Transcript RooFit toy MC sensitivity studies for + and

RooFit toy MC sensitivity
studies for g+fs and Dms
from Bs→Dsp/K channels at
LHCb
Shirit Cohen
NIKHEF MSc Colloquium
May 11th 2007
Outline




Introduction
The LHCb detector & physics goals
CP violation & interest in Bs→D-sπ+,
Bs→DŦsK± decay channels
RooFit sensitivity studies: concept, experimental and
physics input parameters, decay models and likelihood
function description


Results from sensitivity studies
Summary & conclusions
11th May 2007
Shirit Cohen
Master Colloquium
2
Introduction





Matter dominated universe
Matter-anti matter difference in weak force, CP
violating processes
In the Standard Model via the quark-mixing (CKM)
matrix, via its phases
LHCb experiment designed to study CP violation,
performing measurements in the b-quark sector
Motivation for measuring the CKM phase g
11th May 2007
Shirit Cohen
Master Colloquium
3
The LHCb detector
~ 10-250 mrad yz
~ 10-300 mrad xz
p
p

11th May 2007
Non bending plane view
Shirit Cohen
Master Colloquium
4







Single arm forward spectrometer
Limited angular acceptance but very
good time and mass resolutions
Optimal luminosity 2∙1032cm-2s-1
Detector
detailed
1012 bb pairs produced per year
Bending magnet 4.2Tm bending power
VeLo very close to interaction point
Good separation of p-K
qb
11th May 2007
Shirit Cohen
Master Colloquium
qb
5
Main LHCb physics goals

CKM matrix angles, a, b, g
for example via time dependent CP
asymmetry observable


VCKM
fs mixing phase
Precision measurement of Dms
mass difference
 Vud

  Vcd
 V e  ib
 td
b
CDF measurement
0
B
Δms = 17.77 ± 0.1(stat.) ± 0.07(syst.) ps-1 s



DGs decay rate difference
Rare decays measurements
Signs of New Physics
b→sg transitions through loop
11th May 2007
diagrams,
sensitive to NP
Shirit Cohen
V*tb
Vus Vub e ig
Vcs NP
Vcb
Vts
Vtb
t
W
s
Vts
Vts





s
Bs0
W
t
*
Vtb
b
SM
Master Colloquium
6
Bs meson system
flavour eigenstates
Bs0  b s
Bs oscillations box diagram
0
B
,
s  bs
b
mass eigenstates
BH,L  p B
0
s
0
s
qB
0
s
BH,L 0
W
t
B
mass
eigenstates time dependence
im H ,L GH ,L / 2t
BH,L t   e
V*tb
Vts
s
Bs0
t
W
s
Vts
Vtb*
b
decay amplitude into a final state f
A f  f T Bs0
0
A

f
T
B
,
f
s
if there is more than one contribution, the
decay amplitudes can be written as a sum
,
i k if k
A f   A
e
e
k
k
A f   Ake i k eif k
Example: Bd → pp
k
strong phase keeps value, weak phase
11th May 2007
Shirit Cohen
changes sign under CP transformation

q Af
 f Colloquium
Master
p Af
,
p Af
f 
q Af
7
Bs time dependent decay probability
2

GB 0  f t   A f 1  f
s
2


eGs t 
DGst
DGst
 cosh
 D f sinh
 C f cosDmst  S f sin Dmst 


2
2
2
decay
G
0
Bs f
Df 
t  
2
Af
2 Re  f
1  f
2
2

p
1  f
q
Cf 
2
oscillations


eGs t 
DG t
DG t
 cosh s  D f sinh s  C f cosDmst  S f sin Dmst 

2 
2
2
1  f
2
1  f
2
Sf 
2 Im  f
Bs →Ds-K+
2
Bs →Ds-K+
1  f
Feynman calculus is in f !
Bs →Ds+K-
For charge conjugate final states:
f → f, λf → λf, Af→Af, p/q → q/p
11th May 2007
Shirit Cohen
* In this project we assume |p/q|=1
Bs →Ds+KMaster Colloquium
8
CP violation in Bs meson system

