RooFit

x

p

q

!"

F

(

x

;

p,

q

)

#

x

p

q

$% && % '

% ' ( ! %'

)

)

' * ( +,,,

- ) . (

( / 0+ 1 *

/! ( 2 304 1 (

/! 051

( . *

'

-* / 6

788 -+ *

7 3 9

:

x, p

!

f

(

x

)

!

F

(

x

;

p,

q

)

9

x

;

x

max

x

_min

f

(

x

)

d

x

dF/dx

*<("

−

data

log(

F

(

x

i

,

p

)

<

x

k

! %' = 6

EPJ Web of Conferences

, 02005 (2010)

DOI:10.1051/epjconf/20100402005

© Owned by the authors, published by EDP Sciences, 2010

!

"#$%&&'()*+,*+-,.(+-,.(/- !

($%&&'()*+,*+-,.(+-,.(/- %

' % - =

' . .

- (

; % -

(

; - ' % %

- .. 6

'',',)*+,*+ !

..,.,+ !

,.,/ !

$% ,%',., ,',., !

$-' ''

) -' -

>- '

; ''. .'

-0012 " !

$%&&( '3' .3. .3 - 3 *

0012 '" !

&&' 3 + )*+ ) *+

0012 " !

+'456+ $%&& 3 *

(%-+'7/+8 ) &&' 3 +

+'9:7+8 ) &&. 3 +

+'9+8 ) && 3 /

- ' %'

' ' )

) ?"'

' )' )%

- &&

0012 &&.3)7 !

0012 &&" !

"""

! - ( 6 - ?

',. %

! ! "

@ % ( -'

> (

-6' "' > (

,1 ;< !

; 1 ;<' ( 788

7;A ('

( (

* () .

' %/! -' (

- (6

"#$%&&'()*+,*+-,.(+-,.(/- !

%

%- (

1

1 0'%1

1 %

- . =.

)%

) 5 * *

> +4

-

- % %*

%"

% ) ' )

% ) =

% " % %

88 > $% % %# ' .

"#$%&&7',.,.7(9- !

88 > >?#? #. @% %.

"#>?#?&&?',A+()*,*-,*()*,*-,7()*,*-B !

/!

B $%',.,. * =

B <'',? * $%

B #.',A+,*,7"""B *

B >?#?',A+,*,7,"""B * 7

B C',.,? * A* & *@

B %',.,? * <

B ',.% *

B %C$* >

B D* C * "

B E#* D

> - # '

' %; )

? % % # "

6<F ><F

"# <F &&.#G''H#I )H'G,'(+,*+-,#(+,*+-,(/-,(9- !

"#><F &&.#7G''H#I )H'G,'(+,*+-,#(+,*+-,(/-,(9- !

<F $ /

1.% '><F '

( # % 6

' '

' *

> ' )'' 9

) **?

"#'&&.G+H#I*G,#()*+,*+-,+(*"+/-,*(7"6,+,*+- !

"#$%&&'()*+,*+-,.,(/- !

C )*

G

(

x, μ

= (

a

0

·

y

+

a

1

)

, σ

)

* $%

9 # /! '

*) ' % E

! "#$!$$ %

# $ % &! ' " (("(

( " )'

')

= %'

88 J $% """

"#$%&&'()*+,*+-,.()*+,*+-,(/,+"*,*+- !

88 J . '

H . 3 &&'". !

88 """ '

&&"0. !

88 .

.)2 !

! + ) ' )

/! 2 /

.#1/ 11 '& / 1D*

D ,.# ,&&',.#D !

& ' &&

1 > "%( ) "

&&"1 !

1 -

) 6

&&." !

&&. 3 +"+5944 I8) +"+K56/K* )*+ ) *+

&&" !

&& 3 /"*++*: I8) +"+67/*/7 +"* ) *+

> ?

H . 3 &&'". !

"0. !

&&"0. !

88 ' ' . ? . %

&&".0., !

.)2 !

! 4 ' 1 %

- )' %

' 3;A2; ' % '

' 1

0012 %H 3 &&"1, !

0012 )2 !

%& ..L > %& 7947"+7, . ..%.& 4"*79/9)+6

.' @%#& %, % .'

