July 4, 2002νFact02@Imperial CollegeLondon

Translation from Near to Far t K2Kat K2K

T KobayashiT.KobayashiIPNS, KEK

for K2K beam monitor groupfor K2K beam monitor group(K.Nishikawa, T.Hasegawa, T.Inagaki,

T.Maruyama, T.Nakaya, ....)a uya a, a aya, )Especially for T.Maruyama(KEK Chicago) who

played major role in PIMON i / / l i

1

construction/measurement/analysis

Strategy of K2K

π+ νμπμ+

Target+Horn200

ＳＫ

100 250k

Pion monitor(PIMON)

MUMON FD

200mdecay pipe

100m ~250km

( )

12

x1010

8x104

νμ spectrum@productionνμspectrum @SK

（ＭＣ）

Extrapolate bymultiplying ratio(≠0)

11.21.41.6

4

8

4

6

8 （ＭＣ）

w/o osc.

arb.

uni

t

uni

t

0.20.40.60.81

10 2 43 5E (GeV)ν

4

2

4

（ＭＣ）w/ osc?a

arb.

2

00.20 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

E (GeV)ν10 2 43 5E (GeV)νmeasure w/ FD

measured by PIMON

What’s new in the treatment of far/near extrapolation

• Before– Observable for osc. analysis:

• total # of events

– added syst. error from each energy bins linearly (= 100% iti l ti ) t b f100% positive correlation) to be safe.

• New– Observables for osc. analysis

• total # of events,E rec h f 1 i lik t• Eν

rec spec. shape for 1-ring μ-like events

– Correlation for far/near ratio btw energy bins are taken into account

3

taken into account

Far/Near ratio in oscillation Far/Near ratio in oscillation l i ( th d1)l i ( th d1)analysis (method1)analysis (method1)

Maximum Likelihood Method

)()()( fLfLfLL systshapenormtot ⋅⋅=Maximum Likelihood Method

)()()( fff systshapenormtot

systematics parameterssystematics parameters

),,,,,,( 116F/N nnEsksknQE ffffffff εΦ=spec

nQE/QEFar/near

( ffi i )εSK(efficiency)SK Enegry scale

O

4

Overall Norm ErrorFor Jun99 and Nov99-

Normalization termNormalization term

))(,( fNNPoissonL b=MC PfN )(

))(,( exp fNNPoissonL obsnorm

⋅= MCKT

oscMCSKobs

KT fNPfNNNexp )(

),(

∑ ⋅⋅ΔΦ⋅⋅=

Φji

SKijijji

MCSKNiFi

obs

fmPEffN ,

22/ )()2sin,()( εσθ

∑ ⋅⋅Φ⋅⋅=

Φji

KTijijji

MCKTi

KT fEfN

,)()( εσ

i: energy bin indexi: energy bin indexj: processes (=QE, nQE)

Spectrum meas in FD(f ) cancels first order

5

Spectrum meas. in FD(fΦi) cancels first orderbut far/near ratio fF/N does not.

EEννrecrec spectrum shape term for FC spectrum shape term for FC

1R1R1R1Rμμ∏

29

)( recEPL Total 29 events∏=

≡1

)(i

ecishape EPL Total 29 events

for Nov99~ data

P: reconstructed Eν distribution for 1Rμ (gen’ed by using MC)

( ) ( )truerec EEP Φ∫ Detector response from MC( ) ( )( ) ( ) ( )

ttruerec

QEtrueR

QEtrue

QE

trueSK

rec

EErEE

EEP

νννμ

ν

νν

εσ⎥⎤

⎢⎡ ⋅⋅

⋅Φ= ∫,1

Detector response from MC

( ) ( ) ( )( ) ( ) ( )