In mixing, if |p/q|1, giving

In decay, if |Af||Af|, giving
expected to be small
~10-2 in Bs section
probBs0  Bs0  probBs0  Bs0 
GBs0  f  GBs0  f 
can occur also in charged
mesons and baryons
can occur only if two decay amplitudes
with different strong and weak phases
contribute to the same final state
In interference, when B  f
and Bs0  Bs0  f possible,
and there is a relative phase
between mixing(e.g

 arg(q/p)=fs) and decay (e.g.
arg(Af/Af))
B  Ds K
0
s
0
s

11th May 2007
Shirit Cohen
q Af
f 
p Af
Master Colloquium
,
 f  Af

p Af
f 
q Af
Af
9
Bs→Dsp decay channel
d
0
Bs
b
u p
c
s
s
+
Ds-




GB 0 D  p  t  e
Gs t
s
s
GB 0 D  p  t  e
Gs t
s
s
11th May 2007


DGst
 cosDmst 
cosh


2


DGst
 cosDmst 
cosh


2
Shirit Cohen
Single decay diagram
→ no CP violation
Flavour specific decay
Branching fraction:
(3.4±0.7)·10-3
One diagram means
 f=λ f =0 (|Af|=|A f |),
leading to
Df=Sf=0, Cf=1.
(two unique Bs→Dsp
equations)
→ Parameters to
measure: Δms, ΔΓs
Master Colloquium
10
Bs→DsK decay channel
T1
0
Bs
b
u
c
s
s
Ds
b
c
u
s
s
s
+
-
Ds +
s
T2
0
Bs
K+
s
K-
Branching fractions
Bs→ D-sK+
Bs11th
→May
D+2007
sK
(2.0±0.6)·10-4
(2.2±0.7)·10-5
0
Bs
s
b
0
Bs b
b
s
s
c
u
Ds K+
s
Non flavour specific decay, four decay
diagrams exist (four Eq.)
 2 diagrams and a relative phase →
 Time dependent CP violation
 |λf|=|λ f | → Df, Cf, Sf coefficients non 0
→ Parameters: |λf|, arg(λf), arg(λ f )
to extract g+fs, ΔT1/T2

g+fs = [arg( f ) - arg( f )] /2
Shirit Cohen
ΔT1/T2 = [arg( f ) + arg(  f )] /2
Master Colloquium
11
Bs→Dsh decay channels
p/K
Bs0
Primary Vertex
~1cm
Ds
K
K
SV ~6mm
p
btag
Event topology



The topology of the decay channels Bs→Ds-π+ and
Bs→DsŦK± is very similar
Bs→Ds-π+ can be used for Δms measurement
Bs→DsŦK± can be used to extract the CP angle g +fs


Standard Model prediction g≈ 60°
fs ≈ 0.02° can be determined by Bs→J/f channel
11th May 2007
Shirit Cohen
Master Colloquium
12
Toy MC sensitivity studies

Goal 

Approach –





Define decay models Probability Distribution Functions (PDF’s) according to
decay equations & including experimental effects
Generate events for all decay flavours, simulating 5 years of data taking
Fit decay models back to the events. Simultaneous fit of both decay channels
in order to achieve best sensitivities and have correlations taken care of
Repeat experiment many times, estimate sensitivities from collected output
Input data 


Obtain expected sensitivity for measuring Dms and g+fs at LHCb from
Bs→Dsp and Bs→DsK decay channels
Experiment-related parameters from full LHCb GEANT4 simulation
Physics parameter values agreed with WG
Tools 

RooFit toolkit for data modeling & ROOT data analysis framework
Ganga, LHC(b) interface for running jobs on the GRID/ CERN
11th May 2007
Shirit Cohen
Master Colloquium
13
Experimental
parameters (1/2)