. % I8) <

)))))))))))))))))))) ))))))))))))))))))))))))))

. 5"944+)+7 I8) K"56)+7

/"*++7I++ I8) 6"7/)+7

0012 )2J' " !

7'7 .'

M + M * M

)))))))))))))))))))))))))))))))

+ M * +"++7K/5

@

#

88 """ '

&&"0., %L<H !

! 5'

x

-10

-8

-6

-4

-2

0

2

4

6

8

10

Projection of g

0

0.005

0.01

0.015

0.02

0.025

x

-10

-8

-6

-4

-2

0

2

4

6

8

10

Projection of g

0

0.005

0.01

0.015

0.02

0.025

A RooPlot of "x"

>2 *

# = *

-

x

-10

-8

-6

-4

-2

0

2

4

6

8

10

Events / ( 0.2 )

0

5

10

15

20

25

30

35

40

0.099

±

m = 0.085

0.072

±

s = 3.100

x

-10

-8

-6

-4

-2

0

2

4

6

8

10

Events / ( 0.2 )

0

5

10

15

20

25

30

35

40

A RooPlot of "x"

=

- *

#

-

) * +

3 ' (

3 #

+'

x

-10

-8

-6

-4

-2

0

2

4

6

8

10

Events / ( 0.8 )

0

5

10

15

20

x

-10

-8

-6

-4

-2

0

2

4

6

8

10

Events / ( 0.8 )

0

5

10

15

20

A RooPlot of "x"

:#

*

*

% )

N

6

S

(

x

) =

c

0

·

F

0

(

x

) +

c

1

·

F

1

(

x

) +

...

+

c

n

−

1

·

F

n

−

1

(

x

) +

1

−

n

−

1

i

=0

c

i

F

n

(

x

)

+"

;/! '

;J

88 C% $% """" $; ?

)2#$%&&%*'(+,*+-,.*(7-,.(*- !

)2#$%&&%7',.7(/-,. !

)2#%C$&&%','+(K"+-,()*- !

88 ?. ? % ? ;J

)2#;J&&.*(+"9-H%*, 7(+"*-H%7, % !

'

H . 3 &&'". !

&&."0. !

88 % . #

&&."0.,>.&&% ,#? !

7 ) - ' '

' *

" ! F

%

; ' $

+ ;

'

> # ' *)'

x

0

1

2

3

4

5

6

7

8

9

10

Projection of model

0

0.005

0.01

0.015

0.02

0.025

x

0

1

2

3

4

5

6

7

8

9

10

Projection of model

0

0.005

0.01

0.015

0.02

0.025

A RooPlot of "x"

:#

*

S

2

(

x

)

=

f

·

F

1

(

x

) + (1

−

f

)

·

F

2

(

x

)

S

3

(

x

)

=

f

1

·

F

1

(

x

) + (1

−

f

1

)

·

(

f

2

·

F

2

(

x

) + (1

−

f

2

)

·

F

3

(

x

))

S

4

(

x

)

=

f

1

·

F

1

(

x

) + (1

−

f

1

)

·

(

f

2

·

F

2

(

x

) + (1

−

f

2

)

·

(

f

3

·

F

3

(

x

) + (1

−

f

3

)

·

F

4

(

x

)))

/ ) ( ;J

)2# ;J&&.*H%*, 7H%7, % !

;J 7

%7 %7I%' %7

%I%7I%

7 - %%( ;

% ( '

−

log(Poisson(

N

obs

, N

exp

))

(

'

N

exp

!

f

sig

N

exp

→

N

sig

=

f

sig

·

N

ex

N

bkg

= (1

−

f

sig

)

·

N

exp

,

%3< (

7

;J

)2#;J&&.$*(+,*+++-H%*, $7(+,*+++-H%7, $/(+,*+++-H% !

> 1

,

% "

%

M

(

x,

p,

q

) =

T

(

x,

p

)

⊗

R

(

x,

q

)

; '% *

3

M

(

x,

p,

q

) =

∞

−∞

T

(

x,

p

)

·

R

(

x

−

x

_,

_q

₎

_dx

R

T

; '

# )

x

'

M

% #

x

max

x

_min

∞

−∞

T

(

x,

p

)

·

R

(

x

−

x

_,

_q

₎

_dx

_dx

/! '

B > &*"'

B A !

