Report Proper Time

1
Report Proper Time MixingMeasuring fs
including acceptances

• Tristan du Pree, Nikhef
• 14 March 2007
• LHCb week, CERN
• Physics Session

2
Outline

• Optimizing Bs?J/??
• Dima Volyanskyy
• Trigger induced lifetime acceptance
• Jonas Rademacker, Vladimir Gligorov
• Bs?J/?? with angular acceptances
• Background subtraction
• Jon Imong

3
Measuring fsCPV in the mixing for b?ccs

• Bs?J/??
• Smaller BR
• Pure CP-eigenstate
• ACP sinfssin?mst
• No angular analysis

• Bs?J/??
• Larger BR
• Mixture CP-eigenstates
• ACP (1-2A?)sinfssin?mst
• Angular analysis required

4
Smaller BR J/?? BR depends on ss content
7.66 10-6 10.2
10-6
5
Photon select on angle(?,?0)
?(?,?0) lt 8
6
Final selection
After 23M different sets of cuts, maximizing
S/sqrt(SB)
Better to cut on lifetime than on IP
7
Resolution better than J/??Acceptance very steep
rise
lts(trec)gt 25.4 fs
8
Toy-MC s(fs) 0.08 rad
lts(fs)gt0.072 rad
lts(fs)gt0.087 rad
Same toy as Luis, Benjamin, Sergio
Dima Volyanskyy
9
Summary J/?? Dima Volyanskyy

• Selection cuts optimized
• Annual yield 3.6k - 4.8k
• Average proper time resolution 25.4 fs
• Very steep proper time acceptance
• After one year s(fs) 0.08 rad
• LHCb note will be published soon

10
A proposed method to reconstruct lifetime
acceptance effectsinduced by the trigger

• Jonas Rademacker (Bristol) Vladimir Gligorov
  (Oxford)

11
The trigger bias

• The L1 trigger introduces an acceptance bias
  through IP cuts
• The proposed method, in use at CDF, corrects for
  this on an event-by-event basis
• It does not require either a lifetime cut-off or
  an assumed MC-acceptance curve to work.

inaccessible
lifetime/ps
Data After Trigger
Example acceptance function
lifetime/ps
lifetime/ps
Jonas Rademacker, Vladimir Gligorov
12
Correcting for the bias
direction of B
Acceptance
Jonas Rademacker, Vladimir Gligorov
time
13
Average acceptance function signal fit Full MC
Sample Size 10.2k Sample type Signal
chi2/ndof 1.42 chi2 prob 4
lifetime/microns
fitted value 1.542 0.018 ps generator value
1.534 ps
Heidelberg 13th September 2006
13/16
14
Summary time acceptanceJonas Rademacker,
Vladimir Gligorov

• Idea vary the parameter of interest (here time)
  and thus reconstruct the acceptance
• Method works
• Difficult to maintain unless integrated with
  trigger software
• There is an active collaboration between physics
  and trigger group
• Work is ongoing

15
Angular acceptance in Bs?J/??Tristan du Pree,
Gerhard Raven, Loek Hooft van Huysduynen

• Determining fs
• Fitting with acceptance
• Normalization functions
• Toys

fs?
16
Introduction determining fs

• Time-dependent CPV fs
• for Bs?J/??
• A? fraction CP-odd
• A? reduces amplitude oscillation, so influences
  estimation fs
• Very important to know value A? and error
• Perform angular analysis

17
Extreme acceptance example

• CP-even (1-A?)(1-cos2?) CP-odd A?cos2?
• ? transversity angle
• Imperfect acceptance (e.g. thick line left)
• A?(PDG ) ? fraction CP-odd (right) to determine
  fs
• You want to know the real and measured fraction
  CP-odd

18
The problem in words

• Amplitude distribution is angle dependent
• We determine A? by analyzing the angular
  distribution
• An angular acceptance will change the angular
  distribution
• The acceptance will cut differently on CP-even
  and CP-odd (since they are distributed
  angle-dependent)
• Solution
• Find functions which weigh the different refused
  fractions of the different CP-even and CP-odd
  distributions

19
Bs ? J/?(µµ-) ?(KK-)without acceptance

• Four-body decay, described by 3 angles Oi
• Note angles in decay frame (not wrt detector)
• 3 final CP-states with amplitudes Aj
• Angular and amplitude dependence factorize in
  distribution g
• (e.g. (1-A?)(1-cos2?)
• A?cos2? )
• Normalized pdf

