RooFit toy MC sensitivity studies for g fs and Dms from Bs?Dsp/K channels at LHCb

1
RooFit toy MC sensitivity studies for gfs and
Dms from Bs?Dsp/K channels at LHCb

• Shirit Cohen
• NIKHEF MSc Colloquium
• May 11th 2007

2
Outline

• Introduction
• The LHCb detector physics goals
• CP violation interest in Bs?D-sp, Bs?DTsK
  decay channels
• RooFit sensitivity studies concept, experimental
  and physics input parameters, decay models and
  likelihood function description
• Results from sensitivity studies
• Summary conclusions

3
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 ?

4
The LHCb detector
10-250 mrad yz 10-300 mrad xz
p
p
?
Non bending plane view
5
Detector detailed

• Single arm forward spectrometer
• Limited angular acceptance but very good time and
  mass resolutions
• Optimal luminosity 21032cm-2s-1
• 1012 bb pairs produced per year
• Bending magnet 4.2Tm bending power
• VeLo very close to interaction point
• Good separation of ?-K

6
Main LHCb physics goals

• CKM matrix angles, a, b, g
• for example via time dependent CP asymmetry
  observable
• fs mixing phase
• Precision measurement of ?ms mass difference
• CDF measurement
• ?ms 17.77 0.1(stat.) 0.07(syst.) ps-1
• DGs decay rate difference
• Rare decays measurements
• Signs of New Physics

b?sg transitions through loop diagrams, sensitive
to NP
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Bs meson system
flavour eigenstates
Bs oscillations box diagram
,
mass eigenstates
mass eigenstates time dependence
decay amplitude into a final state f
,
if there is more than one contribution, the decay
amplitudes can be written as a sum
,
Example Bd ? pp-
,
strong phase keeps value, weak phase changes sign
under CP transformation
8
Bs time dependent decay probability
decay
oscillations
Bs ?Ds-K
Bs ?Ds-K
Feynman calculus is in lf !
Bs ?DsK-

• For charge conjugate final states
• f ? f, ?f ? ?f, Af?Af, p/q ? q/p

Bs ?DsK-
In this project we assume p/q1
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CP violation in Bs meson system

• In mixing, if p/q?1, giving
• In decay, if Af?Af, giving
• can occur only if two decay amplitudes with
  different strong and weak phases contribute to
  the same final state
• In interference, when
• and possible, and there is a relative phase
  between mixing (e.g arg(q/p)?s) and decay (e.g.
  arg(Af/Af))

expected to be small 10-2 in Bs section
can occur also in charged mesons and baryons
,
10
Bs?Dsp decay channel

• Single decay diagram
• ? no CP violation
• Flavour specific decay
• Branching fraction (3.40.7)10-3
• One diagram means
• ?f? f 0 (AfA f ), leading to
• DfSf0, Cf1.
• (two unique Bs?Dsp equations)
• ? Parameters to measure ?ms, ?Gs

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Bs?DsK decay channel
T1

• Non flavour specific decay, four decay diagrams
  exist (four Eq.)
• 2 diagrams and a relative phase ?
• Time dependent CP violation
• ?f? f ? Df, Cf, Sf coefficients non 0
• ? Parameters ?f, arg(?f), arg(? f )
• to extract gfs, ?T1/T2

T2
Branching fractions
Bs? D-sK Bs? DsK- (2.00.6)10-4 (2.20.7)10-5
gfs arg( l f ) - arg( l f ) /2 ?T1/T2
arg( l f ) arg( l f ) /2
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Bs?Dsh decay channels

• The topology of the decay channels Bs?Ds-p and
  Bs?DsTK is very similar
• Bs?Ds-p can be used for ?ms measurement
• Bs?DsTK can be used to extract the CP angle g
  fs
• Standard Model prediction g 60
• ?s 0.02 can be determined by Bs?J/??? channel

13
Toy MC sensitivity studies

• Goal -
• Obtain expected sensitivity for measuring ?ms and
  ??s at LHCb from Bs?Dsp and Bs?DsK decay
  channels
• Approach
• Define decay models Probability Distribution
  Functions (PDFs) 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 -
• 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

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Experimental parameters (1/2)

• Common Bs?Dsh selection, topological cuts
• For Dsp require bachelor particle reconstructed
  as p
• For DsK require bachelor particle reconstructed
  as K and a cut on ?LKp in order to get rid of
  misidentified ps
• Signal event yields
• Bs reconstructed mass from Ds-p and DsT K
  channels (after the trigger)
• Reconstructed Bs mass resolution 14MeV
• B/S limits and central values
• Specific central values used for toy MC

Bs reconstructed mass from Bs?Dsp, signal and
major background
Results for B/S ratios
Bs reconstructed mass from Bs?DsK, signal and
major background
Channel B/S at 90 CL (bb combinatorial) B/S at 90 CL (bb specific)
Bs?Ds-p 0.014,0.05 C.V 0.0270.008 0.08,0.4 C.V 0.210.06
Bs?DsT K 0,0.18 C.V 0.0 0.08,3 C.V 0.70.3
Event yields for 2fb-1 (define as 1y)
Bs?Ds- p 140k 0.67k (stat.) 40k (syst.)
Bs?DsT K 6.2k 0.03k (stat.) 2.4k (syst.)
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Experimental parameters (2/2)

