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15/04/2004 IFAE 2004, Torino 1 Experiments to detect M.Apollonio Universita’ di Trieste e INFN

Experiments to detect q 13

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Experiments to detect q 13. M.Apollonio Universita’ di Trieste e INFN. Layout of the talk. q 13 and motivations to its measurement Chooz limit Appearance and disappearance experiments Accelerators (A) Nuclear Reactors (R) (A) Approved projects (Phase I) Phase II Phase III (R) - PowerPoint PPT Presentation

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Page 1: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 1

Experiments to detect M.Apollonio

Universita’ di Trieste e INFN

Page 2: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 2

Layout of the talk• and motivations to its measurement

• Chooz limit• Appearance and disappearance

experiments• Accelerators (A)• Nuclear Reactors (R)

• (A)• Approved projects (Phase I)• Phase II• Phase III

• (R)• Double-Chooz and similar

Page 3: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 3

13• Scenario: MiniBoone

disfavouring LSND• “standard picture”

– 2 m2ij (m2

12, m223)

indipendent– 3 mixing angles (12, 23,

13)– 1 CP phase

• Mixing Matrix PMNS– 1-2 solar mixing– 2-3 atmospheric

mixing– 1-3 o e3 mixing: 1-3 o e3 mixing: 1313

describes oscillations describes oscillations ee at the atmospheric at the atmospheric frequencyfrequency

– CP introduces CP violation effects

2323

2323

1313

1313

1212

1212

321

321

e3e2e1

cs-

sc

cs-

sc

cs-

sc

UUU

UUU

UUU

U

0

0

001

0

010

0

100

0

0

CP

CP

i-

i-

e

e

Current experimental Current experimental results:results:

• mm2223 23 ~ 2x10~ 2x10-3-3 eV eV22

• mm2212 12 ~ 7x10~ 7x10-5-5 eV eV22

• mm2223 23 >>>> mm22

1212

• 1212~35~35oo

• 2323~45~45oo

Page 4: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 4

Why measuring 13?• The least known among the

parameters in PMNS

• Coupled to ei(Ue3)

13>0 would allow to access

• CP violation in the lepton sector

0.70.50.5

0.70.50.5

s0.70.7

UUU

UUU

UUU

U13

321

321

e3e2e1

i

e

Page 5: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 5

What do we know about 13

today?1. 13 must be small

(maybe null)2. The best limit up to

date comes from the reactor experiment CHOOZ:

13 < 10o-17o

(1.3x10-3<m232<3x10-

3) [J.Bouchez, NO-VE 2003]

[CHOOZ coll., Eur.Phys.J.C27(2003),331-374]

Page 6: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 6

3 families scenario:appearance experiments

• Accelerators• NB: P sensitive to (correlated with 13)

42

313

213

1132

cos2sincos

2sinsin

2sin

A

A

A

A

e

P

231

221

231213

213

2

122

232

4

3

2

2

232

1

2sin2sin4

ˆ

ˆsin2sincos

ˆ1

ˆ1sinˆ

ˆsincos

ˆ1

ˆ1sinˆ

ˆsinsin

ˆ1

ˆ1sinsin

m

m

θθcE

LΔmΔ

A

AθθA

A

A

A

AξA

A

A

A

AΔξA

A

ΔAθA

[P.Migliozzi, F.Terranova arXiv:hep-ph/0302274]

• should be considered• sign(m2

13) is present in A

Page 7: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 7

Accelerators

• general concept: conventional beam– Broad band (BBB)– Narrow band (NBB)

• Super Beam (SB)• Off-Axis Beam (OA)• -Beam (B)• Neutrino Factory (NF)

Page 8: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 8

(A) General concept

,K

p

targetdecay(had+ stop)

Production & focusing

detection (,e,)

(>99%)

e(<1%)

oscillation

ee

e-

e-

CC

Main backgrounds:• Initial e contamination in the beam• 0 production (NC)Near/Far detection

Page 9: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 9

Proposed rotating tantalum target ring

(A)-SB

• It is a conventional proton beam whose power is of the order of MW

• Produces ()

• Proton-driver: technically feasiblePB: target Sol.: R&D

Page 10: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 10

• Examples: E at 2 different energy scales for Ep at several OA angles

(A)-OA• Detector laying out of the main

beam axis• Kinematics beam

energy almost independent from Ep

• Monochromatic suppresses the high energy tails

• You pay it in terms of flux

Target Horns Decay Pipe

Page 11: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 11

(A)-Beams[P.Zucchelli, Phys.Lett. B532:166,2002]

