# Presentation: 005200

## Measurement of the First and Second Moment of the Hadronic Mass Distribution in Semileptonic B Decays

- O.Buchmüller(SLAC)
- and
- H.Flächer(RHUL)

- Preliminary Results foreseen for EPS03 in Aachen

- Related Documentation:
-  BAD 663 (EPS conference contribution)
-  BAD 552 (Supporting Document)
-  BAD 465 (ICHEP02 hep-ex/0207084)
-  BAD 409 (Supporting Document)

## OPE and the Moments

* **moments of hadron mass spectrum and *
*the lepton energy spectrum from b****cl**** events *
*as well as *
*for moments of the photon energy spectrum from b****s**** events*

**Parameterization of decay rate in terms of Operator Product Expansion in HQET in powers of ********s****(m****b****)********0**** and ********/m****B:**
******************are non-perturbative parameters**
******1****    (-) kinetic energy of the motion of the b-quark**
******2      ****chromo-magnetic coupling of b-quark spin to gluon****	**
**from B*-B mass difference, ********2****=0. 12GeV****2**
****** ****= m****B**** – m****b**** + (********1 ****- 3**** ********2****)/2m****B**** ...**
**+ Additional parameters enter at higher orders (**************************************************** )**
**	****use theoretical estimates –1/m****B****3**** **

## Another “triangle” to be tested ...

**b********s********, X****s****ll**
**BR ~10****-4**
****** ****m****b****, **************

**b********ul******
**BR ~10****-3**
****** ****V****ub                    **

**b********cl******
**BR ~10****-1**
**V****cb****,**
** ****m****b****, **************** **

- “shape function”
- - OPE link not yet established -

- OPE link established

- OPE link not yet established

**b********s********: **Large potential for new
- physics but still the issue of the
- rather high photon energy cutoff.
**b********X****s****ll: **“Flag ship analysis” for
- future b exp. (LHCB, BTEV,1035-36)
-    Theoretical uncertainties on
- Xsll will dependent on the
- knowledge of the b quark mass
- and its fermi motion in B meson.

- Vub/Vcb: The largest uncertainty is due
- to the imperfect knowledge of the b quark
- mass and its fermi motion (Vub).

***We need Theory and Experiment to not only****** establish****** the ******missing links****** ***
***    ******in the “OPE triangle” but also to check its ******consistency******!  ***
**The measurement of the hadronic mass moments is one step in this direction ...**

## Basis of the Analysis: Fully Reconstructed B’s 

- Basis of the Analysis: Fully Reconstructed B’s

- Data set:	89 M BB events  (ICHEP02: 55 M BB events)
- Analysis based on events with one fully reconstructed B decay:

- cut

-  _The events are further selected:_
** ****= 1 e or ******** with p* > 0.9 GeV/c**
** ****|Q| ≤ 1 **
** ****Q’****l**** = Q’****B****  for B****± ****and B****0 **
** ****|E****miss****-|P****miss****|| <0.5 GeV**
**  ****E****miss ****>0.5 GeV**
** ****|P****miss****|**** ****>0.5 GeV**
-  _Final Sample:_
**7114 Signal Events ****(5819 ICHEP02)**
**2102 Background ****(3585 ICHEP02)**
****** ****S/B > 3:1 ****(ICHEP02 1.5:1)**

- ICHEP02

## Basis of the Analysis: Kinematic Reconstruction

- X-System
- (3(4) measured parameters)

- Lepton
- (3 measured parameters)

- Missing Neutrino
- (3 unmeasured parameters)

- B reco candidate
- (4 measured parameters)

- BB -> Breco (X,l,Pmiss)

- Apply Energy and Momentum conservation
- E**Breco**+ E**X** + E**l**** **+ E****  - E**PEPII** = 0
**P****Breco**+ **P****X** + **P****l**** **+ **P******  - **P****PEPII** = 0
- 4 Constraints
- + Mass Constraints
- M(Breco)=M(X,l,)
-  + 1 Constraints

-  2C Fit (NDF = 5 – 3 = 2)

_***Observable:***_
-  **Invariant mass of X-System **
**:= Mx**

**Better resolution and smaller bias!**

## Reminder: Preliminary Results For ICHEP02

- Strong dependence of moments on p*min
- For p*min=1.5 GeV/c and
- 	 =0.35 ± 0.13 GeV [1]
- 	(reliance on b  s spectrum)
-   1= - 0.17 ± 0.06 ±0.07GeV2
-   CLEO
-   1= - 0.226 ± 0.07  0.08 GeV2

- <MX2-MDspin2>

- p***min** [GeV/c]

- OPE (Falk,Luke)
-  = 0.35 GeV

- But
- these parameters do not describe P* dependence of the moments!