Bs reconstructed mass from Bs→Dsπ,
signal and major background



Common Bs→Dsh selection, topological cuts
For Dsπ: require bachelor particle reconstructed as π
For DsK: require bachelor particle reconstructed as K
and a cut on ΔLKπ in order to get rid of misidentified
π’s
Signal event yields
Bs reconstructed mass from Ds-π+ and DsŦ K±
channels (after the trigger)

Reconstructed Bs mass resolution 14MeV
B/S limits and central values

Specific central values used for toy MC
Results for B/S ratios
Bs reconstructed mass from Bs→DsK,
signal and major background
Event yields for 2fb-1 (define as 1y)
Bs→Ds- π+
140k ± 0.67k (stat.) ± 40k (syst.)
11th May 2007
Bs→DsŦ K±
Shirit Cohen
6.2k ± 0.03k (stat.) ± 2.4k (syst.)
Channel
B/S at 90% CL
(bb combinatorial)
B/S at 90% CL
(bb specific)
Bs→Ds-π+
[0.014,0.05]
C.V 0.027±0.008
[0.08,0.4]
C.V 0.21±0.06
Master Colloquium
Bs→DsŦ K±
[0,0.18]
C.V 0.0
[0.08,3]
C.V 0.7±0.3
14
Experimental parameters (2/2)

Proper time per-event error
distribution






most probable
value 30fs
Due to detector resolutions on
vertices, tracking, momenta etc.
PT per-event error distribution
parameterization used in toy MC
Acceptance function after triggers
and offline selection

mean value 33fs
Low PT Bs’s rejected due to
misplaced vertex requirements and
low significance impact parameter
Fraction of high PT Bs’s rejected
due to high impact parameter
Acceptance parameterization used
in toy MC
Proper time per-event error distribution
Tagging efficiency etag=0.5812,
mistag fraction w=0.328
11th May 2007
Shirit Cohen
Master Colloquium
Acceptance function
15
RooFit sensitivity studies (1/2)




Following previous work done with FORTRAN (LHCb-2003-103)
Building PDF components using the RooFit package
From the components we construct a decay PDF described by
PDFB→f(trec,mrec|Δtrec) for the Bs→Dsp and Bs→DsK decay channels
(and for the different flavours)
Events are generated according to decay PDF, meaning an event is a
set of “trec,mrec,Δtrec”
11th May 2007
Shirit Cohen
Master Colloquium
16
RooFit sensitivity studies (2/2)

The components that are used in PDFB→f(trec,mrec|Δtrec):







Signal trec distribution – Bs decay equation, include ω smearing
Signal mrec distribution – Gaussian distribution
Background trec distribution – decaying particle with ttBs/2
Background mrec distribution – flat distribution
Resolution function: per-event proper time error (with scale factor)
Acceptance function on trec
Construction

Implementing the acceptance function on signal proper time distribution (and
same for background)



Constructing PDFsig = PDFsig(trec,mrec| Δtrec) and same for background
Adding signal and background with fsig, fbg (calculated from B/S ratios)
Generate events from each decay flavour separately, fit the
desired parameters from all decay flavours simultaneously
 
 
 
 
 
L a, b  LB 0  f a, b  LB 0  f a, b  LB 0  f a, b  LB 0  f a, b
11th May 2007
s
s
Shirit Cohen
s
Master Colloquium
s
17
Likelihood description
Likelihood function