• Original solution: radioactive ions with short lifetime – acceleration– storage– decay

• Es.: - (6He) e, + (18Ne) e

Page 12: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 12

(A)-NF

Page 13: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 13

(A) Experiments [J.Bouchez, NO-VE 2003]

Phase I: use an existing facility and approved projects (13>5o)

Phase II: go for 1st generation of Super-Beams (13>2.5o)

Phase III: 2nd generation of Super-Beams (13>1o)[Phase IV: Neutrino Factories see relevant talk]

20065oL-Ar732200.17ICARUS

20067oEmulsion732200.17OPERA

20055oCalorimeter73030.4MINOS

Starting date

Sens to 13

detectorL (km)

E (GeV)

Power(MW)

Experiment

2018 ?0.5oWC/L-Ar [500kT]1300.3-0.6

0.2 -Beam

~20151oWC/L-Ar [500kT]1300.274.0SPL-SB

2020 ?1oWC (HyperK) [500kT]

2950.74.0T2K-II (OA)

20092.3oWC (SuperK) [20kT]

2950.70.8T2K (OA)

2008 ?2.5oFine grained calorimeter[20kT]

700/900

20.4NuMI-OA

Phase

II

Phase

III

Phase

I

Page 14: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 14

(A) Experiments (cont’d)• Requirements for Super-Beams

(e appearance case)

– Beam side:• Low e contamination

• Good knowledge of e/• Good understanding of the beam (near to

far)

– Detector side:• Good e- efficiency• Good 0 rejection• Good understanding of bkg

Page 15: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 15

Which energy?• Low or high?

– Focalisation of neutrinos ~2~E2

– Solid angle factor @ L ~1/2~1/E2

– () ~~E – p flux ~1/~1/E

• The 0th order approximation cannot help that much in the choice

• Other considerations mandatory

~1

Page 16: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 16

Low (E<1GeV) or High (E>1GeV) ?[choice related to bkg considered]

• WC technique gives a good 0 (NC) vs e- separation (2-ring vs 1-ring)

• Less e (below K threshold)

• Fermi momentum poor E resolution

• No matter effects

• Better use fine grained detectors or L-Ar TPC

• Need good 0 rejection

• More e bkg

• Better resolution in E• Matter effects can arise sign(m2

13)

intrinsic e contamination and 0 mimicking e-

caveat:

sta

y b

elo

w

thre

shold

Page 17: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 17

Underground or not?

• In principle not: just a matter of choosing the right (low) duty cycle [phase II, 20 kton]

• BUT it is a must if your detector is “multi-purpose” (e.g. searching for other effects like proton decay) [phase III, 500 kton]

Page 18: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 18

Near/Far• Best way to determine e bkg: measure it at a near

location (before oscillation)• Try to ensure equality of conditions between near and

far detectors: i.e. same beam, same target nuclei (cross sections and 0 production do depend on nuclei)

• Near detector sufficiently far from the source point-like assumption (~ 2 km)– If you go closer then the source is not point-like anymore

• Near detector able to understand the different interactions (QE/non-QE)

• Ideally TWO near detectors (~300 m, ~2 km):– One giving a clear clue about interactions– The other as much as identical to the FAR detector

Page 19: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 19

Near/Far (cont’d): strategies for beam understanding

• Cheap solution:– N sees a point-like source– F and N use the same detection technique (1/L2 law)

– Good for discovery though it does not allow a precise measurement of 13

Beam Near(~2km) Far(700km) N F

• “Pricey” solution:– VN N1: similar detection techniques allowing beam understanding– N1 N2: different in () and detector performances can be compared– F and N2 using the same detection technique– Should be optimal for high statistics phase III where you want to reduce systematics (less dramatic for

phase II)

N1 Beam V-Near(300m) Near(~2km) Far(700km)

F

VN

N2

Page 20: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 20

Time to have a look at some projects …

Page 21: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 21

Icarus, Opera

Page 22: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 22

CNGS• Tuned to reach max sensitivity to appearance

(off-peak) E > Ethre()~17 GeV CNGS~O(10-1) 2 ~ O(10-2)