B & *

> . '

T

R

A ! ' (

T

R

' ) *

R

T

&

) ' 3;A2; #'

R

T

t

-10

-5

0

5

10

15

20

25

30

Events / ( 0.4 )

0

100

200

300

400

500

600

700

t

-10

-5

0

5

10

15

20

25

30

Events / ( 0.4 )

0

100

200

300

400

500

600

700

landau (x) gauss convolution

<*

=)*

*

"

<*

!

&!!* * /*

! (

>0 >0 6

88 J 1' '

"#%&&1'()*+,/+-,.N(9,)7+,7+-,N(*,+"*,*+- !

"#$%&& ',.N(+-,N(7,+"*,*+- !

88 @% 1 .

&&'"C*++++,? !

88 J 1 % J' 3 1' H '

"#>0 &&J',1, !

88 J %) %. % J' 3 1' H '

"#>0 &&',1, !

! G

M

)+HHHH'

") ? IF('(I'

!! 6 ( +HHHH

% +HH & ' (

>0 ( J ' !!

@ !!* * *

' ( % '

9 ! '

T

R

) ) 7 (

&&'"C "'

1>

T

)

R

#

T

;

) '

'

! '

T

R

9

)

M

T

#

' # +HK

' 1>&&C%

! L ) <

⊗

= %

# "' +HK" GHK" ! (

' '

#

"#

! /!

P

(

x, ...

) =

k

t

-10

-5

0

5

10

15

20

25

30

Projection of landau (X) gauss

0

0.005

0.01

0.015

0.02

0.025

0.03

t

-10

-5

0

5

10

15

20

25

30

Projection of landau (X) gauss

0

0.005

0.01

0.015

0.02

0.025

0.03

landau (x) gauss convolution

7 *

!

*

"'

+HK *

" GHK *

"

! %'

B

0

B

0

_/

_B

¯

0

%

Υ(4

s

)

&*

c

0

= 1

±

Δ

w

f

0

=

e

−|

t

|

/τ

c

1

=

±

(1

−

2

w

)

f

1

=

e

−|

t

|

/τ

·

cos(Δ

m

·

t

)

9 6 >

c

k

f

k

'

%J

f

k

(

x, ...

)

⊗

R

(

x, ...

)

9 >

- ' ( >0

; )

% #'

'

88 >% # ? %

"##&&#N.()7+,7+-,%(*"945-,1%?J ,% !

88 >% # ? $% %

"##&&#N.*,%,$%J&&.*,(+-,*(*- ,% !

88 >% # ? %)$% %

"##&&#N.7,%,

JA.*,$%J&&.7,,7(9- B,(+"9- ,% !

H . 3 &&".)*+,*+ !

&&#N."0. !

&&#N.*"0.,#? !

&&#N.7"0.,# !

.)2

! J %

- . /0 /

@ ' *

;/!' *

t

-10

-8

-6

-4

-2

0

2

4

6

8

10

Projection of decay_tm

0

0.01

0.02

0.03

0.04

0.05

0.06

t

-10

-8

-6

-4

-2

0

2

4

6

8

10

Projection of decay_tm

0

0.01

0.02

0.03

0.04

0.05

0.06

A RooPlot of "t"

>

*

* "'

= "

= *

"

$ !% &

* *

3 6

H

(

x, y

) =

F

(

x

)

·

G

(

y

)

H

(

x

) =

i

F

i(

x

i)

;

F

(

x

)

G

(

x

)

#'

H

(

x, y

)

# *

#A*' '

/! " '

0

"#$%&&''()*+,*+-,.'()7,)*+,*+-,'(/,+"*,*+- !

"#$%&&##()*+,*+-,.#(4,)*+,*+-,#(*,+"*,*+- !

"# 0&&'#',# !

$ ' !%

2 * /! * '

% 4* =' )

88 $ # ',#

H 3 &&'#" &&',&&# ,*++++ !

88 "" $',# ',#

&&'#"1H !

3 * #

& * -

x

y

% '

*

88 = """ ' #

H .' 3 &&'". !

H .# 3 &&#". !

)20.# ! &&'#)20.# !

88 J 7 ""

1D7H ??N 3 &&'#"D.',# !

