# Presentation: 683950

## Hadronic Moments in Semileptonic B decaysPreblessingCDF 6754, 6972, 6973

- Alex, Hung-Chung, Laurent, Marjorie, Ramon

## Contents

- What are these moments? Why are they interesting?
- Analysis strategy
- Selection of lD*/lD+ samples
- Montecarlo validation
- ** selection & optimization
- Raw mass distributions
- Background modeling
- Background Subtraction
- Acceptance corrections
- Final fit to m**
- Extraction of QCD parameters

## Introduction

- Vcb connected to BXcl
- Xc=anything(c)      Inclusive
- Xc=D0/*/+                       Exclusive
- Hadronic mass moments:
- Hadronic mass distribution from semi-leptonic decays:
- BXc l 
- D, D*, D**
- only D** component needs to be measured

- Spectroscopy of D mesons

## Inclusive Vcb Determination and hadronic moments

- Inclusive semi-leptonic B decays:
- (BXcl) = |Vcb|2 f(,1,2,...)
- Moments:  g(,1,2,...)
- one can measure the moments to improve the knowledge on  Vcb
- currently the theory uncertainties dominate
- general test of non-perturbative aspects of HQET
- measuring ,1 in several ways and finding consistency would be a powerful test of the OPE treatment of HQET
- Experimentally:
- CLEO, BABAR: inclusive technique with fully reconstructed B on the away side
- DELPHI: inspired our approach

## Moments Definition

- Spectral Moments:
- lepton energy: En(d/dE)dE / (d/dE)dE
- photon energy in bs
- hadronic mass:
- dsH sHn (d/dsH) / dsH (d/dsH)
- where sH = mX2
- usually  sH=mX2-m2Dspin
- (mDspin = 0.25mD+0.75m D* spin averaged mass)

## Hadronic Mass

- Hadronic mass spectrum:
- Explicitly measure only the D** component, f**(sH), normalized to 1. Only the shape is needed.
- PDG values for D and D* masses and b.r. will be inserted.

## Channels with charged B

- B-  D**0 l- __
- D**0  D+ -   OK
- D**0  D0 0  Not reconstructed. Half the rate of D+ -
- D**0  D*+ -
- D*+  D0 + OK
- D*+  D+ 0 Not reconstructed. Feed-down to D+ -
-  bckgd shape from channel above (D0-), rate is half
- D**0  D*0 0 Not reconstructed. Half the rate of D*+ -
-          We can reconstruct all the Xc spectrum

- Neutral B would add statistics but involve neutrals

## Event Topology

- D0, D+, D*+: 3D vertex of K()
- Lepton +D: 3D vertex
- Additional track (**) for D**
- use the track’s d0 w.r.t. the B and Primary vertices to tell ** from prompt tracks

- B- D**0l-

- PV

- l-

- -  (aka **)

- +

- +

- K-

- D+

## The strategy

- Correct for (m**), (D+)/(D*)

- Selection:
- Optimize on MC+WS combinations
- Cross check on *
- ** Background
- Combinatorial
- D’
- BDD
- cc
- ...

- Collect as many modes as possible:
- (K)*
- (K)*
- (K0)*
- K
- Check yields
- Validate MC

- Measure selection bias on m** from:
- MC
- D* candidates
- Rely on MC (& PDG) for:
- (D+)/(D*)
- Unseen modes (Isospin)
- Lepton spectrum acceptance

- Subtract backgrounds
- Use PDG to go m**m**
- Compute <m**2> & <m**4>
- Include D(*)0
- Extract , 1
- Systematics

- CDF6754

- CDF6972/6973

## D(*)+ Reconstruction

## Dataset & Initial Selection

- Dataset:
- Jbot2h/0i: muon + SVT
- Jbot8h/4i: electron + SVT
- Refit:
- G3X (standard B, phantom layer), beamline 19
- ISL, L00 hits dropped
- COT scaling: (curv,d0,0,,z0)=(5.33,3.01,3.7,0.58,0.653)
- LeptonSvtSel: default cuts

- Thru run 165297

## Track & Vertex Cuts

- TrackSelector:
- COT hits:  >20 Ax,  >20 St
- Si hits:  3 Ax
- K, :   pT > 0.4 GeV/c
- leptons: pT > 4 GeV/c (from LeptonSvtSel)
- D vertex:
- 3D fit
- one track has to be matched to the SVT track
- Lepton+D vertex:
- 3D fit
- **:
- 20+20 COT hits
- Si hits:  3 Ax, 3 SAS+Z (-30% stat, x2 S/B)
- Pt>0.4 GeV/c