223

213

4 2sincos P Suppression factor

223

213

2 sinsin2sin eP

• They open a window to 13

NB: •High cross sections (-CC), (e-CC)•High granularity (and detection of e processes): high BKG suppression (NC(0), (e)X)

full mixing, 5 years run@ 6.76 1019 pot/year

Page 23: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 23

Relative importance of the terms in P: case OFF-

PEAK:=/2

42

313

213

1132

cos2sincos

2sinsin

2sin

A

A

A

A

e

P

O1 and O3 leading

2

3131132 2sincos2sin

aa

P e

•Effect (-13) O3

•Sign(m213)

Deterioration effect from Deterioration effect from

1313 ~ 3 ~ 3oo

Ai~O(1), ACNGS ~ 1.6|1-A|<<1 sin2[(1-A)]/(1-A)2 ~ 2

O1

O3

O2

O3

[P.Migliozzi, NO-VE 2003]

Page 24: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 24

Icarus:Lar-TPC• T~89K, E~.5 kV/cm• tracking, dE/dX, e.m. + had.

calorimetry• e/ id // e/ separation E/E~13%/sqrt(E) (e.m.) E/E~30%/sqrt(E) (had)• Conceived to detect events with production allows detection of e and therfore the study of channel

• Being built @ LNGS– T600– 2xT1200 T3000

wire pitch

d

d

Drifting

Ionizing Track

e-

Electric Field

InductionPlane I

InductionPlane II

Collection Plane

PMT

UV Light

Amplifier

in LAr

E1

E2

E3

Page 25: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 25

Icarus: expected results for 13

@ m223 = 2.5 x 10-3

C.M

onta

nari

-LN

GS, 2

2-m

arz

o-2

00

4

Page 26: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 26

Opera: emulsions + -spectrometer

• Direct observation of the decay products from (CC)

• High granularity: ~ m (track separation)

• E/E ~ 20%/sqrt(E) (e.m.)

Page 27: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 27

Opera: expected results

for 13

detection

signal

(m2 = 1.3 x 10-3

eV2)

signal

(m2 = 2.0 x 10-3 eV2)

signal

(m2 = 3.0 x 10-3 eV2)

BKGD

Final Design

4.7 11.0 24.6 1.06

2.5x10-3 eV2

0.06 7°

Page 28: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 28

CNGS (cont’d)• Sensitivity to 13 (sign(m2)& effects):

sin

22 1

3

yrs

0.01

0.02

0.03

0.04

10 1001

CNGS

bkg 10%

bkg 5%

bkg 2%

5 yrs

[P.M

iglio

zzi, F

.Terr

anova a

rXiv

:hep-p

h/0

30

22

74

]

Page 29: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 29

• OA: ~2o, JHF-PS(50 GeV p) SK[I] HK[II]• Maximize the potential discovery (on-peak) ,13,sign(m13

2) • L~295 km, <E>~0.76GeV on peak• |A|~5x10-2 matter effects negligible• Phase I: use SK detector (20 kton)• Phase II: go for a more ambitious device

HK (500 kton)

50 ktonWater Cherenkov

T2K [I/II]

Max. osc. energy for 3×10-

3eV2

OA3°

OA2°OA1°

2200 CC νμ / year800 CC νμ / year

Eπ vs. Eν

0.0゜

1.0゜

1.5

2゚.03゚.05゚.0゜

Page 30: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 30

p

140m0m 280m 2 km 295 km

μ ν ν

15.2m

Total mass : 1000ton

Fid. Mass : 100ton

ν beam

Fine grained scintillater detector

5m

8m

8m

Water Cherenkov detector

Muon detector

Page 31: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 31

OAB (2degree)

K-decay

-decay

e

0.2%

SuperKamiokande• Water Cerenkov

detector– Sub-GeV good 0/el. separation

– 13: 2.5o sensitivity after 5 yrs of data taking

Signal for non-zero θ13 in JHF-SK (νμ→νe)BG (NC π0

….)

SK-90%CL allowed

T.

Kajit

a,

Ferm

ilab –

May

200

3

Page 32: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 32

HyperKamiokande• Goals:

– Improve 13 sensitivity

– Go for CP violation measurement

Page 33: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 33

T2K-I vs CNGS• Sensitivity to 13

as a function of • T2K: O2 even in

• CNGS: O3 odd in

Page 34: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 34

T2K I/II vs CNGS• Sensitivity to 13:

sin

2 1

3

yrs

0.01

0.02

0.03

0.04

0.05

10 1001

CNGS

bkg 10%

bkg 5%

bkg 2%

5 yrs

T2K-I

T2K-II: 1yr!