truetruerec

nQEtrueR

nQEtrue

nQEnQE

QEQEQE dEEErEEf ν

νννμ

ν

νννν

εσ ⎥⎥⎦⎢

⎢⎣ ⋅⋅+ ,

,1

( ) ( ) ( ) ( )22/ ,2sin mPRffE oscNF

MCFD

meastrueSK Δ⋅⋅Φ=Φ Φ θν

6

( ) ( ) ( ) ( )/ ,ff oscNFFDSK Φν

Systematic constraint termSystematic constraint termyy( ),

1, 2/exp nQEFD

TnQEsyst fMfL Δ⋅⋅Δ−≡ Φ

−Φ

( )( )1

/1//

2/

2/exp T

NFNFT

NF

fMf

fMf

ΔΔ×

Δ⋅⋅Δ−×−

− Far/near ratio

( )( ) ( )2

11211

26

26

1

2exp2exp

2/exp

nnnn

SKSKTSK

ff

fMf

σσεεε

−⋅−×

Δ⋅⋅Δ−×

( ) ( )( )22

111166

2/exp

pp

EskEsk

nnnn

f

ff

σΔ−× 1−≡Δ ff

MFD, Mπ, MSK: error matrix of syst. errors.ll f J 99σn6: overall norm. err. for Jun99 (=+0.80−0.68 evts)

σn11:overall norm. err. for Nov99~ (=5.34%)

7

n11σEsk: SK Enery scale error (3%)

QeustionsQeustions

• Central values of far/near ratio (relative to MC prediction)p )

fF/NiF/Ni• Correlation of far/near ratio btw. energy

bins (error matrix)bins (error matrix)

MMπ

8

A tool:Pion Monitor (PIMON)N(pπ, θπ) Neutrino flux Φ(Eν) at any distance

using only decay kinematics

R(Eν)≡ΦSK(Eν)/ΦFD(Eν)l f i i

To decay volume

200150

2750

Sphericalmirror

Top viewPion monitorGas volume

as a result of pion monitor

Blind

470

230

900

Foca

l le

ngth 34

64mm

Gas o u e~ Design on May 11,'98 ~

190

2448

Gas Cherenkov detector

From2nd Horn

910Beam window

275

2100

to avoid signal from 12GeV protons

332

Photo detector 20 PMTs

200

10

Beam view12GeV protonsinsensitive to pπ

<2GeV (Eν<1GeV)

9

600

110

9

( ν )PMT array

Strategy to obtain f error matrixStrategy to obtain fF/N, error matrixAbove 1GeV PIMON• Above 1GeV PIMON

• Below 1GeV Beam MC(Sanford-Wang parameterization fitted to previous data) validated by p p ) yPIMON measurement at >1GeV

• Error matrixMC part:

⎟⎞

⎜⎛ 0MC

1GeV

(2x2)

MC part:Fit previous pion production databelow ~2GeV/cmove paraemters within error

⎟⎟⎟

⎜⎜⎜ 0

1GeV(2x2) move paraemters within error

get error matrix

⎟⎟⎟

⎜⎜⎜ 0 PIMON

(4x4)

No correlation w/ PIMON part

10

⎟⎠

⎜⎝

(4x4)

Pion Monitor Resultsθ

pπ

θπ

w1 w2 w3 w4 …..: :

: :

11

Pion Monitor Result(relative weight)5)45

mra

d)beam axis

π+ θ

23

(*10

m

01

angl

e

-10

Pio

n

-3-2

-5-4

12

52 3 4 5 6 7Pion momentum (GeV/c)

Pion distribution to far/near ratio (i l t i )(incl. error matrix)

From PIMON fitting ( )SKFD W,φContribution to ν fluxfrom each p-θ bin

5

ad)

Relative weight Wi(i=1~50)( )ji Wφ

(by MC. To 1st order,depend only on decay kinematics &geometry

01234

angl

e (*

10m

ra

Eν

( )WjSKFD

iSKFD

i =Φ ∑50

,, φ FD,SK flux

-4-3-2-10

Pio

n a ( )

( ) ( )WWR FDi

SKii

jjii

ΦΦ=

∑=1

φ ,

Ratio as func. ofweights

-5-4

2 3 4 5 6 7Pion momentum (GeV/c)

50x50 error matrix on weightjdR

U =

( ) ( )iii weights

Dependence

πE50x50 error matrix on weight

iij dW

U =

TR π

of R on W (50x4 matrix)

Error matrixtransformation

13

ijE UEUE TR ⋅⋅= π

(4x4) (4x50) (50x50) (50x4)

transformationfrom π weight

far/near ratio

Other systematic errrosOther systematic errrostreated in matrix form as describedtreated in matrix form as described

1. move syst. parameter within error2. Check correlation btw energy bins

Rj

Ri

14

νμ spectra from Pion Monitor Measurement

15Agree with MC very well.

