19th July 2007CPWG1 Model independent determination of γ from B ± →D(K 0 S π + π − )K ± Jim...
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Transcript of 19th July 2007CPWG1 Model independent determination of γ from B ± →D(K 0 S π + π − )K ± Jim...
19th July 2007 CPWG 1
Model independent determination of γ from B±→D(K0
Sπ+π−)K±
Jim Libby (University of Oxford)
19th July 2007 CPWG 2
Outline
Current e+e− B-factory and LHCb status Explanation of the model independent
method Implementation to LHCb environment and
results Background Acceptance
Experimental systematic uncertainties Conclusions
19th July 2007 CPWG 3
0D
)(GeV/ 22 cm
)/GeV( 2
2
c
m
Current status of this measurement of γ
Decays of D0 or D0 to common final state gives sensitivity to γ For B+→D(K0π+π-)K+
Assume model for amplitudes
Fit D-Dalitz plots from B-decay to extract γ, rB and δB
cbV
*usV
ubV
*csV
BAKDBA )( 0 )(0)( i
BB erAKDBA
),(),(
),(),(22)(22
22)(22
mmfermmfA
mmfermmfAi
B
iB
amplitudes Dalitz ),( and massinvariant 220mmfKm S
iN
jj
ij bemmAeammf j
1
2222 ,,
)(GeV/ 22 cm
19th July 2007 CPWG 4
Current results Current measurements:
BABAR and Belle use large samples of flavour tagged D*+D0π+
events to find parameters of the isobar model Model uncertainties from assumptions about the resonance
structure in the model NB scaled to the BELLE value of rB BABAR model error is ~6°
Recent studies for LHCb showed that the model-dependent fit would yield an uncertainty on γ between 7-12° for an rB=0.1 Range represents differing assumptions about the background Uncertainties 1/rB
However, the best current model uncertainty is 10° with an rB=0.1 Without improvements LHCb sensitivity will be dominated by
model assumptions within 1 or 2 years of data taking
[BABAR] model))(12)syst(11)stat(4192(
[Belle] model))(9)syst(3)stat(53( 15183
19th July 2007 CPWG 5
Pincer movement The largest and most challenging aspects of
the model uncertainty come from Kπ and ππ S-wave Lauren Martin (CPWG 24/05/07) investigating
these issues in the model-dependent fit A model-independent method that relies on a
binned analysis of the Dalitz plot Obvious problem is that information is lost via
binning Rest of this talk will discuss this method and its
first implementation at LHCb
19th July 2007 CPWG 6
Binned method Proposed in the original paper by Giri, Grossman, Soffer and Zupan
and since been extended significantly by Bondar and Poluektov GGSZ, PRD 68, 054018 (2003) BP, Eur. Phys. J. C47, 347 (2006) BP, hep-ph/0703267
If one bins the Dalitz plot symmetrically about m−
2= m+2 number of entries in B decay given by:
)(),(),(2
),(),(
222222
2222222
iiDD
DBDi
sycxdDmmfdDmmf
dDmmfrdDmmfN
ii
ii
# events in bin of flavour tagged D0 decays
)sin()cos( BBBB ryrx
Average cosine and sine of strong
phase difference between D0 and
D0 decay amplitudes (ΔδD) in this bin
19th July 2007 CPWG 7
Binned method continued The original GGSZ paper concentrated on trying to determine si
and ci at the same time as extracting γ, rB and δB from B data 3 + 2×Nbins free parameters (ci =c-i and si =−s-i) Huge loss in γ sensitivity and not practical until you have O(106)
events (cf 2500/fb-1 @ LHCb)
However, CP-correlated e+e−→ ψ″→D0D0 data where one decay is to KSππ and the other decays to a CP eigenstate or KSππ allows si and ci to be determined KL ππ equally sensitive
CLEO-c are collecting a ~750 pb-1 sample of ψ″ data at the moment – running at ψ″ will finish later this year Analyses underway to measure ci and si
Bondar and Poluektov estimate that the uncertainties on c i and si
from this data set will lead to 3° uncertainty on γ in a model dependent fit
19th July 2007 CPWG 8
Implementation to LHCb Bondar and Poluektov show
that the rectangular binning is far from optimal for both CLEOc and γ analyses 8 uniform bins has only
60% of the B statistical sensitivity
c and s errors would be 3 times larger from the ψ″
Best B-data sensitivity when cos(ΔδD) and sin(ΔδD) are as uniform as possible within a bin
Absolute value of strong phase diff(BABAR model used in LHCb-48-2007)
Good approximation and the binning that yields smallest s and c errors is equalΔδD bins-80% of the unbinned precision
NimmNi D /)(2),(/)(2 2122
21
19th July 2007 CPWG 9
Implementation at LHCb Generate samples of
B±→D(K0Sππ)K± with a mean of
5000 events split between the charges
Bin according to strong phase difference, ΔδD
Minimise χ2
(γ=60°, rB=0.1 and δB=130°)
data] gflavour ta from [measured ),(
factorion normalizat
2),,(
bin in events )( ofnumber
)),,(()),,((
222
2
th0
8
)0(8
222
dDmmfK
h
ysxcKKKrKhhyxN
iKKDBn
n
hyxNn
n
hyxNn
iDi
iiiiiBii
Si
ii i
ii
i
ii
Bin Ki,ci and si amplitudes calculated from model
In reality from flavour tagged samples and CLEO-c No attempt to add this uncertainty yet in detail take the BP 3°
19th July 2007 CPWG 10
No background with predicted 2 fb-1 yield
5000 experiments
γ=60°, rB=0.1 and δB=130°
The four Cartesian coordinates and normalization are free parameters
All pulls are normal therefore calculate γ, rB and δB with propagated Cartesian uncertainties