Page 35: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 35

Minos• L/E tuned to the first MAX at the atmospheric scale

(~730km/3GeV)• Magnetized (1.5 T) calorimeter: 8m octagonal steel

(5.4 kton) & scintillator (484 planes)– 23%/sqrt(E) (e.m.)– 55%/sqrt(E) (had.)

• Taking cosmics• GOALS:

– Demonstrate oscillation behavior– Precise measurement of oscillation parameters– Precise Determination of Flavor Participation– Number of CC e events far/near: Sensitive to e oscillation

down to about 2%. Discovery/first measurement of Ue3?

Page 36: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 36

Minos (cont’d)

m2 = 0.0025 eV2

MINOS 3 discovery limitsSensitivity to 13

Page 37: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 37

NuMI-OA

• OA: ~0.7o

• L~712 km, <E>~2.2 GeV on peak

• |A|~0.2 matter effects NOT negligible sensitivity to sign(m2

13)

Page 38: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 38

Relative importance of terms in P: case ON-PEAK:~/2

42

313

213

1132

cos2sincos

2sinsin

2sin

A

A

A

A

e

P

O1 and O2 leading

2

3131132 2sincos2sin

AA

P e

•Ai~O(1)•Effect (-13)

Deterioration effect from Deterioration effect from

1313 ~ 3 ~ 3oo

O1

O2

O3

O4

Ai~O(1), AJPARC ~ 0

Page 39: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 39

(A) sensitivity to 13 (90% C.L.)

0.001 0.01 0.1

Minos

CNGS

Numi-OA

T2K-I

sin2(213)

/OPERA alone

OPERA alone5y HI beam

• as a function of

• =3x10-2

• Ignorance on phase• Ignorance on sign(m2)

[P.M

iglio

zzi, F

.Terr

anova a

rXiv

:hep-p

h/0

30

22

74

]

Page 40: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 40

13 at (A)• Measurement made difficult by matter effects

and CP violation

• Sensitivity to 13 strongly depends on

• Synergies among different experiments could help

• Ex.: sens. to 13 in T2K + Numi-OA: start T2K in -mode and Numi-OA in -modem2>0 m2<0

Page 41: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 41

• If 13>7o then: indication of appearance at 90% C.L.

• Ex1: 13=10o

• CNGS: 3 yrs of data taking (T2K-I start), m2<>0

• 8 yrs CNGS d.t. + 5 yrs T2K d.t.

• Ex2: 13=5o

13=10° 13=5°

Page 42: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 42

disappearance exp.: Reactors• Reactors: P NOT sensitive to can do a

pure measurement of 13

• Tipical reaction: e+p e++n

– Detection: “prompt” signal from positron (1) + delayed capture of n on Gd (p) (2) [a la Chooz]

e

n

e+

2

2113

2 2sin1 AA

ee

P

231

221

213

212

213

42

21

4

2sincos

sin

m

m

ELΔmΔ

ΔθθA

ΔA

[F.D

aln

oki

-Vere

ss, La

thuile

20

04

]

(1)

(2)

Page 43: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 43

Ch

ooz

epnnemMMEEE )(

νe+p→n+e+

Cross section (~10-42 cm2)

νe+p→n+e+

Cross section (~10-42 cm2)

Spectrum e

(10-8 /s MeV GWth)

Ob

serv

ed

sp

ectr

um

Ob

serv

ed

sp

ectr

um

(in

tera

cti

on

s/M

eV

ton

(i

nte

racti

on

s/M

eV

ton

d

ay)

day)

10

5

0

Page 44: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 44

P(ee)

22

1132 2sin1 AA

ee

P

P(n

e

ne)

km

13: amplitude

A1=A1(): atmospheric modulationA2: solar modulation

[F.D

aln

oki

-Vere

ss, La

thuile

20

04

]

[Huber

at

al., hep-p

h/0

30

32

32

]

RI 400 t GW yRII 8000 t GW y

Page 45: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 45

Chooz: an example of reactor experiment

• Relied on– calculation of e flux from the two reactor

cores– computation of the active mass of the

target– evaluation of the absolute efficiency

– knowledge of e cross section

• Systematics kept at 2.8% finally limited the experimental result

Page 46: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 46

• The key for a successful new reactor experiment (measuring 13) is reducing the systematics (<1%) and reach enough statistics (<0.5%)