## K

|  | K  | K0 | K  | K |
| --- | --- | --- | --- | --- |
|  Yield | 3890  63 | 6638  98 | 2994  57 | 15067  182 |

- K

- K0

- K

- e

- e

- e

- 

- 

- 

- K

- 

- e

## MC samples and validation

## Montecarlo Generation

- Bgenerator/EvtGen/CdfSim/TRGSim++
- “realistic simulation” with representative run number
- Different samples:
- MC Validation
- D samples  inclusive BXcl
- * tracking (** proxy)  exclusive BD*l
- Optimization  inclusive BlD**
- Efficiency, M** bias  individual D** mesons
-                        (e.g. BD1l, D1D*, D*D0, D0K)

## Approach to MC validation

- Cross-check kinematic variables
- B spectrum modeling
- Trigger emulation
- Compare many data/MC distributions using binned 2
- Every possible decay mode
- Sideband subtracted before comparison
- Duplicate removal (D0K)

## Kinematic Comparisons: D*, D0K

- Kinematic Comparisons: D*, D0K

| Ptl | PtD | PtlD | d0l |
| --- | --- | --- | --- |
| mlD | LxylD | LxyD | LxylDD |
| Pt*
 | d0K | RlD | RlK |
| PtK | Pt |  |  |

## Slide 18

| Matching-2 
prob  (%) | K |  | K(0) |  | K |  | K |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
|  | e |  | e |   | e |   | e |  |
| pT(l) |   4 |  12 | 43 | 40 | 38 | 11 | 16 |   1 |
| pT(D) |   3 |   7 |   8 |   2 |  6 | 79 | 12 |   4 |
| pT(l-D) | 41 | 17 | 30 |   2 | 49 | 22 |   9 |   4 |
| d0(l) | 10 | 92 | 75 | 27 | 30 |   4 | 95 |   2 |
| m(l-D) |   2 |   3 | 50 | 61 | 48 | 69 | 16 | 42 |
| LXY(l-D) | 48 | 23 | 41 | 12 | 32 | 69 | 29 |   0.07 |
| LXY(D) | 23 | 88 | 69 | 99 | 95 | 47 | 87 |   2 |
| LXY(B to D) | 61 | 29 |  6 | 13 | 17 | 89 | 24 |   2 |
| pT(*) >0.4 GeV | 28 |  42 | 21 | 70 | 38 |   1 |  –  |  –  |
| do(K) | 68 | 72 | 83 | 54 | 74 | 15 | 17 | 72 |
| R(l-D) | 34 | 29 | 26 | 51 | 86 | 33 | 57 | 30 |
| R(l-K) |  17 | 12 | 33 | 66 | 38 | 2 | 29 |   2 |
| pT(K) | 22 | 20 | 49 | 52 | 83 | 10 | 25 | 15 |
| pT() | 90 | 20 | 14 | 59 | 2 |   8 |  –   |  –  |
| pT(2) |   –    |  –  |  –  | – | – |  – | 67 |  64 |

## Can we “predict” relative yields?

- Two methods (a,b) to derive this BR

- Based on inclusive bD(*)+l
- Based on exclusive BD(*)+l, D**l

- +PDG BR + MC efficiency ratios

- Assume MC predictions and use 13% systematics

## D**

## Optimization

- The relevant discriminants are:
- Pt
- R
- d0PV
- d0BV
- d0DV
- LxyBD
- Signal model: MC
- Background model:
- WS **l charge
- Optimize significance

- PV

- BV

- DV

- **

- D0D+

- d0PV

- d0BV

- d0DV

## Discriminating Variables

- ** Pt (GeV)

- R (**-lD)

- ** 2d IP signif.WRT PV

- ** 3d IP signif.WRT BV

- ** 3d IP signif.WRT DV

## Optimization!

- Generate D** montecarlo (the shape)
- Normalize D** MC to data with reasonable cuts
- Now we can turn the crank and optimize...
- But what?