 
LB0  f a , b 
s
Bs0  Dsp

 
Pr ob t rec , mrec , Dt rec a , S sig , Sbg , w 
i
with
Bs0  Ds K
i
a Gs,Dms,DGs 
,

b  f , f ,Gs,Dms,DGs

Pr ob t rec , mrec , Dt rec b , S sig , Sbg , w


acceptance function

Pr ob t rec , mrec , Dt rec a
, Ssig , Sbg , w 



 1  f  m  m  G  t a , w   A  t   G t  t
bg
0
sig
rec
sig
sig
rec
, Dt rec , Ssig 
resolution function:
proper time per-event
error, with signal scale
factor

  fbg mbg  mrec  Gbg  t   A  t   Gbg  t  t rec , Dt rec , Sbg   dt
signal proper time
bg proper time
including mistagged
events
11th May
2007
signal
reconstructed
Bs mass
Master Colloquium
bg reconstructed
Bs mass
Shirit Cohen
resolution function:
proper time per-event
error, with bg scale18
factor
Parameter
Input value
ΔΓs/Γs
0.1
Δms
17.5 (ps)-1
|λf|
0.37
Arg(λf) = ΔT1/T2 - (g+fs)
-60° = -1.047 rad
Arg(λ f ) = ΔT1/T2 + (g+fs)
60° = 1.047 rad
ω
0.328
Event yield (1y) Dsπ
Event yield (1y) DsK
140K
6.2K
B/S ratio for Dsπ
B/S ratio for DsK
0.2
0.7
εtag
0.5812
σ(mrec)
14MeV
11th May 2007
Physics and
experimental input
parameters
for toy MC

Physics


central values of
specific background
used for B/S
estimation
acceptance function
per-event proper time
error distribution
Experimental
Shirit Cohen
Master Colloquium
19
Example for single decay flavor PDF
Bs→Ds-π+ projections on (trec,mrec,Δtrec) (5y)
trec
mrec
Δtrec
Bs→Ds-K+ projections on (trec,mrec,Δtrec)
trec
11th May 2007
Shirit Cohen
mrec
Master Colloquium
Δtrec
20
Sensitivity results from tagged events



Two Dsπ equations, four DsK equations, simultaneous fit performed
Collected data from many “experiments” of 5y tagged data,
scaled results to 1y
Fit a Gaussian to the fitted values from all the “experiments”, make pull
distribution
Data from 400 “experiments”
Parameter
Δms (ps)-1
ω
Arg(λ f) rad
Arg(λ f ) rad
|λf|
g+fs °
ΔT1/T2 °
input value
17.5
0.328
1.047
-1.047
0.37
60
0
fitted value
17.5
0.328
1.056
-1.042
0.37
60.29
0.5
resolution
5y
0.003
0.001
0.116
0.143
0.03
5.68
5.43
resolution
1y
0.007
0.003
0.26
0.32
0.07
12.7
12.14
pull fitted
mean
0.04
-0.07
0.06
0.1
0.1
-0.01
0.1
pull fitted
sigma
1.02
1
1.05
1.04
1.01
1
1.03
11th May 2007
Shirit Cohen
Master Colloquium
21
# events
Example for distributions for 400 exper.
# events
Δms (ps)-1
# events
# events
values
Δms pull
11th May 2007
Shirit Cohen
g+fs°
values
g+fs
pull
Master Colloquium
22
Bs→DsK untagged events


Meaning events with no information if the decaying meson
was a Bs or a Bs
Decay equations for Bs→DsK untagged events:
G t
2
2 e s

DGst
DGst 
GB 0 / B 0  f t   A f 1  f
 cosh
 D f sinh

s
s

2
2
2 


2 eGs t

G 0 0 t   A f 1 f 
Bs / B s  f

 2
2
Df 



2 Re  f
1  f
2
Df 

DG t
DG t 
 cosh s  D f sinh s 

2
2 
2Re f
1 f
2
One cannot observe the Bs oscillations using untagged events
Untagged events still hold information on the phases through Ref, Ref

Add untagged events to the analysis in order to increase the sensitivities
to the phases
11th May 2007
Shirit Cohen
Master Colloquium
23
Bs  Dsp 
Bs  Dsp 
Adding
untagged
DsK events
Bs  Ds K 
Bs / Bs  Ds K 
Bs  Ds K 
Bs  Ds K 
Bs  Ds K 
Bs / Bs  Ds K 
Projections over
proper time (ps)
11th May 2007
Shirit Cohen
Master Colloquium
24
Results from tagged+untagged events


