1

Translation from Near to Far at K2K

T.KobayashiIPNS, KEK

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

a, T.Nakaya, ....)Especially for T.Maruyama(KEKChicago) who played major role in PIMON construction/measurem

ent/analysis

July 4, 2002Fact02@Imperial CollegeLondon

2

00.20.40.60.81

1.21.41.6

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Strategy of K2K

Pion monitor(PIMON)

MUMON FD

+

Target+Horn

200mdecay pipe

ＳＫ

100m ~250km

10 2 43 5E (GeV)

4

8

12

x1010

10 2 43 5E (GeV)

2

4

6

8x104

spectrum@productionspectrum @SK

measure w/ FDmeasured by PIMON

（ＭＣ）

（ＭＣ）

（ＭＣ）w/o osc.

w/ osc?

Extrapolate bymultiplying ratio(≠0)

arb.

uni

t

arb.

uni

t

3

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% positive correlation) to be safe.

• New– Observables for osc. analysis

• total # of events,

• Erec spec. shape for 1-ring -like events

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

4

Far/Near ratio in oscillation Far/Near ratio in oscillation analysis (method1)analysis (method1)

)()()( fLfLfLL systshapenormtot systematics parameters

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

nQE/QEFar/near

SK(efficiency)SK Enegry scale

Overall Norm ErrorFor Jun99 and Nov99-

Maximum Likelihood Method

5

ji

KTijijji

MCKTi

ji

SKijijji

MCSKNiFi

obsKT

MCKT

oscMCSKobs

KT

fEf

fmPEff

N

fN

PfNNN

,

,

22/

exp

)()(

)()2sin,()(

)(

),(

Normalization termNormalization term

))(,( exp fNNPoissonL obsnorm

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

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

6

EErecrec spectrum shape term for FC spectrum shape term for FC

1R1R

29

1

)(i

recishape EPL

P: reconstructed E distribution for 1R (gen’ed by using MC)

Total 29 events for Nov99~ data

true

truerecnQE

trueRnQE

truenQEnQE

truerecQE

trueRQE

trueQE

trueSK

rec

dEEErEEf

EErEE

EEP

,

,1

1

22/ ,2sin mPRffE oscNF

MCFD

meastrueSK

Detector response from MC

7

Systematic constraint termSystematic constraint term 22

211

211

26

26

1

/1//

,1

,

2/exp

2exp2exp

2/exp

2/exp

2/exp

EskEsk

nnnn

SKSKTSK

NFNFTNF

nQEFDTnQEsyst

f

ff

fMf

fMf

fMfL

MFD, M, MSK: error matrix of syst. errors.n6: overall norm. err. for Jun99 evts)

n11:overall norm. err. for Nov99~ (=5.34%)

Esk: SK Enery scale error (3%)

1 ff

Far/near ratio

8

Qeustions

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

fF/Ni

• Correlation of far/near ratio btw. energy bins (error matrix)

M

9

A tool:Pion Monitor (PIMON)

To decay volume

From 2nd Horn

910

Blind

Beam window

470

230

200

900

2100

2750

Sphericalmirror

Photo detector 20 PMTs

600

200

110

910

Top view

Beam view

Pion monitorGas volume

~ Design on May 11,'98 ~

1 9 0

N(p, ) Neutrino flux (E) at any distanceusing only decay kinematics

R(E)≡SK(E)/FD(E)as a result of pion monitor

Gas Cherenkov detector

to avoid signal from 12GeV protons insensitive to p <2GeV (E<1GeV)

PMT array

10

Strategy to obtain fF/N, error matrix

• Above 1GeV PIMON• Below 1GeV Beam MC(Sanford-Wang parameterizati

on fitted to previous data) validated by PIMON measurement at >1GeV

• Error matrix

0

0

MC

PIMON

1GeV

1GeV

(4x4)

(2x2)

MC part: Fit previous pion production data below ~2GeV/c move paraemters within error get error matrix

No correlation w/ PIMON part

11

Pion Monitor Results

p

w1 w2 w3 w4 …..: :

: :

12

Pion Monitor Result(relative weight)

- 5

- 4

- 3

- 2

- 1

0

1

2

3

4

5

2 3 4 5 6 7P i o n m o m e n t u m ( G e V / c )

Pio

n an

gle

(*10

mra

d)

beam axis

+

13

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

- 5

- 4

- 3

- 2

- 1

0

1

2

3

4

5

2 3 4 5 6 7P i o n m o m e n t u m ( G e V / c )

Pio

n a

ngl

e (*

10m

rad

)

Relative weight Wi(i=1~50)

ijE

50x50 error matrix on weight

i

jij dW

dRU

From PIMON fitting

UEUE TR

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

E

jSKFDi W,

WWR

W

FDi

SKii

jj

SKFDi

SKFDi

50

1

,,

Contribution to fluxfrom each p- bin(by MC. To 1st order,depend only on decay kinematics &geometry

FD,SK flux

Ratio as func. ofweights

Dependenceof R on W (50x4 matrix)

Error matrixtransformationfrom weight far/near ratio

14

Other systematic errrostreated in matrix form as described

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

Ri

Rj

15

spectra from Pion Monitor Measurement

Agree with MC very well.

16

PIMON result for F/N ratio

Good Agreement!

0

0 .1

0 .2

0 .3x 1 0

-5

0 1 2 3E ( G e V )

Fa

r/n

ear

rati

o

P io n m o n ito r

N e u trin o B e a m S im u la tio n

In te g ra te da b o v e 2 .5G e V

17

Far/Near Error MatrixFar/Near Error Matrix

0-0.5 0.5-1 1-1.5 1.5-2 2-2.5 2.5-

“sqrt” of error matrix (%)

ijij MM sign

Beam MC PIMON

18

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

Center: 80.1evts (%)

Jun99

(4.55evts)Total

+1.0%

0.9%

Nov99~

(75.5evts)

Spectrum+0.6%

0.6%

nQE/QE+0.5%

1.1%

Far/Near+4.9%

5.0%

Norm 5.0%

Total+7.7%

6.7%

19

Summary• K2K uses pion distribution measured in-situ(>1G

eV) and beam MC(<1GeV) for spectrum extrapolation

• The beam MC is validated by the PIMON measurements

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

• Still far/near ratio is major source of systematic error

• Expect precise data from HARP (measurement in Aug.26~). Many many thanks to HARP collaborators

20

Syst. error: far/near spectrum diff.Typical OA beam(80mDV)

280m

295km

K2K case (MC)

FD(300m)(xLSK

2/LFD2)

SK

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

Large(~x2) effectaround peak!!

21

4.81019 POT for Analysis

200kA 250kA

POT

PIMON meas.

22

Stability of Energy Spectrum

Muon Energy of MRD events

Muon Energy in KT on ’01, ‘00

Everymonths

23

Exp’ed EExp’ed Erecrec spectrum for 1R spectrum for 1R estimated by estimated by

FD measurementsFD measurements

24

PIMON in target station

25

26

K2K osc. analysis overview

spectrum @ production

near/far extrapolation

oscillation probability

neutrino interaction in water

detector responce(1kt, scifi) detector responce(SK)

FD observation1KTScifi

SK observationtotal # of eventsE

rec spectrum shape(1ring -like events)

PIMONp- dist

Want to know this!!

Near Far

(1R)