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Approval Presentation, 17.08.11

Motivation for Measurement

- The final state Ds-K+ is accessible by both Bs and Bs:

- Both diagrams are similar in magnitude, hence large interference between them is possible.
- Using flavour tagging, we can measure four decay rates
- Bs or Bs to Ds+K- or Ds-K+
- From these rates, γ can be extracted in an unambiguous and theoretically clean way.
- A review of the γextraction can be found in e.g. LHCb note 2007-041.

Branching Ratio Strategy

- A reliable extraction of γ requires a considerable amount of data
- Aim is to present first γ measurement from Bs→DsK at Moriond 2012.
- First step towards measuring γ is to observe Bs→DsK in our data, and measure its branching ratio (BR) relative to Bs→Dsπ.
- Most systematics cancel in the ratio
- Main differences between the modes are the bachelor PID requirements and the smaller Bs→DsK yield.
- Analysis strategy for the relative BR measurement follows that used for the hadronic fd/fs measurement from 2010 data.
- Independently, the hadronic and semileptonic fd/fs measurements from 2010 data can be combined to extract BR(Bs→Dsπ). This is then used to measure BR(Bs→DsK) absolutely.

Current Experimental Status: DsK

- PDG value is BR(Bs→DsK) = (3.0 ± 0.7)*10-4(23% relative error)
- Calculated by rescaling Belle(*) measurement: BR(Bs→DsK)= (2.4 +1.2/-1.0(stat)± 0.3(syst) ± 0.3(fs) )*10-4. This uses 7±3 signal events.
- In addition, CDF(**) measures BR(Bs→DsK)/BR(Bs→Dsπ) = 0.097 ± 0.018 ± 0.009 with ~100 DsK candidates, using a combined mass-PID fit.

Bs→DsK

Belle

Bs→Dsπ

CDF

(*) PRL 102 021801

(**) PRL 103 191802

Current Experimental Status: Dsπ

- BR(Bs→Dsπ) = (3.2 ± 0.5)*10-3(16% relative error), from combining
- Belle(*): (3.67 ± 0.34(stat)± 0.43(syst) ± 0.49(fs) )*10-3 with 160 events
- CDF(**) : (3.03 ±0.21(stat)± 0.45(syst) ± 0.46(fd/fs) )*10-4with 500 events

Belle

CDF

(*) PRL 102 021801

(**) PRL 98 061802, rescaled to new BR(Bd→Dπ)

What about LHCb?

- Today we are requesting approval of preliminary results for BR(Bs→DsK)/BR(Bs→Dsπ), BR(Bs→Dsπ) and BR(Bs→DsK).
- We plan to write a paper in the very near future.
- Plots for approval are marked with

For Approval

Data Sample and Trigger/Stripping

- The analysis uses ~336pb-1 of 2011 data.
- Trigger requirements are
- L0: Hadron TOS or Global TIS
- HLT: HLT1Track and HLT2 Topo BBDT TOS (2,3 or 4 body)
- Stripping lines from B2DX module (with D2hhh)
- No PID is used, to allow inclusive selection of all the relevant modes
- Relative efficiency of reconstruction, trigger and stripping is checked on MC that has been reprocessed with a 2011 TCK (0x006d0032)
- Results on later slides

Offline Selection: BDTG

- For the 2010 fd/fs analysis, TMVA was used to check the performance of different provide classifiers as an offline selection, using kinematic and geometrical variables
- Role of the MVA is to minimise combinatorics (not physics backgrounds)
- The best performing MVA was the Boosted Decision Tree with Gradient boosting (BDTG).

- In the current analysis, the 2010 BDTG is retained, but optimal cut is re-evaluated
- Optimal working point need not be the same, as the trigger has changed

- Re-optimisation for 2011 is performed using 10% of the Bs→Dsπ data (uniformly distributed in time)

BDTG (Re-)Optimisation

- Figure of merit is

- Here, B refers to combinatoric bkg only, and 1/14 is the expected Cabibbo suppression factor between Bs→Dsπ and Bs→DsK.

- Choose start of significance plateau (BDTG>0.1) as our working point.
- This cut loses 6% of signal, for a background reduction of 45%.

