Summary of Results data-Fit/Scaled MC, E <

Ecut (candidates for + decay)

data-Fit/Scaled MC, E > Ecut

raw MC 375.8±15.1(stat) 79.5±9.2(stat)

reweighed MC 372.1±15.0(stat) 106.8±11.0(stat)

Scale method 1 1015.6 -211.8

Scale method 2 1001.8 -213.9

Scale method 3 806.2 -234.6

Scale method 4 1640.7 -43.2

Scale method 5 540.3 -53.45

Fit method 1 546.4 1.9

Fit method 2 -283.2 -138.9

Fit method 3 1395.4 -265.4

Expected to be negative

Should be ~0 if data/MC from

horn-off is trust worthy in this

region

Should be 0 by construction

Should be real nubars from +

all methods all methods (except fit method 2)

from + decay candidates from + decay candidates

In Scale Method 5 C(E) is approximated with:

Main idea of scaling methods is:

),()(),( KECK MCvv

Overall method:),(),,()( KK v

DATAvv

),,(),,(

KK

MCv

DATAv

Question is: how good is this approximation?

),(

),(

),,(

),,(

K

K

K

KMCv

DATAv

MCv

DATAv

Pol 4th deg

Then we have: ),,()1(),(

),,()1(),(

KfK

KfKMCv

MCMCv

DATAv

DATADATAv

Let be the fraction of + in the spectrum (Data)

Let be the fraction of + in the spectrum (MC)

DATAfMCf

Clearly if then MCDATA ff )(

),(

),(

),,(

),,(EC

K

K

K

KMCv

DATAv

MCv

DATAv

thus giving:

),,(

),,(

1

1

),(

),(

K

K

f

f

K

KMCv

DATAv

MC

DATA

MCv

DATAv

MCf

Conservative scenario: differs from by 100%: DATAf MCf

MC

DATA

f

f

1

1

MCDATA ff 2

0DATAf

The data/MC horn-on ratio is then:

dataScaled MC, no +

dataScaled MC, no +

subtraction subtraction

from + candidates from + candidates

Proceeding with the analysis:

data-Fit/Scaled MC, E < Ecut (candidates for + decay)

data-Fit/Scaled MC, E > Ecut

raw MC 375.8±15.1(stat) 79.5±9.2(stat)

reweighed MC 372.1±15.0(stat) 106.8±11.0(stat)

Scale method 5 514.2±183.7(stat)±225.2(syst) 83.7±143.7(stat)±138.2(syst)

from + candidates

Stat

from + candidates

Syst

from + raw MC from + raw MC

KKL

+

+ component, ME+ component, LE

Difference between the two curves in previous slide

ME non-mu+ components – LE non-mu+ components