20
Including acceptance in fit

• Fitting with acceptance e(O)
• So when we maximize the likelihood
• The exact shape of e(O) is irrelevant
• The weights ?i take into account the acceptance
  of every amplitude function

?i Integrated efficiency per amplitude
21
In case the previous was not clear

• Take c and e out of logarithm (A-independent)
• Take hi out of normalization integral
  (O-independent)
• Rewrite integral as sum

The measure events are generated according to
gdO in MC. gdO is chance to get certain O ?write
as sum
boolean
normalization constants
22
Normalization weights

• In practice
• Dont need the exact shape of the acceptance!
• Determine weights ?i from MC
• Fit data with normalization hi?i
• Fast and simple!
• Note
• Independent of Ai
• ?i only needed to know up to constant
• Easy to generalize to time-dependent case
• For reference
• Described by Stéphane TJampens (thesis)
• https//oraweb.slac.stanford.edu/pls/slacquery/BAB
  AR_DOCUMENTS.DetailedIndex?P_BP_ID3629 (French)
• Used in BaBar analyses
• hep-ex/0107049, Phys.Rev.Lett. 87 (2001) 241801
• hep-ex/0411016, Phys.Rev. D71 (2005) 032005

23
Toy mcs

• Approach
• Acceptance toy block-function
• Determine Fs once,
• with a large first sample (M events)
• Fit the other 500 samples of 10K events with this
  normalization
• Input value in MC
• A? 0.16

• Later
• Determine Fs with different A?s
• Include resolution

24
Angular, time-integrated fits

• Fit A? 0.16010.0005
• s(A?) 0.01150.0004
• ltpullgt 0.000.05
• s(pull) 1.030.03
• Note large sample needed to determine ?s

0.16
25
Check A? simulation ? A? data

• ?s in theory independent of used As, depend
  only on acceptance
• You dont want the ?s to depend on the real
  value of A?!
• So this method is robust!
• As long as one determines the normalization
  consistently with the A? one used for the
  simulation, one can use this method.
• Also if the value of A? in the simulation does
  not equal the A? in reality

26
With angular resolution

• With angular resolution R(O,O)
• Resolution changes O-dependence pdf,
• so changes normalization integral,
• so changes ?s
• So resolution changes maximization
• Resolution should be good (d-like) enough to
  still use normalization trick

27
Realistic resolutions

• Resolutions from full MC DC04 study
• s(?)0.02 rad s(f)0.02 rad s(?)0.015 rad
• Resolutions R(O,O)R(O-O)
• Same angular efficiencies as before

28
Fits with realistic resolutionsand toy acceptance

• Fit A? 0.16030.0007
• s(A?) 0.01170.0005
• ltpullgt 0.010.06
• s(pull) 1.060.04
• Also works for twice as bad resolution for this
  acceptance

29
Summary angular acceptance in J/??

• Correct A? important for determination fs
• Fitting with nontrivial acceptances works
• Good angular resolution needed
• Can be used without knowledge of true A?
• Use a large MC sample to determine the ?s
• The simulation should simulate acceptance
  realistically
• B0?J/?K(Kp) also S?VV, more data
• Check these points by measuring A? in B0?J/?K!

30
Likelihood fitting with background

• Jon Imong (Bristol)

31
Describing background

32
Subtracting background
Pseudo Log Likelihood
S
S
33
Error recalculation
Used at Babar, CDF
34
Pull toy-MC
Uncorrected error s(pull) 1.330.07
Corrected error s(pull) 1.040.05
35
ConclusionsDetermining fs with acceptances

• J/?? needs no angular analysis to find fs,
  s(fs) 0.08, steep time acceptance
• Method to reconstruct proper time acceptance in
  progress
• Working method to take into account angular
  acceptance J/??
• Angular acceptance method still usable with
  background by using pseudo log-likelihood

36
Backup

• Bs?J/??