********(0.9 GeV/c)** – **********(1.5 GeV/c)
- = 0.22±0.04±0.05 GeV2

- OPE  (Falk, Luke)
- , 1 free param.

- NB:  Data points highly correlated

-  BABAR Preliminary
-  CLEO

- No non-resonant
- states  (MC)

## Reminder: Extraction Method For ICHEP02

- Binned 2 fit to M**X** Distribution:  4 Contributions
- D = fD PD+ fD* PD* + fHX PHX  + fBG(fixed)P BG

***Ref.:***
***BAD409***

-  Extraction method “ala CLEO” .....

## Outstanding Issues with the Extraction Method

-  Model dependence for high mass final states  - shape of non-   	resonant MX  distribution and so < Mxnreso>   (Goity-Roberts model)
- 	****** ****makes the analysis very model dependent and eventually leads to a large**
**	****     ****systematic uncertainty (especially at low P* cuts) **
-  Branching fractions have to be measured  - need to extract the 	relative fraction of D*,D and high mass final states
**                  ******** ****leads again to a strong model dependence because the shapes of all**
**	****     ****individual components of the Mx distribution have to be taken from the MC**
-  High correlation between data points  - per construction lower P* 	cuts always includes all cuts at higher P*
- 	****** ****due to the used extraction method it is almost impossible to calculate the**
**	****     ****correlations between the different measurements**
**	****                          ******** ****no quantitative interpretation possible!**

## Direct Measurement of <Mxn>

- Requirement:
- <MXn>TRUE   <MXn>DATA

**Different Modes used in the MC**

- NPDF: individual modes
- Ri: relative fractions

- For  <MX>TRUE - <MX>DATA  0
- we have only a small dependence on the Ri (BR) for the individual
- Mx components (D*, D and Xh).

- small BR dependence!

## Calibration Curve

_***True modes:***_
- D
- D*
- D** (two narrow +two broad)
- XH (4 spin dependent D(*)PI)
**Large variety of different models**
**    ****and different final states**

**M****x****true**** binning (example)**

- Define calibration curve independent of underlying model!

-  binning in bins of Mxtrue

## Calibration Curve

- P1=0.9950.011
- P2=0.0100.022

- P1=0.9950.011
- P2=0.0210.046

- P1=0.7990.007
- P2=0.2560.016

- P1=0.7350.007
- P2=0.6060.030

- <MX>TRUE

- <MX2>TRUE

- <MX>

- <MX2>

- 4 x XH

- 4 x D**

- D*

- D

_***Two Important Conclusions:***_

**1. We find a linear relation between <M****X****n****>****TRUE**** and <M****X****n****>****RECO** (red curve).

**2. Applying the calibration on an ****event-by-event level**** we can correct for mass biases**
**                                              ****of all utilized modes** (blue curve).

**Linear calibration curve represents a model independent way**
**	****to fully correct for detector related mass biases!**

**(more details in BAD552 and BAD663)**

## The New Extraction Method

- Define calibration curve for observable <Mxn> from MC
- Calibrate the Mxn data sample on event-by-event bases

- 3. Subtract the remaining peaking background  (fraction F and mass <Mxn>BG)
- Intensive studies have been carried out to test the reliability of the MC
-     simulation by using the wrong sign data sample (see BAD552). It turns
-     out the largest uncertainty stems from the purely know “branching fractions”
-     of the “right sign” background (D(*), Ds).
- 4. Correct for acceptance effects (e.g. lepton acceptance)

## Model Uncertainty 

**P*>0.9**

**P*>1.1**

**“****old extraction”**

**“****new extraction”**

**P*>1.1**

**P*>0.9**

**Variation of all possible **
**model combinations defines**
**the model uncertainty**

- RMS(P*>0.9) =
- 0.01 GeV2

- RMS(P*>1.1) =
- 0.01 GeV2

- RMS(P*>0.9) =
- 0.06 GeV2

- RMS(P*>1.1) =
- 0.05 GeV2

**The new extraction method leads  to a significant improvement **
**in the model uncertainty (~factor 5 better than old method) and makes**
**the measurement almost model independent.**

## New Photon Selection

**<M****X****2****-M****Dspin****2****>**

- E

- 

- LAT

- In the past year several studies have been carried out
- to test the reliability of the photon simulation (SP4)
- for the X system in semileptonic B decays
- (Jan Erik Sundermann, Robert Kowalewski, Recoil Vub task force, ...)