PID Calibration

- Correctly calibrating the PID cut efficiencies is crucial for this analysis.
- Extensive use is made of the tools developed by the RICH group.
- The D* (for K and π) and Λ (for proton) calibration samples are binned in momentum and pT, and the resulting efficiency map is used to weight signal events.

- Magnet Up and Magnet Down data are calibrated separately
- PID performance is not constant in time, as RICH calibration needs to be propagated to the more recent data
- Separation between K and πis poor above 100GeV, hence apply a cut of p<100GeV on the bachelor.

K eff

π misID

Example: DLL(K- π)>5 (1D binning for visualisation)

PID Cuts: D Daughters

- For the moment, only the Ds→KKπ mode is considered
- Other modes could be added in the future
- To obtain clean samples of Bs→Dsh, PID cuts need to be applied to the D daughters to suppress Bd→D+h and Λb→ Λch.
- Hence on the Ds+→ K-K+π+ candidate we require:
- DLL(K- π) > 0 for the K- and DLL(K- π) < 5 for the π+ (to suppress combinatorics)
- DLL(K- π) > 5 for the K+ (to suppress D+ →K-π+π+)
- DLL(p-K) < 0 for the K+ (to suppress Λc+ →K- p π+)
- K+ failing DLL(p-K) < 0 are retained if Kpπ mass is outside the Λc mass window
- Applying these cuts and a mass window of [1944,1990]MeV gives:
- Efficiency of 78% for Bs→Dsπ (using momentum distributions from MC),
- MisID of 1.2% for Bd→D+π(using momentum distributions from data),
- MisID of 1.7% for Λb→ Λcπ (using momentum distributions from MC).

Bs→Dsπ Purity after PID Cuts

- After these cuts, the Bs→Dsπ peak is rather pure

PID Cuts: Bachelor

- For the Dsπ fit, a cut of DLL(K-π)<0 is applied, to eliminate any residual contamination from DsK.
- A hard cut of DLL(K-π)>5 is applied before doing the DsK fit, to suppress the favoured Dsπ mode.
- As a cross-check, DsK fit is also done with a loose cut of DLL(K-π)>0, and a very tight cut of DLL(K-π)>10.
- The efficiencies of these cuts, applied after the p<100GeV cut, are:

Efficiency Ratios from MC

- Ratio of generator level efficiencies is found to be 1.027±0.010. Until the reasons for this are understood, the 1.027 is used as a correction factor, and a systematic of 2.7% is applied.

- Ratio of efficiencies for reconstruction, trigger, BDT cut and upper momentum cut on the bachelor is 1.03±0.01. This correction factor is applied, and the associated systematic is conservatively set to 3%.

Signal Lineshapes

- The B mass uses the D(s) mass constraint (improves resolution).
- Different shapes are tested on the MC signal samples.
- Deafult shape is double Crystal Ball, with common mean & sigma
- Radiative tail is smaller for modes with bachelor K than bachelor π.

Bs→Dsπ

Bs→DsK

MisID Background Shapes

- The physics bkgs to the different modes often involve misidentified hadrons. So getting the misID’d mass shapes correct is important.
- Example: the shape for Dsπ bkg to DsK is obtained as follows:
- Firstly, a clean sample of Dsπ is extracted from the Dsh data by applying DLL(K-π)<0 on the bachelor
- This cut biases the bachelor momentum, however the original momentum distribution can be recovered from the whole Dsh sample
- This works because the Dsπ and DsKbachelor momenta are very similar
- Then the mass is recomputed under the DsK hypothesis
- Next, the shape is weighted according to the momentum spectrum of the misidentified bachelors
- This from the original momentum distribution and the misID rate as a function of momentum

MisID Background Shapes

- The shape for Dπ bkg to Dsπ is obtained in a similar way, changing D daughter mass hypothesis instead of the bachelor.
- The shape for the DKbkg to DsK should be the same as the Dπ bkg to Dsπ.

- The shapes for Dsπ and Dπ under the DsK are sufficiently similar that in the fit only the Dsπ shape is used

Under the DsK mass hypothesis

An Incidental Discovery…

- A bump was seen in the DsKfit at around 5500MeV, that was not described by the misidentified Dsπ shape.
- The bump was investigated, and it turned out to be Λb→Dsp!