37
Dependence f on Aperp

• (1-2Aperp)sinf const
• gtsin f const/(1-2Aperp)
• dsinf/dAperp
• 2const/(1-2Aperp)2
• 2sinf/(1-2Aperp)
• ?sinf/sinf
• 2 ?Aperp/(1-2Aperp)
• f ?Aperp/Aperp

• Sanity checks
• Aperp1/2 sinf infinetely sensitive, since no
  oscillation
• Aperp0 sinf insensitive, since no dilution by
  Aperp

38
fs vs A? (Loek)

• For A? 0.2
• 10 in A? 7 in fs

Overestimation A? ? Overestimation fs
39
Pros and cons

• Advantages
• Branching ratio (93)10-4 relatively large
• 2008 a lot of Bs-mesons
• Bs L sbb b?Bs 51032cm-2/s 500µb 10
  1011y-1
• Bs (Bs?J/?f) (J/??µµ-) (f?KK-)
• gt 1011 10-3 6 50 gt millions per
  year! (2x incl Bsbar)
• Theoretically clean
• No SM pollution (penguins suppressed), small
  uncertainty
• SM-phase very small gt new processes involved
  easy to recognize
• But especially J/?f?µµ-KK- easy to
  reconstruct
• Oscillations should be no problem to measure
• DISADVANTAGE
• Mixture of different CP-eigenstates (large
  statistics, angular res/eff needed)
• Study angular distribution ( angular res/eff)

Bs?J/? ?
40
Bs?J/?f

• Feynman diagram similar to Bd?J/?Ks
• (used for sin2ß)
• CP-asymmetry in interference mixing and decay
• Final state is CP-eigenstate
• ACP
• 
  
• 
  
  
• Advantage J/?f direct decay in two charged
  leptons
• Disadvantage endproducts both vector mesons, so
  mixture of CP-eigenstates
• G(Bs ? f) - G(Bsbar ? f) ACP?(angles)
  fraction ? as function of spatial angles
• Angular analysis like B?J/?K

2
2
-
cc

sin2? sin?mst
? ?SM ?NP
41
Angular distribution
e.g. hep-ph/9804253

• Bs?J/?f is P ?VV
• spin Bs 0, so two daughters in B-frame equal
  (but opposite) helicities
• spin J/?, f 1
• f ? KK- spin 0s,
• J/? ? µµ- no a0
• Decay amplitude
• Angular distribution
• Now take all possible combinations and just fill
  in

42
Transversity frame

• CP(J/?KK-)(-1)?(J/?)1
• Transversity t(J/?KK-) ?(J/?) spin projection
  on z
• For Bsbar some signs flip (especially terms with
  ?)

43
Reco decay topology boosts
?
?
K

• Lorentz transformations do not form a group
• Lx,Ly-iRz ?? L(v3 ) RL(v2)L(v3)
• So always boost via Bs!

?-
Bs
J/?
?
1cm
K-
Bs-frame
K
?-
K-
Bs
lab-frame
J/?-frame
?
is rotated!
lab
?
Bs
L boost R rotation
44
Possible cause acceptance

• Extreme backboost
• Particles decaying in the direction opposite to
  the direction of the flying B, might get
  reconstructed worse because of their lower
  momentum in the lab-frame

45
DaVinci

• Can study mc-particles and reconstructed
  simulation
• From sharp peak reco we can already see very good
  resolution
• Proper time resolution
• double Gaussian, s 0.03 ps

reco
mc
46
Angular resolution

• Problem angles boosted in labframe
• Advantage boost everything in detector
• Maybe disadvantage for angular analysis
• sphi 6, 31 mrad spsi
  19 mrad stheta
  6, 24 mrad
• Even less than one tenth of these red lines

phi
47
Fitting procedure (in short)

• Distribution
  with acceptance
• Fitting solve
• Equivalent to

48
Fitting with acceptance

• Acceptance e might be angle dependent (O)
• Normalization changes
• Fitting (likelihood maximization)

49
Normalization

• Three tricks to easily include acceptance
• Maximalization independent of A-independent
  terms, so take these terms out
  of logarithm
• Norm integral independent of O-independent terms
  hi, so take these terms out of integral
• Rewrite integral to sum
  this sum we can
  determine with MC

50
Normalization functions

• Normalization method
• Fast and simple (with MC)
• No analytic description of efficiency needed
• For reference
• Described by Stéphane TJampens (thesis)
• https//oraweb.slac.stanford.edu/pls/slacquery/BAB
  AR_DOCUMENTS.DetailedIndex?P_BP_ID3629 (French)
• Used in BaBar analyses
• hep-ex/0107049, Phys.Rev.Lett. 87 (2001) 241801
• hep-ex/0411016, Phys.Rev. D71 (2005) 032005