- a is the ratio of background events between signal and sideband region (a<1, usually)
- S is the MC signal (right sign combinations, signal region)
- SWS is the WS data in the signal region
- SBRS is the RS data in the sideband region
- SBWS is the WS data in the sideband region

## Optimal point:

- We have to live with different selections for D**D+  and   D**D*(K)

- Pt(**)>0.4 GeV
- R<1.0
- |d0PV/|>2.5
- |d0BV/|<3.0

- S/sqrt(...)8

- D*

- D+

- |d0DV/|>0.8
- Lxy(BD)>0.05 cm

- S/sqrt(...)6.6

## m**

## Current Mass Distributions

- DELPHI:
- ~80 (K)
- ~80 (D+)

## Background

## Backgrounds

- Background from B decays:
- Know how to model
- Study using Bgenerator/EvtGen/TRGSim++/CdfSim
- “Feeddown”
- Combinatorial background under D peaks:
- side-band subtraction
- Prompt pions in D(*)+-l-:
- Mostly from fragmentation
- wrong-sign combination D++l-
- cc
- D0 impact parameter distribution

## Physics Background

- Physics background studied with BD(*)+Ds-
- Size wrt signal:
- 100% uncertainty

- ~7%

- ~7%

- ~1

- Other modes

## Background: Feed Down

- Irreducible D**0 D*+( D+0)- background to  D**0 D+- subtracted statistically:
- M shape of D+- combination above is like D0- from D**0 D*+( D0+)-
- Rate is one half (isospin) times the relative efficiency in both channels time the ratio of the D0 and D+ B.R.’s used in the analysis

## Pollution from ccbar?

- We are cutting hard on Lxy(B) (500m), this is known to “solve” the lifetime problem
- Look at D+/D0 impact parameter for evidence of prompt objects: we do not see any

## Efficiency Corrections

## Pl*

- Theory prediction depends on Pl* cuts. We cannot do much but:
- see how our efficiency as a function of Pl* looks like
- Use a threshold-like correction
- Evaluate systematics for different threshold values

- Pl*

## MC efficiencies

- (M) is dependent on:
- D** decay Model
- Pl* cut
- Use different models/cuts to evaluate systematics:
- Individual resonances
- Goity-Roberts
- Phase space (not shown)
- Baseline: BR weighted
-   (EvtGen) average of modes

## Corrections to MC efficiencies

- Worried about possible shortcomings of the MC simulation:
- Efficiency for requiring Si hits
- ** separation variables not perfectly reproduced by MC
- Use * candidates from data to derive corrections

## * probes Si hit efficiency

- D0/+ reco is based on trigger tracks
- Si requirements can bias (D0**)
- (D0)m**
- Take COT-only *
- Apply 3Ax+3 (Stereo+SAS)
- Measure fraction as a function m**
- Use slope (error) as correction

## ** Separation Variables

- ** Separation Variables

- 124/49

- 137/43

- 146/45

- Data MC comparison
- Behavior is similar, but there are discrepancies
- Derive corrections from this comparison

## Data vs MC efficiencies

- Apply to * the same tracking requirements we usually apply to ** (including Si hits)
- Measure efficiencies for ** selection cuts applied to *
- Take the ratio of  MC and Data efficiencies as a function of Pt

## Moments ExtractionProcedure

## Computing the D** Moments

- All the pieces are put together in an unbinned procedure using weighted events
- Signal right sign (SRS)  w = +1
- Signal wrong sign (SWS) w = -1
- Sideband right sign (SBRS) w = -ai
- Sideband wrong sign (SBWS) w = +ai
- Apply efficiency corrections: efficiencies are propagated on weights
- W=w (aPt**+b)/[MC(m**)(cm**+d)]

## More Backgrounds

- Feed-down pseudo-events are formed from the D0** mass in Kevents (in SRS,SWS,SBRS,SBWS). The weight is
- Physics background events are generated and assigned a weight
-        where  =0.07 is the efficiency of the background relative to the signal. The weight is then corrected with the efficiency factor from MC.

## D+, D*+ Relative Normalization

- Relative normalization of D* channels is irrelevant since they all have the same underlying M distribution.
- D+ channel has a different M distribution. All D+ events have their weights modified as:
- Systematics:
- BR uncertainties from PDG (7%)
-  ratio from studies on data (13%)

## Resulting m** distribution

## Computing the Xc Moments

- The D0 and D*0 pieces have to be added to the D**0 moments, according to
-        where the fi are the fractions of Dil events above the pl*cut. Only ratios of fi’s enter the final result.