??N)2% !

; * * '

#

- '# %

g

xy

(

x, y

)

dy

- '#

g

xy

(

x, y

)

dx

! I %

# #

g

x

(

x

)

g

y

(

y

)

x

-10

-8

-6

-4

-2

0

2

4

6

8

10

Events / ( 0.2 )

0

50

100

150

200

250

300

x

-10

-8

-6

-4

-2

0

2

4

6

8

10

Events / ( 0.2 )

0

50

100

150

200

250

300

A RooPlot of "x"

y

-10

-8

-6

-4

-2

0

2

4

6

8

10

Events / ( 0.2 )

0

100

200

300

400

500

600

700

800

y

-10

-8

-6

-4

-2

0

2

4

6

8

10

Events / ( 0.2 )

0

100

200

300

400

500

600

700

800

A RooPlot of "y"

x

-10 -8

-6 -4

-2 0

2 4

6

8 10

y

-10

-8

-6

-4

-2

0

2

4

6

8

10

Events / ( 0.4 x 0.4 )

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

Histogram of gxy__x_y

:# 4* =

G

(

x, y

) =

G

(

x

)

·

G

(

y

)

6 -

x

"' -

y

" * "

$ !% &

* *

'

F

(

x

;

p

)

→

F

(

x, p

(

y, q

))

→

F

(

x, y, q

)

! %'

m

=

S

(

m, m

0

, σ

)

' (

y

;

y

* %

S

₍

_{x, m}

₀

₍

_m

true

0

, y,

p

)

, σ

)

; /! * *

%

&& &&'&!$!$$ %

g

' *

x, y

( %

y

;

g

(

x, y

)

' ?

y

'

y

! ,

;

y

( ' %'

x

y

'

g

(

x

|

y

)

*

g

(

x, y

)

#

x

-10

-8

-6

-4

-2

0

2

4

6

8

10

Projection of g

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

x

-10

-8

-6

-4

-2

0

2

4

6

8

10

Projection of g

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

A RooPlot of "x"

y

-10

-8

-6

-4

-2

0

2

4

6

8

10

Projection of g

0

0.002

0.004

0.006

0.008

0.01

y

-10

-8

-6

-4

-2

0

2

4

6

8

10

Projection of g

0

0.002

0.004

0.006

0.008

0.01

A RooPlot of "y"

x

-10 -8

-6 -4

-2 0

2 4

6 8

10

y

-10

-8

-6

-4

-2

0

2

4

6

8

10

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

Histogram of g__x_y

:# =

G

(

x, y

) =

G

(

x, f

(

y

)

, σ

)

6 -

x

"' -

y

" * "

- '#

( )

88 'M# ',#

'#"1,>0# !

7 %

( ' "

' %

88 $ ',# . 'M# #

H '# 3 &&'#"&&#,# !

88 = % 'M# '

H .' 3 &&'". !

'#"0.',=&&#,# !

! -'

g

(

x, y

)

dy

1

/N

data

data

g

(

x, y

i

)

> ' '

#0F 1 6(

f

·

S

(

x

|

y

) + (1

−

f

)

·

B

(

x

|

y

)

)

S

B

y

'

! ' '

H

(

x, y

) =

G

(

x

|

y

)

·

F

(

y

)

> # '

G

(

x

|

y

)

F

(

y

)

. . C % %

gxy

&&# 0&&'#7'#M#,<'&&##,()*- !

! +H

-$( )% * #

> . *.

x

-10

-8

-6

-4

-2

0

2

4

6

8

10

Projection of g2

0

0.005

0.01

0.015

0.02

0.025

0.03

x

-10

-8

-6

-4

-2

0

2

4

6

8

10

Projection of g2

0

0.005

0.01

0.015

0.02

0.025

0.03

A RooPlot of "x"

y

-10

-8

-6

-4

-2

0

2

4

6

8

10

Projection of g2

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

0.022

0.024

y

-10

-8

-6

-4

-2

0

2

4

6

8

10

Projection of g2

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

0.022

0.024

A RooPlot of "y"

x

-10 -8

-6 -4

-2 0

2 4

6

8 10

y

-10

-8

-6

-4

-2

0

2

4

6

8

10

Events / ( 0.4 x 0.4 )