Two Dsπ equations, four DsK equations + two untagged DsK equations.
Collected data from 400 “experiments” of 5y tagged+untagged data,
scaled results to 1y
Fit a Gaussian to the fitted values from all the experiments, check pulls
Parameter
Δms
ω
Arg(λ f) rad
Arg(λ f ) rad
|λf|
g+fs °
ΔT1/T2 °
0.328
1.047
-1.047
0.37
60
0
fitted value
17.5
0.325
1.064
-1.044
0.37
60.37
0.48
resolution 5y
0.003
0.001
0.105
0.118
0.03
4.59
4.61
resolution 1y
0.007
0.003
0.23
0.26
0.06
10.26
10.31
pull fitted mean
0.06
-0.09
0.1
0.03
0.05
0.06
0.1
pull fitted sigma
1.03
1
1.01
1.05
1.08
0.95
0.97
# events
17.5
# events
input value
Δms (ps)-1
values
11th May 2007
Shirit Cohen
g+fs°
values
Master Colloquium
25
Results with different input values



Including tagged+untagged
events, similar as in last
section
Running with different
strong phase values
(all other parameters
unchanged; g+fs = 60° )
Running with different B/S
ratios for Bs→ DsK channel
(all other parameters
unchanged; g+fs = 60°,
Bs→Ds-π+ B/S value = 0.2 )
11th May 2007
Shirit Cohen
Different strong phase input value
ΔT1/T2 °
-20
0
20
σ(g+fs )°
11.2
10.3
10.4
Different B/S input value for Bs→ DsK
Bs→DsK
B/S value
0.0
0.7
2.0
σ(g+fs )°
9.6
10.3
11.1
Master Colloquium
26
Extra check: fitting mistag fraction & signal
scale factor simultaneously






Signal scale factor used for checking PT error estimation
Mistag fraction and PT errors damp the Bs oscillations
Fitting both parameters simultaneously could be problematic,
correlated effects
Fitting the five regular floating parameters + signal scale factor
Running 400 “experiments”, fits converge
Decreased resolution on ω, signal scale resolution of ~10%.
Weak, strong phase and Δms resolutions remain unchanged.
Parameter
Δms (ps)-1
ω
Arg(λ f) rad
Arg(λ f ) rad
g+fs °
|λf|
Signal
scale factor
ΔT1/T2 °
input value
17.5
0.328
1.047
-1.047
0.37
60
0
1.175
fitted value
17.5
0.328
1.05
-1.04
0.37
60.3
0.43
1.176
resolution 5y
0.003
0.003
0.1
0.11
0.03
4.7
4.65
0.04
resolution 1y
0.007
0.006
0.23
0.25
0.06
10.5
10.4
0.1
0.03
-0.1
0.09
0.04
0.09
0.04
1
1.19
Shirit Cohen
0.98
Master Colloquium
1.07
1
1.01
pull fitted
mean
pull fitted
11th May 2007
sigma
0.11
27
1.28
Summary & conclusions




Code for RooFit toy MC sensitivity studies developed
Sensitivity results look good, pulls are fine
Including untagged events improves the g+fs
resolution 12° → 10°
Expect LHCb to measure s(Δms) = 0.007(ps)-1 and
s(g+fs) = 10.3° for nominal input values
CDF measurement
Δms = 17.77 ± 0.1(stat.) ± 0.07(syst.) ps-1


Obtained resolutions with different input values for
strong phase and Bs→DsK B/S ratio
LHCb-2007-041, results quoted in the “Flavour at the
era of LHC” Yellow Report
11th May 2007
Shirit Cohen
Master Colloquium
28
Backup slides
11th May 2007
Shirit Cohen
Master Colloquium
29
Outlook