- Remember:
- ICHEP02 analysis
- was based on SP3

-  Perform scan of **<M****X****2****-M****Dspin****2****>** in sensitive variables:

**stable within the statistical errors!**** **

**NOT stable within the statistical errors!**** **

**NOT stable within the statistical errors!**** **

- P*=1.5 GeV

- P*=0.9 GeV

## New Photon and Track Selection

- “sensitive variables”

- “insensitive variables”

- Track Selection
- (similar to the one used for ICHEP02)

- New Photon Selection

## Stability of the new Photon Selection

- 

- LAT

- Scan the stability of the moment measurement as function of  and LAT

- A scan over a **large range** in  and LAT confirms that the results are  now stable. All residual
-    variations a fully compatible with statistical fluctuations introduced by the scan procedure.
-  **Use variation to determine a conservative systematic uncertainty **
******  ****red band (add in quadrature to yellow band)****   **** **

- Default measurement

- Yellow Band = Detector error

## DATA –MC Comparison for PXneutral

- DATA –MC Comparison for PXneutral

- Pxneutral = 4-vector of all photons in the X-system

- Pxneutral

- Pxneutral

- Exneutral

- Exneutral

- NEW
- Photon Selection

- OLD
- Photon Selection

***Clear Improvement!***

## DATA –MC Comparison for PXcharged

- Pxcharged = 4-vector of all charged tracks in the X-system

- Excharged

- Pxcharged

- NEW
- Photon Selection

- OLD
- Photon Selection

***No change – as expected***

## DATA-MC: Emiss-Pmiss and Mmiss2

- Emiss-Pmiss

- Mmiss2

***Clear Improvement!***

- NEW
- Photon Selection

- NEW
- Photon Selection

- OLD
- Photon Selection

## One Last Important Cross Check

- P*

- P*

**<M****X****>**

**<M****X****2****>**

**M****X**

**M****X****2**

- MD*

- MD*2

**Verification of the analysis**
**on partial reconstructed**
**B****0********D*****+****l******** events**

- Apply the whole extraction
- procedure to obtain
- <MD*> and <MD*2>

***It Works!***

## Results for <MX> and <MX2>  

## Independent Data Subsets

***Good Consistency!***

## Comparison with ICHEP02

- Major changes with respect to ICHEP02

- Replace SP3 with SP4 MC and improve the photon
-    selection!
- 2.	Change event selection and improve S/B for Breco
-    sample
- 	  **7114 Sig. over 2102 Backg. for 90 Mio BB**
- 	     **(5819 Sig. over 3585 Backg. for 55 Mio BB)**
- 3.	Replace old model dependent extraction method
-   with a complete new model independent approach!
-   Almost no correlation between the two methods

- Depending on the assumption of the correlation
-     for the ICHEP02 points as well as on common
-     systematic errors the new results have shifted
-     downwards by 1.5 to 1.9 sigma.

- ICHEP02

- The largest fraction of the shift stems from the improved photon selection!

## HQET Interpretation 

-  Calculations from Falk and Luke (Phys.Rev.D57:424-430,1998)

- Fit OPE for <Mx2> to BABAR data and extract the two leading HQE
- parameters  and 1 (MS scheme)  all correlations are now taken into account!

- CLEO bs

- P*

- <Mx2>

- OPE prediction using CLEO data only
- <Mx2> and <E> from bs

- OPE fit to
- the BABAR data

- hadron mass moments seem to be consistent (overlap from bands and BABAR ellipse)
-     but 2=1 contour does not overlap with <E> band from CLEO bs

**Notes:**
 Calculations from Falk and Luke (Phys.Rev.D57:424-430,1998) 

## A more Comprehensive Approach

- “External Input”

- “BABAR Input”

**Based on improved OPE calculations in the**
**1s mass scheme ****(Phys. Rev. D67. 05012, 2003)**
**we can now not only include moment **
**measurements in the fit but also ********SL**
**Simultaneous extraction of ****HQE parameters**
**and ****Vcb****!**

**(development of fit code in close collaboration with theorists) **

_**Calculate **__****__**SL **__**from BABAR data only!**_
-   life time measurements and BR(BXl) have
-       by now reached a precession that makes
-       SL (BABAR)** **very competitive!