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

Histogram of g2__x_y

:#4*

H

(

x, y

) =

G

(

x

|

y

)

·

F

(

y

)

6 -

x

"'

y

" * "

t

"

δt

' %

&"

B

)

% =

F

(

t

) =

D

(

t, τ

)

⊗

R

(

t, μ, σ

)

& ' (

;'

F

(

t

)

F

(

t

|

δt

) =

D

(

t, τ

)

⊗

R

(

t, μ, δt

·

σ

)

% - ' * *

σ

) * ; ' )

σ

;

σ

' *

A

σ

' '

*

9

F

(

t

|

δt

)

(

δt

'

* ; ( '

( * '

*

M

(

t, δt

) =

f

sig

·

S

1

(

t

|

δ

t

)

·

S

2

(

δt

) + (1

−

f

sig

)

·

B

1

(

t

|

δ

t

)

·

B

2

(

δt

)

1 0 +

> *" ;

%

+ ,

-> # )

( (

f

(

x

)

χ

2

)

H

(

x

)

'

σ

(

) =

(1

−

))

/n

' " !*7

%

χ

2

; ' % ( )

%'

6

x

c

E

(

c

|

x,

α

) =

δ

(

c

= accept)

·

(

x,

α

) +

δ

(

c

= reject)

·

(1

−

(

x,

α

))

(

x,

α

)

)

E

(

c

|

x

)

(

x

x

'

c

x

;/!

"#'&&G*) IH') 8 G,(+"4,+,*-,(9-,()*,)*+,*+- !

"#<#&&<,%(,=-,GG !

( %(,=- /! >#

) %%(3+,=3*-"=

D

(

x, c

)

'

(

x

)

) #

&&<"1,>0&&' !

H . 3 &&'". !

"0.,<#&& !

"0. !

C <#% 0 ) 6

x

c

N

x

;

' ? LIK ) ! ++

"'

x

(" "

"

x

-10 -8

-6

-4

-2

0

2

4

6

8

10

Events / ( 1 )

0

200

400

600

800

1000

x

-10 -8

-6

-4

-2

0

2

4

6

8

10

Events / ( 1 )

0

200

400

600

800

1000

Data (all, accepted)

x

-10 -8

-6

-4

-2

0

2

4

6

8

10

Efficiency of cut=accept

0

0.2

0.4

0.6

0.8

1

x

-10 -8

-6

-4

-2

0

2

4

6

8

10

Efficiency of cut=accept

0

0.2

0.4

0.6

0.8

1

Fitted efficiency

< 6

x

("

" / 6

>

)

E

(

c

|

x

)

+ . /

)

-) )

! "# $ % &

-) % (= M

(

L

1

(

a, b

)

L

2

(

a, c

)

a, b

a, c

a

;

- ) #

−

log

(

−

log(

L

1

,

2

(

a, b, c

)) =

−

log(

L

1

(

a, b

)) +

−

log(

L

2

(

a, c

))

4"

-

a

! "# $ &$

9 - ) ) -

D

(

x, k

)

D

1

(

x

)

D

2

(

x

)

k

(1

,

2)

>-

F

12

(

x, k

;

a, b, c

)

F

12

(

x, k

;

a, b, c

) =

δ

(

k

−

1)

F

1

(

x

;

a, b

) +

δ

(

k

−

2)

F

2

(

x, a, c

)

,

'

D

(

x, k

)

($4 - - (

+ " 0 /

O ) ) )

α

$% ) ) C

C

α

C "' - ) M

;

α

(

'

O) ') % .%%

J

88 J """ ' . ,C

"#$%&&'()*+,*+-,.()*+,*+-,.(/,+"*,*+- !

"#C&&C',.,.C(/,+"*,*+- !

88 J = """ ',

"#J&&.(.,.C-,.3,.C3C !

> -

D

(

x, k

)

&&.

*7*7,= ,'&& ,

..,* ,..C,7 !

) $%

) 7

sin 2

β

?

' * *

)'

%

O ) - ) ) '

88 J """ . ,C,>,,<,

"#$%&&'()*+,*+-,.()*+,*+-,.(/,+"*,*+- !

"#$%&&C',.,.(/,+"*,*+- !