- f

## Moments ExtractionSystematics

## Systematicsshopping list

- Mass scale and resolution
- Efficiency corrections
- From MC
- from data
- Lepton momentum cut
- Background model
- Radial excitations
- Physics background
- Relative D+/D* normalization
- Semileptonic B branching ratios
- D** mass cut

## Mass scale/resolution

- We are measuring m** and then adding the PDG masses for D+/D*
- Basically insensitive to absolute scale issues
- Mass resolution matters
- The sample with the worst resolution is K0
- Re-smear K0 with 60MeV gaussian and use this as systematic

## Efficiency corrections from MC

- Uncertainty comes from lack of knowledge on the D** BR and phase space structures...
- Two possible MC models:
- BR weighted EvtGen admixture, to the best of today’s knowledge
- Plain phase space
- Switch to evaluate
-  systematics...

## Efficiency Corrections from data

- Efficiencies measured on data have modeling uncertainties/stat. Errors
- Float parameters within ranges and compute the effect on the moments

- Mass-dependent: use stat error on slope

- Pt-dependent: use 0th/1st order polynomial difference

## Lepton momentum cut-off

- We are not “literally” cutting on Pl* (it is not accessible, experimentally)
- Detector implicitly cuts on it
- Assume a baseline cut-off
- Vary in a reasonable range to evaluate systematics

- We use f to derive f**, given f0, f*
- f=f(,1)
- We use experimental prior knowledge on ,1 to evaluate systematics
- Effect is negligible

## Other Systematics

- Physics background:
- Branching ratios are poorly known (100% !!!)
- Relative BD/D*/D** branching ratios
- Take PDG values 1
- Theory parameters (1, i, S, mb, mc) varied according to expectations (100%, 0.5GeV3, 5%, 200MeV, 200 MeV)

- D+/D*+ relative scale:
- PDG BR are varied by 1
- MC based efficiencies 13%, according to studies in CDF6754 (D yields note)

## Distribution Cut-off

- The sample has basically no statistical power above 3.5 GeV (EvtGen predicts ~1% signal above cut)
- We need to apply a cutoff in order not to compromise the statistical uncertainty
- Trade off:
- Drop the statistical error, but increase the size of systematics
- Becoming model dependent (we need a model for the extrapolation of the high tail in order to evaluate systematics)

- Temporarily:
- Evaluate moments with different cut-off (3.5-4.0)

## Background Model

- We have 2 possible problems
- Shape
- Alternative model based on fully reconstructed B (“embedding” work in progress)
- Scale
- Based on the charge multiplicites from embedded B+:
- <20% discrepancy between RS and WS
- ~20% of background comes from B+
- ~4% uncertainty on WS/RS scale

## Radial Excitations

- D’D(*)+ should be accounted for in m**
- Not yet observed
- DELPHI limits:
- Embedding-WS comparison could give another limit
- For the time being we assume no D’

## Systematics size

## Results

- All systematics in place except the background shape model (embedding)

- or

- or

## Conclusions

- Comparison with other experiments
- Plan:
- Embedding (background shape, D’)
- Re-evaluate systematics on m** cutoff at 3.5 GeV
- Bless in 2 weeks

## Backup Slides

## Vcb: exclusive determination

- Measure absolute scale of BD*l
- D** states also important for |Vcb| exclusive determination
- end-point in q2 for BD*l decays
- systematic uncertainty from BD**l background

## Channels with neutral B

- _B__0_  D**+ l- __
- D**+  D0 +   OK
- D**+  D+ 0  Not reconstructed. Half the rate of D+ -
- D**+  D*0 +
- D*0  D0 0 Not reconstructed. Background to D0 +
- D*0  D0    Not reconstructed. Background to D0 +
- D**+  D*+ 0 Not reconstructed. Half the rate of D*+ -
-           We will not deal with neutral B

## Data Stability

- A: (152595-154012) Before winter 2003 shutdown
- B: (158826-165297) After winter 2003 shutdown
- C: (164303-165297) SVT 4/5