_***Two possibilities:***_
**Check consistency of the HQE calculations by **
**           ****comparing hadron moments from BABAR **
**           ****with other moment measurements (“external input”)**
**Use the BABAR hadron moments together with**
**           ********SL ****(BABAR) to obtained an improved **
**           ****determination of Vcb**

## Consistency of the HQE: Hadron mom. vs. Lepton Mom. 

- BABAR only

**Simultaneous extraction of**** ****Vcb, m****b****1s****, and ********1****1s**
** ****from a fit to the HQE in the 1s mass scheme**
**(O(1/m****b****3****) parameters are fixed in the fit)**

**Vcb - m****b****1s **** plane **

** ********1****1s**** - m****b****1s **** plane **

**Note: ********2****=1 contour include already part **
**of the theory errors. Only O(1/m****b****3****) uncertainties **
**are not included!****	**

** ****Good agreement between BABAR moments and other hadron moment measurements**
-  ******2****=1 contour of hadron moments and lepton moments do not overlap**
**  ********indication for large O(1/m****b****3****) corrections or maybe even more ...?**
**	****(bear in mind that ********SL ****is common in both fits!)**

## |Vcb| extracted using BABAR data only

**Caveat:** We still have to establish the consistency of the the OPE
- to at least the same level of accuracy we would like to achieve for Vcb (<1%)!

- The most precise measurement of Vcb from one single
- experiment (life time, branching fractions, moments) and also
- very competitive (3% total error)!

**[previous inclusive Vcb measurement from BABAR: |Vcb| = 42.3********0.7(exp)********2.0(theo) ~5% (Phys. Rev. D67, 2002) ]**

- BABAR only

## Summary and Conclusion

-  **We have measured the first and second moment of the Mx distribution**
**    ****for different P* cuts (0.9 to 1.6 GeV).**
** ****With a completely new and unique extraction approach we were able to **
**   ****overcome outstanding issues (like model uncertainty and point-to-point **
**  ****correlations) which lead to a significant improvement of the new results**
** ****The new results are ~1.5(1.9) Sigma below  the results presented in ICHEP02**
**  ****(mainly due to the improved photon selection). **
-  **Using a** **simultaneous extraction of**** ****Vcb, m****b****1s****, and ********1****1s ****from a fit to the HQE **
**  ****calculations we obtain a improved measurement of Vcb which is based on BABAR**
**  ****data only!**
** ****A comparison with other hadron moment measurements from CLEO and DELPHI**
**  ****demonstrates a good agreement.**
** ****A consistency test of hadron and lepton moments in the framework of the OPE leads **
**  ****to inconclusive results and demonstrates again the importance of the determination**
**  ****of all the O(1/m****b****3****) parameters from data. **
**	****	******** *****More moment measurements from different***
***                   ******physics processes will be needed to test HQET+OPE to the level of <1%.***** **

****** ****BABAR is the perfect Experiment for this task and we are just at the beginning ... ******** **

## FIT RESULTS

## More on the Fit

## Does it work? – Crosscheck on MC 

## Cross Checks on the MC: <Mx2>

- Cross Checks on the MC: <Mx2>

- raw <Mx2>
- bias corrected <Mx2>

- Low MC statistic
- for high mass final States
- (only 5 events)
- > Large statistical uncertainty
- in bias correction. Interpolation
- or more MC stat. will fix this!

- <Mx2> - <Mx2>true

- <Mx2>

- Applying the whole
- analysis chain on the
- generic MC yields the
-  <Mx2>true
- in the MC

**It Works!**

## Cross Checks on the MC <Mx>

- We can also measure
- <Mx>  (with even
- higher precession)

- Low MC statistic
- for high mass final states
- (only 5 events)
- > Large statistical uncertainty
- in bias correction. Interpolation
- or more MC stat. will fix this!

## Wrong Sign Background: DATA vs. MC

- B0

- B+

- P* bins:    0.8-1.0 GeV          1.0-1.4 GeV         >1.4 GeV

- B0 mixing

## Breco Sample: Comparison ICHEP02 and EPS03

- ICHEP02

- EPS03

## Correlation Matrix for <Mx2>

## Systematic Errors on <Mx2>