"#$%&&',.,.>(/,+"*,*+- !

"#$%&&<',.,.(/,+"*,*+- !

"#$%&&',.,.<(/,+"*,*+- !

88 J = """

"#J&&.(.,.C,.>,.,.<,.-,

.3,.C3C,.>3>,

.3,.<3<,.3 !

' ' ;

J>0<

%'

"#$%&&'()*+,*+-,.()*+,*+-,.(/,+"*,*+- !

"#(.,.C,.>,.- !

"#J>0<&&.,OP.., !

J>0< ( ' #

.., ' )

.'.N .N... ";

' '

; % B

* '

? %)%) B ) %

=

D

(

x, y

)

%

y

88 #

&&#"C7+, !

88 > ))# % %# ? . ? % # GG %.

"#C>#&&%&&#,GG !

88 GG GG ? % % # G%# G

"#&&,% !

2 % " /3 45+

9 '

3< *

1

@ "1 ) '

' #' #

( % )

' ( '#

( 6

88 >% ? %

88 J;1 ..L ? ?

J.L .H !

88 J.L ? ? . . %

.".

88 . % # . . % % 78Q7

."? !

( ( /! -

"

H . 3 .". !

)20. !

(

1

' & ( 9 '

)'*+ /( # I

, / % #

- . / % &

> ( ' # /!

( - J.L #

B 7 % '

B

B #

' "

B ;)' ( *

* )' % #

) ; % ) 5G ' G && ) 7

sin 2

β

5 +H

1 ' 23!'34 5 ,

# ( /! /

3;A2;0G1 ( J.L (

3;A2; ' *

#

0123." ! (

χ

2

"

" (

? '(

455 7 *

" (

σ

ˆ

(

p

)

2

_{= ˆ}

_V

₍

_p

_{) =}

d

2

log

L

dp

2

₋

1

/ %

N

2

01)( 7 " ) ( )

L

=

L

min

+ 0

.

5

) "% ) (

( %

?

>

10

−

20

"

'()6(+3 !#

L

=

L

min

+

X

3

1 5

! ' 3;A2; ) "

) )

'

) ; )

# 3;A2;("

# /! 3;A2;

E )

&&<

1( ' 6 & 23!7 8

3;A 9 C$99$ '%

; ( %" '

;3;A 9 C$99$ '

( (

; ( %

' ' ! +4

( ) C$99$

3;A 9

p

-6

-4

-2

0

2

4

6

8

-log(Likelihood)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

p

-6

-4

-2

0

2

4

6

8

-log(Likelihood)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

A RooPlot of "p"

$%

* (

*

6 3;A 9 *

)

*

( "

Δ(

L

) = 0

.

5

' C$99$ *

) *

*

%

"

Δ(

L

) = 0

.

5

1 )

9' #' (

B # '

B # # '

; #' # *

( #

( )* +,+-&. / -&.0 1

& && 2+ "3#4$ -, *5 6 7 1

8 & 9 / 7:!;##3 &:'"<

*= &:& &:& :7 :'

>? /$ /9/ 0 9 / . 9 &6 @ &:&:'"< &:&:'"<

:7:!;##3 :':'

> ' ( 3;A2;93;=/> *

A D

(' ) +5

>/=29 ( ) ? "9

>/=29 ' ( 6

; ' #

( *

" .. "

m

5.2 5.215.225.235.245.255.265.27 5.285.29 5.3

Events / ( 0.0025 )

0

10

20

30

40

50

m

5.2 5.215.225.235.245.255.265.27 5.285.29 5.3

Events / ( 0.0025 )

0

10

20

30

40

50

Argus model and data

m0

5.288

5.2885

5.289

5.2895

5.29

5.2905

5.291

5.2915

5.292

5.2925

5.293

Projection of nll

0

2

4

6

8

10

12

14

m0

5.288

5.2885

5.289

5.2895

5.29

5.2905

5.291

5.2915

5.292

5.2925

5.293

Projection of nll

0

2

4

6

8

10

12

14

-log(L) scan vs m0

m0

5.288

5.2885

5.289

5.2895

5.295.2905

5.291

5.2915

5.292

5.2925

5.293

Projection of nll

0

2

4

6

8

10

12

14

m0

5.288

5.2885

5.289

5.2895

5.295.2905

5.291

5.2915

5.292

5.2925

5.293

Projection of nll

0

2

4

6

8

10

12

14

-log(L) scan vs m0, problematic regions masked

<6>/=29 3 6<(

# / 6<(

.. /! 3;A2;

; '3;=/> '

3;=/> 3

)% % ! %'

= ' GH

σ

# > ( *

(

1 2 / #

9) ' (

' ( #

% C$99$

( % 6& )

= =

)2#$%&&*'()7+,7+-,.()*+,*+-,.N*(/- !

