007).[9] Y. Y. Ding et al., Journal of Rare Earths 25, 310 (2007);

Y. Y. Ding et al., Nucl. Instr. and Meth. A584, 238 (2008).[10] M. Yeh et al., Nucl. Instr. and Meth. A578, 329 (2007).[11] L. J. Wen et al., Nucl. Instr. and Meth. A564, 471 (2006).[12] Y. Declais et al., Phys. Lett. B338, 383 (1994).[13] W. G. K. Schreckenbach, G. Colvin and F. von Feilitzsch, Phys.

Lett. B160, 325 (1985).[14] A. F. von Feilitzsch and K. Schreckenbach, Phys. Lett. B118,

162 (1982).[15] A. A. Hahn et al., Phys. Lett. B218, 365 (1989).[16] P. Vogel, G. K. Schenter, F. M. Mann, and R. E. Schenter, Phys.

Rev. C24, 1543 (1981).

[17] T. Mueller et al., Phys. Rev. C83, 054615 (2011).[18] P. Huber, Phys. Rev. C84, 024617 (2011) [Erratum-ibid. 85,

029901(E) (2012)].[19] V. Kopeikin, L. Mikaelyan, and V. Sinev, Phys. Atom. Nucl. 67,

1892 (2004).[20] F. P. An et al., Chin. Phys. C33, 711 (2009).[21] B. Zhou et al., Chin. Phys. C36, 1 (2012).[22] J. Cao, proceeding of Neutrino 2010, to appear in Nucl. Phys.

B Proc. Supp. [arXiv:1101.2266] (2011).[23] S. F. E. Tournu et al., EPRI 2001.1001470, Palo Alto, CA

(2001).[24] C. Xu et al., Chin. J. Nucl. Sci. and Eng. 23, 26 (2003).[25] S. Rauck, SCIENCE V2 nuclear code package - qualification

report (Rev A), Framatome ANP Document NFPSD/DC/89, 14(2004).

[26] R. Sanchez et al., Nucl. Eng. Tech. 42, 474 (2010).[27] R. R. G. Marleau, A. Hebert, and R. Roy, A User Guide for

DRAGON, Report IGE-236 Rev. 1 (2001).[28] D. Stump et al., Phys. Rev. D65, 014012 (Appendix B) (2001).[29] The survival probability used in the χ2 was

Psur = 1− sin2 2θ13 sin2(1.267∆m231L/E)−

cos4 θ13 sin2 2θ12 sin

2(1.267∆m221L/E) where,

∆m231 = 2.32× 10−3eV2, sin2 2θ12 = 0.861+0.026

−0.022 , and∆m2

21 = 7.59+0.20−0.21×10−5eV2. The uncertainty in∆m2

31 [30]has not been included in the fit. The fit sin2 2θ13 will changeby +0.0007 and -0.0004 when ∆m2

31 changes by one standarddeviation.

[30] P. Adamson et al. (MINOS Collaboration), Phys. Rev. Lett. 106,181801 (2011).

[31] Without correcting for the non-linearity of the detector re-sponse, we have performed a preliminary shape analysis thatyielded a consistent result for sin2 2θ13.

sin2 2θ13 = 0.092 ± 0.016(stat) ± 0.005(syst) in a three-neutrino framework.



19



: CP-Phase

e - x e – x_

e – x_

µ - eµ - x µ -

1000cossin0sincos

cos0sin010

sin0cos

cossin0sincos0001

1212

1212

1313

1313

2323

2323

i

i

e

eU

Mas

sen-

diffe

renz

m

2


2 = 2.3 × 10-3 eV2 m132 = 2.3 × 10-3 eV2 m12

2 = 7.9 × 10-5 eV2



10-4

m12

2

m

132

m

232


0.1 1 10 0.1 1 0.1 1



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: CP-Phase

e - x e – x_

e – x_

µ - eµ - x µ -

1000cossin0sincos

cos0sin010

sin0cos

cossin0sincos0001

1212

1212

1313

1313

2323

2323

i

i

e

eU

Mas

sen-

diffe

renz

m

2


2 = 2.3 × 10-3 eV2 m132 = 2.3 × 10-3 eV2 m12

2 = 7.9 × 10-5 eV2



10-4

m12

2

m

132

m

232


0.1 1 10 0.1 1 0.1 1

Daya Bay: 8°

NEU!


Die absolute Neutrinomasse

20


Die absolute Neutrinomasse

20

2010 2020

10

1

0.1

Mainz, Troitsk

KATRIN


Methodenübersicht

21

Neutrino-Oszillationensensitiv nur auf Massendifferenzen2

Kinematische (“direkte”) MethodenMassenbilanz bei Zerfällen und/oder Reaktionen mit Neutrinos im Endzustand; Beispiel Tritiumzerfall/KATRIN

Flugzeitmessungenmv ≤ 2 eV erfordert sehr lange Flugstrecken; Untersuchung des Neutrinopulses von einer (galaktischen) Supernova, z.B. SN1987a

Neutrinoloser Doppel-Beta-Zerfall (“0vßß”)erfordert Majorana-Natur des Neutrinos und Kenntnis nuklearer Matrixelemente...; HD-Moskau, GERDA...

kosmologische AbleitungenNeutrinos sind die häufigsten massiven Teilchen im Universum, Einfluss auf Massenbilanz (klein) und Strukturbildung (gross)

ν-Masse


Methodenübersicht

22

KosmologieSumme mi, HDM

modellabhängig (Multiparameter)Status: mi < 0.6 - 2 eVPotenzial: mi = 20-50 meVPlanck, Gravitationslinseneffekte

Kinematik ß-Zerfallabsolute -Masse: m

modellunabhängigStatus: m < 2.3 eVPotenzial: m = 200 meVKATRIN, (MARE)

Suche nach 0ßßeff. Majoranamasse mßß

modellabhängig (CP)Status: mßß < 0.35 eV, Evidenz?Potenzial: mßß = 20-50 meVGERDA, EXO, CUORE

Neutrinomassen-experimentelle Techniken

[Drexlin]

Kern- und Teilchenphysik SS2012KT2012 Johannes Blümer IKP in KCETA Oszillationsmuster 7 13....

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