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Report Proper Time

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Report Proper Time & Mixing. Measuring fs including acceptances. Tristan du Pree, Nikhef ... Described by St phane T'Jampens (thesis) ... – PowerPoint PPT presentation

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Title: 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
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