51
300 fits with single small ?i-set

• In 0.16 out 0.18
• Large pull

52
Other samples(Every first dataset has a
different random seed)

• One establishes ?i with first sample
• Apparently fit very dependent on random first
  sample
• Typical error Aperp 0.016
• Might influence estimation fs same order
• One then should establish (MC or theory) this
  error

53
NB

• ?s are independent of amplitude with which you
  generate, but they do depend on the specific
  sample with which you determine the ?s.
• When one determines the ?s on a datasample which
  has amplitudes Ai, but one thinks it are Bi,
• when using these ?s and trying to establish Ci,
  
• one will find Ci?Ci
• In other words
• It is very important to know what has been put
  into the simulation with which you establish the
  ?s.
• If you calculate the ?s with different Ais than
  you put in,
• IT GOES WRONG!

54
LHCb resolutions 10 times as bad

• Fit Aperp 0.15100.0007
• ltpullgt -0.850.06
• s(pull) 1.060.04
• BIAS!

55
Backup

• Plotting toy acceptances
• (M prod events)

56
Plotting with acceptance

• Using Legendre polynomials

57
Plotting problem

• With normalization constantsplot of fit not
  correct
• The constants give correct weight for total
  acceptance to fit
• But they are not enough information to plot
• We need more information to recover the shape of
  the acceptance
• ...Fitting is easier than plotting!

58
Plotting method

• Similar to fit method
• Write acceptance e ?i eiBi
• Choose orthonormal basis Bi
• e.g BnPnsqrt(2n1)/2 PnLegendre
  polynomials
• Then plot ? gacc g?i eiBi

59
Plotting example

• Toy example acc(2cos?-cos2?)/4
• Estimated
• e0/e0 1, e1/e0 0.35, e2/e0-0.18, egt2/e0O()
• Calculated
• e0 1, e1 0.35, e2 -0.18, egt20

60
Example block function (7th order)(als het lukt
het middelste plaatje veranderen)

• e0/e0 1 , e1/e0 0.34, e2/e0 -0.26,
• e3/e0 0.11, e4/e0 0.04,
• So here higher orders not negligible
• (but we expect less sharp acceptance)

?
Reconstructed block acc.
61
Other acc toy examples

• acc(1cos?)
• e05.0 105
• e13.0 105
• egt1O(103)
• acc flat
• e01,6 106
• egt0O(103)

62
What is needed?

• We want each B meson candidate reconstructed in
  DaVinci to have an associated trigger acceptance
  function
• In order to do this, the online trigger needs to
  be run many times on each event, to allow
  swimming of the event
• We need to be able to call the trigger from
  within an algorithm, passing the particles and
  primary vertices on which to trigger and
  retrieving the decision
• A DaVinci tool, acting as an interface to the
  trigger, seems the most flexible way to do this
• We also need a new class which contains the
  information on the acceptance function

Jonas Rademacker, Vladimir Gligorov
63
Example block function (4th order)

• e013 105, e14.4 105, e2-3.4 105,
• e31.4 105, e40.5 105
• So here higher orders not negligible

Reconstructed block acc.
64
Different orders
1st

• So in this extreme case we need higher orders
• Depends on specific shape acceptance
• We expect a less sharp shape

65
Summary

• Fitting with nontrivial acceptance works
• Good resolution needed
• Use large sample to determine ?s
• Watch the input amplitudes!
• We have a working plotting method
• Order depends on shape acceptance
• Whats next
• Determine real acceptance with DaVinci

66
Backup new EvtGen model

• Code PVVCPLH
• Full-ang time-dep fits to Gauss-data

67
Code EvtPVVCPLH (vs SVVCPLH)
Calls this
wrong
Old, did not take into account tauH
if(mixed) mother-gtsetLifetime(t)
The new one does
General for positive and negative ???
Its an amplitude, not a rate!
Now the right exponents
And the right conversion
68
Corrections PVVCPLH wrt SVVCPLH

• Minor correction ?ms removed as argument
• (could get defined twice useless and dangerous)
• Lifetime generation with correct ?long (?H)
• General ?? (also negative)
• Formulas transversity amplitudes
• Transformation from TransAmp to HelAmp

69
Standard values (amps B?J/? K)

• Fit can also return standard values with 14k
  events
• Input a0 0.6, a? 0.16, ? ?2.50?? , ?H
  1.54, ?L 1.39

(large t)
(Large t)
70
Negative ??

• Right values
• tauHlttauL
• Component CP-odd smaller

71
After EvtGen presentation

• DØ now investigates new model PVV_CPLH