A peak is also seen at lower mass, compatible with Λb→Ds*p

- A peak is seen at the Λb mass after switching to the Dsp mass hypothesis, applying extremely tight PID cuts (DLL(p-π)>10 and DLL(p-K)>15) on the bachelor, and tightening the BDT cut.
- In the future a measurement will be made of the BR of this mode, but for now…

Λb→Ds(*)p ShapeUnder DsK

- Cutting on DLL(p-K) would lose too much signal, so we must live with this background, and model its shape.
- The shape is taken from simulated events, after reweighting for the efficiency of the DLL(K-π)>5 cut as a function of momentum.
- The Λb→Ds*p shape is obtained by shifting the Λb→Dsp shape down by 200MeV. As a baseline, the relative amount of Λb→Dsp and Λb→Ds*p is assumed to be the same.

- The amount of Λb→Dsp in the DsK fit is estimated by taking the 24 events from the previous slide, and correcting for the efficiency of the tight PID cuts and the BDTG cut.
- This gives an expectation of ~150 events (Λb→Dsp + Λb→Ds*p)

Λb→Dsp plus Λb→Ds*p

Partially Reconstructed (and other) Bkgs

- For partially reconstructed physics bkgs, the shapes are taken from MC, with data-driven momentum reweighting applied where a misidentification is involved. PDFs are made using RooKeysPDF.

- One final type of physics background needs to be considered: charmless modes such as Bs→K*KK
- These can appear if no cut is applied on the flight distance of the D from the B vertex
- They can peak under the signal
- To remove such backgrounds, a soft cut of FDχ2(D from B) > 2 is applied. This will have the same efficiency for Bs→Dsπ and Bs→Dsπ, so will not affect the ratio of BR’s.

Combinatoric Background Shape

- The slope of the combinatoric background can floated in the Dsπ fit.
- However it must be fixed in the DsKfit, due to the low statistics and the presence of the misidentified Bs→Dsπ in the right-hand sideband.
- Fitting to wrong-sign (same-sign D and bachelor) events passing the DsK selection and PID cuts, the slope is compatible with being flat.

- As a cross-check, the wrong-sign events passing the Dsπ selection are also fitted, and the slope agrees well with that found in the Dsπ signal fit.

DsK wrong-sign

Splitting by Magnet Polarity

- Since the PID efficiencies vary slightly between MagUp and MagDown, the misID background shapes change.
- In addition, the signal mean is found to shift by ~1MeV between MagUp and MagDown.
- So we split the data by polarity, and fit the two subsamples independently.
- About 55% (45%) of the data is MagDown (MagUp).
- In the following slides, the MagDown fit is on the left, and the MagUp on the right.

Recipe for Dπ Fit

- This fit is needed to estimate the amount of background Dπ to Dsπ, and to check the mean and sigma of the signal shape with high statistics.
- The tails of the signal mass shape are fixed from the MC fit, but the mean and sigma are floated
- Mean and sigma are allowed to be different for MagUp and MagDown
- The yields of all components are left free.
- The slope of the combinatoric background is also floated in the fit.

Recipe for Dsπ Fit

- The expected number of misID Bd→Dπ is calculated using the fitted Dπ yield, a mass window factor (from MC), and misID from the PID calibration tools.
- It is constrained to be within 10% of this estimate
- The misID Bd→Dπ shape is also reweighted to take misID curve vs momentum into account.
- The signal width is fixed to that found in the Bd→Dπ fit, scaled by the ratio of widths for Bs→Dsπ and Bd→Dπ in the MC
- Signal mean and comb background slope are floating.
- A Λb→ Λcπcomponent was allowed in the fit, but got fitted to zero.
- Some Bd→Dsπ can also be seen
- re-use Bs→Dsπ mass shape, and constrain yield to {known BR ratio*fd/fs} = 1/35 relative to Bs→Dsπ yield.