A possible scenario before the LHCb
measurement of g:
11th May 2007
Shirit Cohen
Master Colloquium
30
Outlook

A possible scenario after the LHCb
measurement of g:
11th May 2007
Shirit Cohen
Master Colloquium
31
Likelihood
function for B→f
Physics parameters
that go in
Backup I
likelihood
description
PDF models, smearing:
mistag fraction,
background, detector’s
acceptance & resolution
11th May 2007
Shirit Cohen
Master Colloquium
Total likelihood
extract from
32
LHCb-2007-041
Backup II
w pull

g+fs pull
11th May 2007
Fitting signal scale factor
and mistag fraction
simultaneously - pull
distributions
Ssig pull
Shirit Cohen
Master Colloquium
33
The LHCb detector
11th May 2007
Non bending plane view
Shirit Cohen
Master Colloquium
34
Interesting parameters

Dsπ case: flavor specific decay, two decay diagrams exist. For this
channel: λf=λ f =0 (|Af|=|A f |), leads to Df=Sf=0, Cf=1.
→ Parameters to measure: Δms, ΔΓ
DsK case: non flavor specific decay, 4 decay diagrams exist,
time dependent CP violation. |λf|=|λ f |.
→ Parameters: |λf|, arg(λf), arg(λ f ) to extract g+fs, ΔT1/T2
 arg(λf) = ΔT1/T2 - (g+fs)
 arg(λ f ) = ΔT1/T2 + (g+fs)
Assume |p/q|=1
Estimated branching
fraction % (used for DC04
selection study)
Only 2 unique D π equations

4 unique DsK equations



s
11th May 2007
Shirit Cohen
Bs→ Ds-π+
(3.4±0.7)·10-3
Bs→ D-sK+
Bs→ D+sK-
(2.0±0.6)·10-4
(2.2±0.7)·10-5
Master Colloquium
35
Bs meson system
flavour eigenstates
Bs0  b s
Bs oscillations
box diagrams
0
B
,
s  bs
mass eigenstates
BH,L  p B
0
s
b
0
s
qB
mass
eigenstates time dependence
im H ,L GH ,L / 2t
BH,L t   e
0
s
t
W
B
BH,L 0
V*tb
s
Vts
s
Bs0
W
Vts
t
V*tb
W
Vtb*
b
decay amplitude into a final state f
A f  f T Bs0
0
A

f
T
B
,
f
s
decay amplitudes can be written as a sum
A f   Ake i k e if k ,
k

A f   Ake i k eif k
k
strong phase keeps value, weak phase
changes sign under CP transformation
11th May 2007

Shirit Cohen
b
0
s
t
B
Vts
s
Bs0
t
W
s
Master Colloquium
Vts
Vtb*
b
36
Bs decay equations
2

GB 0  f t   A f 1  f
s
G
0
Bs f
t  
Df 
Af
2
2 Re  f
1  f
2
2
2


eGs t
2
p
1  f
q
Cf 
2


DG t
DG t
 cosh s  D f sinh s  C f cosDmst  S f sin Dmst 


2
2


eGs t 
DGst
DGst
 cosh
 D f sinh
 C f cosDmst  S f sin Dmst 

2 
2
2
1  f
2
1  f
2
Sf 
2 Im  f
1  f
Bs→Dsπ physics decay model
2
Bs→Ds- π+
Bs→Ds- π+
f : final state, Ds-π+ or Ds-K+
For charge conjugate final states:
B → B ,f → f, λf → λf, Af→Af ,
p/q → q/p
11th May 2007
Shirit Cohen
* In this project we assume |p/q|=1
Master Colloquium
37





Matter dominated universe
Matter-anti matter difference in weak force, CP
violating processes
In the Standard Model via the quark-mixing (CKM)
matrix, via its phases
LHCb experiment designed to study CP violation,
performing measurements in the b-quark sector
Motivation for measuring the CKM phase g
11th May 2007
Shirit Cohen
Master Colloquium
38