)2#;J&&.(+,*-H*,7 !

H 3 &&."&&',*+++ !

%H 3 &&."1H, !

; )

%& ..L > %& 79//"56, . ..%.& +"+++7:*659

.' @%#& % .', % )

. % I8) <

)))))))))))))))))))) ))))))))))))))))))))))))))

9"9K+6)+* I8) 6"*7)+*

. *"454:)+7 I8) K":5)+7

.N* 7"5/K7I++ I8) K"94)+*

.N7 /"7K6/I++ I8) *"+5I++

> ( %' 6

0012 %N.N.)2J' "

4'4 .'

M + M * M 7 M / M

)))))))))))))))))))))))))))))))))))))))))))))))))))))))))

+ M * )+"++:/+K +"K:9: +"K::4

* M )+"++:/+K * +"+7797 )+"+/4+/

7 M +"K:9: +"+7797 * +"564:

/ M +"K::4 )+"+/4+/ +"564: *

'.N* .N7

6 ) )%

"

)> # '

% .N7 3 H .N*

)2#$%&&7',.,(*"+9,+"9,7-,.N* !

( '

)9

'

> 7 *

' 7

) >?#?

1$ )/ 23!7

@ ) (

3;A 9*

= (

L

(

a,b

)

a

"

b

( ' .. "'

) ) (

P L

(

a

) =

L

(

a,

ˆ

b

)

ˆ

a

a

) (

a

(

L

(

a,b

)

#

b

(

) ( *

.. ' )

) ('

Δ(

P L

) = 0

.

5

P*P " ) (*

3;A 9 ' "

) ( 3;A 9

4* % ! 4* ('

)(

a

(

L

(

a, b

)

9

*=% ' (.N7. F

H ' ( ? .N*

88 > ,.N* , .N*

H 3 &&."H !

H * 3 )2&& !

H 7 3 )2&&.N* !

88 ,.N*

H .* 3 &&". !

)20.*,#? ,?1R !

*)20.* !

88 ,.N* .N* .N*

H .7 3 &&.N*". !

)20.7,#? ,?1R !

7)20.7 !

88 % 3+"9,7"+ ,.N*

J% .H !

H ./ 3 ."%&&,&&.* !

frac

0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

Projection of -log(likelihood)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

frac

0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

Projection of -log(likelihood)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

A RooPlot of "frac"

frac

0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

sigma_g1

2

2.2

2.4

2.6

2.8

3

3.2

3.4

3.6

3.8

4

frac

0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

sigma_g1

2

2.2

2.4

2.6

2.8

3

3.2

3.4

3.6

3.8

4

A RooPlot

sigma_g1

2

2.2 2.4 2.6 2.8

3

3.2 3.4 3.6 3.8

4

Projection of -log(likelihood)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

sigma_g1

2

2.2 2.4 2.6 2.8

3

3.2 3.4 3.6 3.8

4

Projection of -log(likelihood)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

A RooPlot of "sigma_g1"

<6 ) ( " ( " /6 )

( " ( " .N* 3 6 7 *

( HG " 4" % 3;A 9

! +F )(

( * -' )

(

) ( ' ) '

) ( ' +*4

=" %

+*4..

! +F 3;A 9' ) %

Δ(

L

) = 0

.

5

4* +* - #

Δ(

L

) = 0

.

5

+* - 3;A 9

) (

Δ(

L

) = 0

.

5

'

4'

6"6

0+1 ?&88""?

041 @: ( (' D (' !' 0+1

051 ? &88""?8%88

0F1 =#' " # $ '?#8+4+*+49

0G1 ! O' %&% ' ( ) ' 7$/A