• This can be achieved by using a pair of “identical” detectors (near/far technique)

• Some ideas are being pursued:– A case: Double Chooz

• CAVEAT-1: you never have 2 identical detectors!– Different bkg (and dead times)– S/N different

• CAVEAT-2:energy scale and relative non-linearities to be held into account

Page 47: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 47

strategies• Faster:

– Use existing facilities/places with proper “refurbishing”

– Try to get some result before or at the same time as LBL exp’s (e.g. T2K-I, Numi-OA)

• Reactors complementarity:– No need to go faster: try instead to

perform a highly precise measurement– Build new brand detectors (sophisticated

too: e.g. with movable baselines)– You pay it with a later start

Page 48: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 48

from CHOOZ to double-CHOOZ4

32

1

• Detector Basics: 2 identical detectors (12.6 m3) at

• 150 m

• 1050 m

1. Gd (0.1%) loaded LS

• ~ 10 ton

2. LS buffer

3. Non-scintillating buffer

4. VETO

H.d

eK

err

et,

NO

-VE 2

00

3

K.A

nders

on e

t al., arX

iv:h

ep-e

x/0

40204

1 v

1 2

6 F

eb 2

004

Page 49: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 49

From CHOOZ to Double-CHOOZ

systematics CHOOZ

D-CHOOZ

Reactor flux 1.9% -

Reactor power 0.7% -

E/fission 0.6% -systematics CHOO

ZD-CHOOZ

LS density 0.3% -

%H 1.2% -

Np target 0.8% 0.2%

(Ee+) 1.5% 0.5%

Target volume 0.3% 0.2%

Relative error: rel~0.6%

sist~1%

Mainly canceled using the near/far technique

Using the same LS/LS+Gd should help a lot to improve thesesystematics

[F.D

aln

oki

-Vere

ss, La

th

uile

200

4/H

.De K

err

et,

NO

-VE 2

00

3]

Page 50: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 50

• Important: reduce the muon flux main cause of correlated background!

• Also present the accidental background from natural radioactivity LS buffer + veto

• BKG can be measured when (if) reactor is OFF

from CHOOZ to double-CHOOZ

Page 51: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 51

CHOOZ: rate_n vs thermal power

•NB: when GW0 you get the bkg (accid.+correlated)

Page 52: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 52

D-CHOOZ • S/B>100 (in Chooz ~ 18)• Increase S by a factor 2.2 (from 5 to 11

tons)• Reduce B by a factor 3 with a careful

design of the detector (double buffer)

schedule•2006: FAR detector•2007: NEAR detector•2008 first results

Page 53: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 53

Sensitivity to 13 (R): D-CHOOZ

New SK AnalysisNOON ’04m2

atm=2.4+.6/-.5 10-3 eV2

Improve sensitivity by ano.o.m. w.r.t. CHOOZ!

Page 54: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 54

Other reactor experiments:

Site Near/Far (tons)

Expected starting date

Sensitivity to 13

Angra dos reis

25t/50t ? <0.02-0.03

Diablo canyon

25t/50t 2009 <0.01-0.02

Braidwood 25t/50t 2009 <0.02-0.03

Daya Bay 50t 2009 0.012

Kashiwazaki 8.5t/8.5t 2008 0.026

Krasnoyarsk 46t/46t ? 0.016

Page 55: Experiments to detect  q 13

15/04/2004 IFAE 2004, Torino 55

Summary• I have considered two categories of experiments investigating about 13

– Accelerator based– Reactor Based

• (A) many possible phases and time scales (20062020)– In general sensitivity to 13 spoiled by our ignorance of CP term (and

sign())– Synergies between different experiments to reduce this effect– Reachable sensitivities

• Phase I (2005-2006): ~ 5o

• Phase II (2008-2009): ~ 2.5o

• Phase III (2015-2020): ~ 0.5o-1o

• (R) several projects as well and time-scales (though less spread)– Here CP term not involved: pure measurement of 13

– But the hard thing is reducing detector systematics: if this is done at the <1% then

– Reachable sensitivies:• In the range [3o-5o]

• Ex.: CNGS starting in 2006+5 yrs of data taking 13<5o in 2011

D-CHOOZ starting in 2006+3 yrs of d.t. 13<5o in 2009/2010

Page 56: Experiments to detect  q 13

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The End