19th July 2007 CPWG 11
No background with predicted 2 fb-1 yield
Model independent average uncertainty 7.7° (c.f. Model dependent 5.9°)
19th July 2007 CPWG 12
Acceptance Acceptance in each bin calculated as a weighted average of the acceptance
function used for model dependent studies I will come back to the use of D amplitudes rather than B amplitudes for this relative differences in weighted efficiency below 3×10-3 in every bin
Modifies the fit function:
Average γ uncertainty increases to 8.1°
))(08.01(1028.0),( where),(),(
2),,(
22322
22222
2
mmmm
K
dDmmmmfa
ysxcKKKrKhahyxN
i
Di
iiiiiBiii
i
19th July 2007 CPWG 13
Background 3 types of background to consider
B→D(KSππ)π (DC04 B/S = 0.24) rB O(10-3) so Dalitz plots are like D0 and D0 for B− and B+, respectively
Combinatoric (DC04 B/S<0.7) Admixtures of two types considered
1. DKcomb: real D→ D(KSππ) combined with a bachelor K Dalitz plot a even sum of D0 and D0 decays
2. PScomb: combinatoric D with a bachelor K Follows phase space
Integrate background PDFs used in model-dependent analysis over each bin, then scaled to background level assumed:
iicomb
iiiiicomb
iii
PPSN
KaKaDKN
KaDN
)(
)()(
)(
21
fractional area of Dalitz space covered by bin
19th July 2007 CPWG 14
γ uncertainties with 5000 toy experimentsScenario 2 fb-1 Mod. Indep. 10 fb-1 Mod. Indep. 2 fb-1 Mod. Dep.
(LHCb-048-2007)
No background 7.9° 3.5° 5.9°
Acceptance 8.1° 3.5° 5.5°
Dπ (B/S = 0.24) 8.8° 4.0° 7.3°
DKcomb (B/S=0.7) 12.8° 5.7° 11.7°
PScomb (B/S=0.7) 12.8° 5.5° 9.1°
DKcomb (B/S=0.35)
+PScomb (B/S=0.35)
12.7° 5.4° 9.8°
19th July 2007 CPWG 15
Systematic related to acceptance The acceptance varies over the Dalitz plane The relative acceptance in each bin can be measured using the B→Dπ
control sample with DK selection applied without bachelor K PID
With the DC04 selection expect 60k events/2 fb-1
Relative relative-efficiency uncertainty 1-3%/ΔδD bin with 2 fb-1
Increased statistics reduces error Toy MC study smearing bin efficiencies in event generation by this amount
leads to an additional 1° uncertainty without background and 2.5° uncertainty with DKcomb B/S=0.7 Small effect compared to statistical uncertainty
NB: the efficiency related to the PID of the bachelor π/K can be factored out and will be determined from the D*→D(Kπ)π data to better than one percent-ignore at present
))D(KN(B),(),( 0
S
22222
i
i
i
Di KK
dDmmmmfa i
19th July 2007 CPWG 16
Asymmetry in efficiency in Dalitz space Concern was raised a while ago about
asymmetries in the efficiency across the Dalitz plane i.e. ε(m2
+, m2 −)≠ε(m2
−, m2 +)
Generated with the efficiency biased relative to one another by up to 10% depending on whether the event had m2
+>m2 − or m2
+<m2 −
Significant biases on x± and y± but they effectively cancel in determination of γ
Maximum bias on γ induced was 0.5° for 10% relative effect and full background
19th July 2007 CPWG 17
Resolution ΔδD binning has some narrow regions in
Dalitz space Preliminary investigation of how
resolution on the Dalitz variables might affected the extraction of γ
Assumed a 10 MeV2/c4 resolution on Dalitz variables and generated toy experiments with this smearing
Found that this led to a few bins with largest (red) and smallest (dark blue) phase difference having a 2-3% relative changes in expected yields due to resolution induced migration
Fit results on toy experiments where resolution included in generation but ignored in fit found no significant bias (<0.5°) on γ Cartesian coordinates exhibit bias but
cancels in extraction of γ
19th July 2007 CPWG 18
Background fractions Combinatoric background rate will be determined
from B and D mass sidebands which will cover at least 2-3 times the area of the signal region Use 10× in DC04 background studies but this will probably
be unrealistic with data If background distributions relatively flat in masses
one can estimate that this leads to B/S will be determined absolutely to around 0.01 or better
Toy studies suggest that there is no impact on γ precision with this kind of uncertainty
Maybe complications depending on Dalitz space distribution of the PS background but can only speculate until we have the data in hand
19th July 2007 CPWG 19
Conclusion Implemented model independent fit
with binning that yields smallest error from exploiting CLEO-c data Binning depends on model - only consequence
of incorrect model is non-optimal binning
Such a measurement will be better than model dependent method after one year of data taking if we can not improve the model error 10 fb-1 statistical uncertainty 4-6° depending on background assumptions
Experimental systematic uncertainties considered can be controlled from data Acceptance determined from B→Dπ sample will contribute ~2.5° with
2 fb-1
Liaison required with CLEO-c to get common binning and to best understand all uncertainties related to the ψ″ data Some further scope to optimise binning for combined statistical
sensitivity
Model independentModel dependent
σ(model)=10°
σ(model)=5°