Title: Report Proper Time
1Report Proper Time MixingMeasuring fs
including acceptances
- Tristan du Pree, Nikhef
- 14 March 2007
- LHCb week, CERN
- Physics Session
2Outline
- Optimizing Bs?J/??
- Dima Volyanskyy
- Trigger induced lifetime acceptance
- Jonas Rademacker, Vladimir Gligorov
- Bs?J/?? with angular acceptances
- Background subtraction
- Jon Imong
3Measuring 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
4Smaller BR J/?? BR depends on ss content
7.66 10-6 10.2
10-6
5Photon select on angle(?,?0)
?(?,?0) lt 8
6Final selection
After 23M different sets of cuts, maximizing
S/sqrt(SB)
Better to cut on lifetime than on IP
7Resolution better than J/??Acceptance very steep
rise
lts(trec)gt 25.4 fs
8Toy-MC s(fs) 0.08 rad
lts(fs)gt0.072 rad
lts(fs)gt0.087 rad
Same toy as Luis, Benjamin, Sergio
Dima Volyanskyy
9Summary 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
10A proposed method to reconstruct lifetime
acceptance effectsinduced by the trigger
- Jonas Rademacker (Bristol) Vladimir Gligorov
(Oxford)
11The 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
12Correcting for the bias
direction of B
Acceptance
Jonas Rademacker, Vladimir Gligorov
time
13Average 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
14Summary 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
15Angular acceptance in Bs?J/??Tristan du Pree,
Gerhard Raven, Loek Hooft van Huysduynen
- Determining fs
- Fitting with acceptance
- Normalization functions
- Toys
fs?
16Introduction 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
17Extreme 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
18The 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
19Bs ? 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
20Including 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
21In 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
22Normalization 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
23Toy 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
24Angular, 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
25Check 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
26With 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
27Realistic 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
28Fits 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
29Summary 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!
30Likelihood fitting with background
31Describing background
32Subtracting background
Pseudo Log Likelihood
S
S
33Error recalculation
Used at Babar, CDF
34Pull toy-MC
Uncorrected error s(pull) 1.330.07
Corrected error s(pull) 1.040.05
35ConclusionsDetermining 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
36Backup
37Dependence 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
38fs vs A? (Loek)
- For A? 0.2
- 10 in A? 7 in fs
Overestimation A? ? Overestimation fs
39Pros 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/? ?
40Bs?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
41Angular 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
42Transversity frame
- CP(J/?KK-)(-1)?(J/?)1
- Transversity t(J/?KK-) ?(J/?) spin projection
on z - For Bsbar some signs flip (especially terms with
?)
43Reco 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
44Possible 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
45DaVinci
- 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
46Angular 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
47Fitting procedure (in short)
- Distribution
with acceptance - Fitting solve
- Equivalent to
48Fitting with acceptance
- Acceptance e might be angle dependent (O)
- Normalization changes
- Fitting (likelihood maximization)
49Normalization
- 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
50Normalization 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
51300 fits with single small ?i-set
- In 0.16 out 0.18
- Large pull
52Other 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
53NB
- ?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!
54LHCb resolutions 10 times as bad
- Fit Aperp 0.15100.0007
- ltpullgt -0.850.06
- s(pull) 1.060.04
- BIAS!
55Backup
- Plotting toy acceptances
- (M prod events)
56Plotting with acceptance
- Using Legendre polynomials
57Plotting 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!
58Plotting 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
59Plotting 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
60Example 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.
61Other acc toy examples
- acc(1cos?)
- e05.0 105
- e13.0 105
- egt1O(103)
- acc flat
- e01,6 106
- egt0O(103)
62What 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
63Example 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.
64Different orders
1st
- So in this extreme case we need higher orders
- Depends on specific shape acceptance
- We expect a less sharp shape
65Summary
- 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
66Backup new EvtGen model
- Code PVVCPLH
- Full-ang time-dep fits to Gauss-data
67Code 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
68Corrections 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
69Standard 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)
70Negative ??
- Right values
- tauHlttauL
- Component CP-odd smaller
71After EvtGen presentation
- DØ now investigates new model PVV_CPLH