Recipe for DsK Fits

- The amount of misID Bs→Dsπ background is floated
- Provides x-check on misID rate estimate
- Any Bd→Dπshould be taken care of by the Bs→Dsπ shape
- Treatment of signal shape is the same as for Bs→Dsπ
- Comb background slope is fixed to be flat (from wrong-sign)

- Amount of Bd→DKisconstrained from the Bd→Dπ under Dsπ, using the Bd→DK/Bd→DπBR ratio
- Relative yields of PartReco backgrounds are constrained using
- Relative reconstruction efficiencies (from MC) when e.g. a charged track or soft pion/photon is missed
- Bs branching ratios from Bdbranching ratios, using SU(3) symmetry
- The yields can ove by 33% from these estimates
- TheBd→DsKyield is floated. The Bs→DsKand Bd→DsKshapes are the same.

- Amount of Λb→Ds(*)p is constrained as detailed earlier.

Remark on Bd→DsK

- While this component is clearly visible in the DsK fits, the amount of background underneath it makes a reliable fit to its yield very difficult, at least with the current dataset.
- Hence we cannot make a competitive measurement of its BR (error in PDG is ~13%).

Systematics Menu for BR Ratio

- Ratio of trigger/stripping/(non-PID) selection efficiencies from MC
- Fit model systematics will be evaluated using a large number of toy fits (as was done for fd/fs analysis).
- But for the moment, we simply apply cross-checks on the data, and assign conservative systematics.
- For the PID, take systematic on efficiency curves quoted by the RICH group, evaluated at our cut values
- PID systematic can enter in three different ways:
- Final PID efficiency correction to obtain BR(DsK)/BR(Dsπ)
- Shape of misID bkgs after reweighting
- Expected number of Dπ/K under Dsπ/K (constrained in the fit)

Systematics Budget for BR Ratio

- The fit model systematic for DsKis the most involved part of the systematics calculation.
- The main contributions to this part are:
- The slope of the combinatoric is fixed to half of the Dsπ slope. This reduces the signal yield by 3%.
- The constraints on the partially reconstructed backgrounds are all varied by a factor of two. This changes the signal yield by ±4%.
- Also, the ratio of the Λb→Ds*p component to the Λb→Dsp component was varied by a factor of two. The change to the signal yield is <0.5%.

Results: BR(Bs→DsK)/BR(Bs→Dsπ)

- Averaging MagUp and MagDown, we get
- N(DsK) = 406±26, N(Dsπ) = 6038±105
- εPID(DsK) = 83.4±0.2%, εPID(Dsπ) = 85.0±0.2%
- εsel(Dsπ)/ εsel(DsK) = 0.945± 0.014
- We obtain

Extraction of BR(Bs→Dsπ)

- Basically we turn the 2010 fd/fs combination on its head, by combining the ratio of yields of Bs→Dsπ and Bd→Dπ from the hadronic analysis, and the fd/fs value from the semileptonic analysis

Input:

Output:

Results: BR(Bs→DsK)

- Combining these two results, we obtain

- This agrees with the Belle result, but is significantly below the CDF result.

Conclusions

- Using 2010 data we measure
- With 336pb-1 of 2011 data we measure
- These are combined to yield
- These are all World’s Best measurements.
- Last but not least, we would like to thank our referees, StefaniaVecchi and StephaneMonteil, for their quick work which has been very helpful in improving our analysis!

Extracting γ from DsK

Strong phase difference

BDT Training (2010)

- The MVA was trained for the fd/fs analysis using a small (2pb-1) subsample of the 2010 data
- Several MVAs were tried, the Boosted Decision Tree with Gradient boosting (BDTG) was found to have the best performance

CDF Measurement

PID variable (uses de/dx)

PID Efficiencies from Calib Tools

These are for the bachelor momentum spectrum, after the p<100GeV has been applied.

Example of PartReco Bkg

Shape for Bd→D*-π+ from 2010 MC, under pion (left) and kaon (right) mass hypothesis for the bachelor

Comparison to Theoretical Expectation

- As a side-product of the 2010 fd/fsanalysis, we measured:

- Whereas we now measure :
- Bd→DKHas only one tree diagram, while the Bs→DsKhas two
- So our result suggests that the two different tree diagrams contributing to the DsK final state interfere destructively

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