• Proper time per-event error distribution
• 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
• Low PT Bss rejected due to misplaced vertex
  requirements and low significance impact
  parameter
• Fraction of high PT Bss rejected due to high
  impact parameter
• Acceptance parameterization used in toy MC
• Tagging efficiency etag0.5812, mistag fraction
  w0.328

mean value 33fs most probable value 30fs
Proper time per-event error distribution
Acceptance function
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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?trec) 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,?trec

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RooFit sensitivity studies (2/2)

• The components that are used in
  PDFB?f(trec,mrec?trec)
• Signal trec distribution Bs decay equation,
  include ? smearing
• Signal mrec distribution Gaussian distribution
• Background trec distribution decaying particle
  with ttBs/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 ?trec)
  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

18
Likelihood description
Likelihood function
with
,
acceptance function
resolution function proper time per-event error,
with signal scale factor
signal proper time including mistagged events
bg proper time
resolution function proper time per-event error,
with bg scale factor
bg reconstructed Bs mass
signal reconstructed Bs mass
19
Physics and experimental input parameters for
toy MC
Parameter Input value
?Gs/Gs 0.1
?ms 17.5 (ps)-1
?f 0.37
Arg(?f) ?T1/T2 - (gfs) -60 -1.047 rad
Arg(? f ) ?T1/T2 (gfs) 60 1.047 rad

? 0.328
Event yield (1y) Dsp Event yield (1y) DsK 140K 6.2K
B/S ratio for Dsp B/S ratio for DsK 0.2 0.7
etag 0.5812
s(mrec) 14MeV

• central values of specific background used for
  B/S estimation
• acceptance function
• per-event proper time error distribution

Physics
Experimental
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Example for single decay flavor PDF
Bs?Ds-p projections on (trec,mrec,?trec)
(5y)
?trec
mrec
trec
Bs?Ds-K projections on (trec,mrec,?trec)
?trec
mrec
trec
21
Sensitivity results from tagged events

• Two Dsp 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 ?ms (ps)-1 ? Arg(? f) rad Arg(? f ) rad ?f gfs ?T1/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
22
Example for distributions for 400 exper.
g fs values
?ms (ps)-1 values
events
events
?ms pull
g fs pull
events
events
23
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
• 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

24
Adding untagged DsK events
Projections over proper time (ps)
25
Results from taggeduntagged events

• Two Dsp equations, four DsK equations two
  untagged DsK equations. Collected data from 400
  experiments of 5y taggeduntagged data, scaled
  results to 1y
• Fit a Gaussian to the fitted values from all the
  experiments, check pulls

Parameter ?ms ? Arg(? f) rad Arg(? f ) rad ?f gfs ?T1/T2
input value 17.5 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
?ms (ps)-1 values
gfs values
events
events
26
Results with different input values

• Including taggeduntagged 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-p B/S value 0.2 )

Different strong phase input value
?T1/T2 -20 0 20
s(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
s(gfs ) 9.6 10.3 11.1
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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 ?, signal scale
  resolution of 10.
• Weak, strong phase and ?ms resolutions remain
  unchanged.

Parameter ?ms (ps)-1 ? Arg(? f) rad Arg(? f ) rad ?f gfs ?T1/T2 Signal scale factor
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
pull fitted mean 0.03 -0.1 0.09 0.04 0.09 0.04 0.11
pull fitted sigma 1 1.19 0.98 1.07 1 1.01 1.28
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Summary conclusions

• Code for RooFit toy MC sensitivity studies
  developed
• Sensitivity results look good, pulls are fine
• Including untagged events improves the gfs
  resolution 12 ? 10
• Expect LHCb to measure s(?ms) 0.007(ps)-1 and
  s(gfs) 10.3 for nominal input values
• CDF measurement
• ?ms 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

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Backup slides
30
Outlook

• A possible scenario before the LHCb measurement
  of g

31
Outlook

• A possible scenario after the LHCb measurement of
  g

32
Backup I likelihood description
Likelihood function for B?f
Physics parameters that go in
PDF models, smearing mistag fraction,
background, detectors acceptance resolution
extract from LHCb-2007-041
Total likelihood
33
Backup II
w pull

• Fitting signal scale factor and mistag fraction
  simultaneously - pull distributions

gfs pull
Ssig pull
34
The LHCb detector
Non bending plane view
35
Interesting parameters

• Dsp case flavor specific decay, two decay
  diagrams exist. For this channel ?f? f 0
  (AfA f ), leads to DfSf0, Cf1.
• ? Parameters to measure ?ms, ?G
• DsK case non flavor specific decay, 4 decay
  diagrams exist,
• time dependent CP violation. ?f? f .
• ? Parameters ?f, arg(?f), arg(? f ) to
  extract gfs, ?T1/T2
• arg(?f) ?T1/T2 - (gfs)
• arg(? f ) ?T1/T2 (gfs)
• Assume p/q1
• Only 2 unique Dsp equations
• 4 unique DsK equations

Estimated branching fraction (used for DC04
selection study)
Bs? Ds-p (3.40.7)10-3
Bs? D-sK Bs? DsK- (2.00.6)10-4 (2.20.7)10-5
36
Bs meson system
flavour eigenstates
Bs oscillations box diagrams
,
mass eigenstates
mass eigenstates time dependence
decay amplitude into a final state f
,
decay amplitudes can be written as a sum
,
strong phase keeps value, weak phase changes sign
under CP transformation
37
Bs decay equations

• f final state, Ds-p or Ds-K
• For charge conjugate final states
• B ? B ,f ? f, ?f ? ?f, Af?Af ,
• p/q ? q/p

In this project we assume p/q1
38

• 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 ?