PIMON result for F/N ratio5

0.3x 10-5

tio

r ra

tPion monitor

Neutrino Beam Simulation

Good Agreement!0.2

/nea

rF

ar/

0.1Integratedabove 2.5GeV

0

16

0 0 1 2 3Eν(GeV)

Far/Near Error MatrixFar/Near Error Matrix“sqrt” of error matrix (%)

( )( ) ijij MM ⋅sign

0-0 5 0 5-1 1-1 5 1 5 2 2-2 5 2 50 0.5 0.5-1 1-1.5 1.5-2 2-2.5 2.5-

Beam MC PIMON17

Summary of systematic errors on total Summary of systematic errors on total # of events w/o osc# of events w/o osc# of events w/o osc.# of events w/o osc.

C t 80 1 t (%)Center: 80.1evts (%)

Jun99(4 55evts)

Total+1.0%−0 9%(4.55evts) 0.9%

Spectrum+0.6%−0.6%

Nov99~(75.5evts)

nQE/QE+0.5%−1.1%+4 9%

Far/Near+4.9%−5.0%

Norm 5.0%

Total +7.7%−6.7%

18

Summaryy• K2K uses pion distribution measured in-

situ(>1GeV) and beam MC(<1GeV) for spectrum extrapolation

• The beam MC is validated by the PIMON measurementsmeasurements

• Correlation of far/near ratio btw energy bins is taken into account (instead of linear sum =taken into account (instead of linear sum = 100% positive correlation

• Still far/near ratio is major source of systematic j yerror

• Expect precise data from HARP (measurement i A 26 ) M th k t HARPin Aug.26~). Many many thanks to HARP collaborators

19

Syst. error: far/near spectrum diff.y p

1600

1800

Typical OA beam(80mDV)

295km16tK2K case (MC)

FD(300m)

800

1000

1200

1400295km

8

12

16b

. uni FD(300m)

(xLSK2/LFD

2)

SK

200

400

600

280m4

8

Arb

SKLarge(~x2) effectaround peak!!

0.8

1

1.2

1.401.2

tio

0

0.2

0.4

0.6

0 0.5 1 1.5 2 2.5 30

0.4

0.8

Rat

00 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Important not only for ν disappearance,

20

Important not only for νμ disappearance,but also for sig/BG estimation for νe search

POT

4.8×1019 POT for Analysis

200kA 250kA200kA 250kA

PIMON meas.

21

Stability of μ−Energy Spectrum

Muon energy spectrum stability1it

μ momentum (ms 25t FC,1-ring,μ)

0.8

0.9

1

99Nov

00Jan

00Feb

00Mar

arbi

trar

y un

it

800

1000 IDEntriesMean

1802 9770

711.3

0.5

0.6

0.700Mar

00May

00Jun

01Jan

01Feb

01Mar

600

800 MeanRMS

711.3 259.1

DATA2001

0.2

0.3

0.401Apr

200

400 DATA2000

Every

0

0.1

0.2

0 0.5 1 1.5 2 2.5 3E (GeV)

0

200

0 250 500 750 1000 1250 1500 1750 2000

ymonths

Muon Energy of

Eμ (GeV)

Pμ(GeV)

Muon Energy in

22

Muon Energy of MRD events

gyKT on ’01, ‘00

Exp’ed EExp’ed Eννrecrec spectrum for 1Rspectrum for 1Rμμ estimated by estimated by

FD tFD tFD measurementsFD measurements

23

PIMON in target stationg

24

25

K2K osc. analysis overviewνμ spectrum @ production

F

near/far extrapolationPIMONpπ-θπ dist

Near Far

oscillation probability Want to know this!!

neutrino interaction in water

d t t (1kt ifi) d t t (SK)detector responce(1kt, scifi) detector responce(SK)

FD observation1KTS ifi

SK observationtotal # of events

26

Scifi Eνrec spectrum shape(1ring μ-like events)

(1Rμ)