## Kinematic Comparisons lD*, D0K

- Kinematic Comparisons lD*, D0K

## Kinematic Comparisons lD*, D0K0

- Kinematic Comparisons lD*, D0K0

## Kinematic Comparisons: D+

## Can we “predict” yields?

- Two methods (a,b) to derive this BR

- Based on inclusive bD(*)+l
- Based on exclusive BD(*)+l, D**l

- +PDG BR + MC efficiency ratios

## What background model for what?

- WS is often used in this kind of analyses as a model for the background
- We can also use our fully reco’d B from other triggers
- We choose to use WS for the optimization
- Embedding is being used as a cross-check for systematics

## What’s available on the market...

- D**D0

- No background subtraction
- ~80 events in D*+
- ~80 events in D+
- ~215 events on D0
-         uncertainty > sqrt(n)

- D**D+

- D**D*

## Estimator Behaviour

## K Optimization

## D+ Optimization

## Combinatorial Background

- WS **
- Already used for the optimization
- Physics can be different
- Fully reco. B
- independent emulation of the background
- Limited statistics
- Needs some machinery for emulating a semileptonic decay!
- Eliminate the B daughters
- Replace the B with a semileptonic B with the same 4-momentum: a template montecarlo where the B decay comes from EvtGen and the rest of the event comes from the data!

## Background Modeling II

- Lxy>500m

- Tight cuts (avoid subtractions)
- Exclude B tracks
- Replace with MC B
- QuickCdfObjects/GenTrig
- Re-decay N times
- Same analysis path from there on

## Signal Fits

## Sample Consistency

## Slide 75

## Embedded MC vs Semileptonics

- MC yield scaled to number of data events

## Pl*

- see how our analysis bias looks like
- Use a threshold-like correction
- Evaluate systematics for different threshold values

- Pl*

## MC efficiencies

- (M) is dependent on:
- D** decay Model
- Pl* cut
- Use different models/cuts to evaluate systematics

## MC Validation

- * is an unique probe:
- Large statistics
- Low background
- “Similar” spectrum to **
- Can reconstruct with minimal cuts (e.g. COT only)
- Technique:
- Search for * with very loose cuts
- Do not include in B vertex
- Study biases to kinematics from tracking
- Study IP resolution(data/MC): Primary, B & D vertices
- Study (data/MC) vs selection criteria

## MC validation

- Cross-check kinematic variables
- B spectrum modeling
- Trigger emulation
- Validate CdfSim model of tracking resolution
- Relative efficiencies
- ** selection/bias

- Compare many data/MC distributions using binned 2
- Every possible decay mode
- Sideband subtracted before comparison
- Duplicate removal (D0K)

## Kinematics

- Can we rely on kinematical biases estimated from MC?
- Rem: we don’t care about absolute scales
- Pt dependent MC/data ratio:

- 400 MeV

- * Pt

- MC
- Data

- MC/Data vs Pt

## Impact Parameters

- 148/34

- 26/30

- 151/45

- 134/32

- 61/30

- 118/43

- 40/33

- 42/42

- 58/52

## Impact Parameters (covr)

- 40/33

- 550/40

- 124/49

- 133/32

- 39/29

- 137/43

- 146/34

- 25/30

- 146/45

## (MC), (data) vs selection criteria

## Another perspective: MC(after/before) / data(after/before)

## MC(after/before) / data(after/before)Plan for the evaluation of systematics

## Ds Background

- Ds Background

- Use  peak in D+ candidates to set the scale
- Measure the relative contribution of Ds decays to D+ fakes using MC
- Extrapolate to the total size of the contribution: 4%
- Build a suitable D** background model
- Subtract

## Cross-feeds

## Cross-feeds (details, sat.)

## Cross-feeds (details, K)

## Cross-feeds (details K)

## D** Moments

- Combine all events of all types in all channels (D*,D+,SRS,SBRS,feed-down, etc.)
- Compute mean (m1) and variance (m2) of M2 distribution with weighted events.
- Errors and correlation computed with MC (for toy MC) or bootstrap (for data).
- For some realizations, one finds a negative value for         m2 = Var(M2) = <M4> - <M2>2.

## Inputs for the D0 and D*0 Contributions

- For the BR’s, results from charged and neutral B decays are combined using isospin: partial widths are assumed equal.
- BR’s, ratio of lifetimes and ratio of production fractions are taken from PDG.
- Toy Monte Carlo is used to propagate the uncertainties from m1, m2, the BR’s, etc., to uncertainties on M1 and M2 and their correlation.

## Slide 94