# Presentation: 223116

## Hadronic Moments in Semileptonic B Decays from CDFII

- Alessandro Cerri

- Hep-ph/0502003 Accepted for publication in PRDRC

## Analysis Strategy

- Typical mass spectrum M(X0c) (Monte Carlo):

-  D0 and D*0 well-known
-  measure only f**
-  only shape needed

- 1) Measure f**(sH)
- 2) Correct for background,
- acceptances, bias
-  moments of D**
- 3) Add D and D*  M1,M2
- 4) Extract ******, ********1**

- Alessandro Cerri         CKM Workshop

- 3/15/05

## Channels

- 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+ -
- D**0 D*00   Not reconstructed. Half the rate of D*+ -

- Must reconstruct all channels to get all the D** states.
-  However CDF has limited capability for neutrals

-  B0D**-l+ always leads to neutral particles  ignore it
-  B- D**0l- better, use isospin for missing channels:

- Possible D’D(*) contributions neglected:
-   No BlD’ experimental evidence so far
-   DELPHI limit:
-                    We assume no D’ contribution in our sample

- Alessandro Cerri         CKM Workshop

- 3/15/05

## Event Topology

- 	      D0 *+                  (Br=67.7%)
- 	                K- +              (Br=3.8%)
-                                   K- + - +    (Br=7.5%)
-                                    K- + 0       (Br=13.0%)

- _Event Topology_

- Exclusive reconstruction of D**:

-   D**0      D+ **-
- 	      K- + +  (Br=9.2%)

- “D+”

- “D*+”

- Alessandro Cerri         CKM Workshop

- 3/15/05

## Backgrounds

- _Combinatorial background_
- under the D(*) peaks:
-  sideband subtraction

- _Physics background:_
- BD(*)+Ds-, D(s)Xl
-  MC,  subtracted

- _Prompt pions faking ____**:_
-  fragmentation
-  underlying event
- separate B and primary vertices
-     (kills also prompt charm)
-  use impact parameters to discriminate
-  model: wrong-sign **+* *-* *combinations

- _Feed-down in signal:_
- D**0 D*+( D+0)-
- irreducible background to
- D**0 D+-.
- subtracted using data:
- shape from D0- in
-  D**0 D*+( D0+)-
- rate:
- 1⁄2 (isospin) x eff. x BR

- Alessandro Cerri         CKM Workshop

- 3/15/05

## Lepton + D Reconstruction

- Lepton + D(*)+:
-  D vertex:
-  3D
-  l+D(+*) vertex (“B”):
-  3D
-  Lxy(B) > 500 m
-  m(B) < 5.3 GeV

- Data Sample:
-  e/ + displaced track
-  ~ 180 pb-1
- ( Sept 2003)

- Track Selection:
- 2 GeV track (SVT leg)
-  e/: pT > 4 GeV
-  other: pT > 0.4 GeV

- Total: ~ 28000 events

- Alessandro Cerri         CKM Workshop

- 3/15/05

## Raw m** Distributions

- _Raw m** Distributions_

- Measured in m**, shifted by M(D(*)+), side-band subtracted.

**D****2*********,D****0*******

**Feed-down**

**D****1****,D****1*********,D****2*******

- Alessandro Cerri         CKM Workshop

- 3/15/05

## Efficiency Corrections

- 1) Correct the raw mass for any dependence of reco on M(D**):
-   Possible dependence on the D** species (spin).
-   Monte-Carlo for all D** (Goity-Roberts for non-resonant), cross-checked with pure phase space decays.
- Detector simulation shortcomings cause residual data/MC discrepancy: derive corrections from control samples (D* and D daughters)
- 2) Cut on lepton energy in B rest frame:
-   Theoretical predictions need well-defined pl* cut.
-   We can’t measure pl*, but we can correct our measurement to a given cut:
-     pl* > 700 MeV/c.

- Alessandro Cerri         CKM Workshop

- 3/15/05

## Corrected Mass and D** Moments

- Procedure:

-  Unbinned procedure using weighted events.
-   Assign negative weights to background samples.
-   Propagate efficiency corrections to weights.
-   Take care of the D+ / D*+ relative normalization.
-    Compute mean and sigma of distribution.

- Results (in paper):

- No Fit !!!

- Alessandro Cerri         CKM Workshop

- 3/15/05

## Final Results

- Pole mass scheme

- 1S mass scheme

- (m1,m2)=0.61

- (M1,M2)=0.69

- Alessandro Cerri         CKM Workshop

- 3/15/05

## Systematic Errors (from the paper)

|  | m1 (GeV2) | m2
(GeV4) | M1
(GeV2) | M2
(GeV4) | 
(GeV) | 1
(GeV2) |
| --- | --- | --- | --- | --- | --- | --- |
| Stat. | 0.16 | 0.69 | 0.038 | 0.26 | 0.078 | 0.057 |
| Syst. | 0.08 | 0.22 | 0.068 | 0.13 | 0.091 | 0.082 |
| Mass resolution | 0.02 | 0.13 | 0.005 | 0.04 | 0.012 | 0.009 |
| Eff. Corr. (data) | 0.03 | 0.13 | 0.006 | 0.05 | 0.014 | 0.011 |
| Eff. Corr. (MC) | 0.06 | 0.05 | 0.016 | 0.03 | 0.017 | 0.006 |
| Bkgd. (scale) | 0.01 | 0.03 | 0.002 | 0.01 | 0.003 | 0.002 |
| Bkgd. (opt. Bias) | 0.02 | 0.10 | 0.004 | 0.03 | 0.006 | 0.006 |
| Physics bkgd. | 0.01 | 0.02 | 0.002 | 0.01 | 0.004 | 0.002 |
| D+ / D*+ BR | 0.01 | 0.02 | 0.002 | 0.01 | 0.004 | 0.002 |
| D+ / D*+ Eff. | 0.02 | 0.03 | 0.004 | 0.01 | 0.005 | 0.002 |
| Semileptonic BRs |  |  | 0.065 | 0.10 | 0.064 | 0.022 |
| 1 |  |  |  |  | 0.041 | 0.069 |
| Ti |  |  |  |  | 0.032 | 0.031 |
| s |  |  |  |  | 0.018 | 0.007 |
| mb, mc |  |  |  |  | 0.001 | 0.008 |
| Choice of pl* cut |  |  |  |  | 0.019 | 0.009 |

- Alessandro Cerri         CKM Workshop

- 3/15/05

## Comparison with Other Measurements

- Pole mass scheme

- Alessandro Cerri         CKM Workshop

- 3/15/05

## Summary

- First measurement at hadron machines: different environment and experimental techniques.
- Competitive with other experiments. Little model dependency. No assumptions on shape or rate of D** components.
- Through integration with other experiments and other “moments” we can seriously probe HQET/QHD
- Let’s do it!

- Alessandro Cerri         CKM Workshop

- 3/15/05

## BACK-UP SLIDES

## Motivation (I)

*F**theory** * evaluated using OPE in HQET: expansion in s and 1/mB  powers:
- O(1/mB)   1 parameter:                      (Bauer et al., PRD 67 (2003) 071301)
- O(1/mB2)  2 more parameters:  1, 2
- O(1/mB3)  6 more parameters:  1, 2, T1-4

- _Motivation (I)_

- (4S), LEP/SLD, CDF measurements.       Experimental  |Vcb|~1%

- Theory with pert. and non-pert.  corrections.  |Vcb|~2.5%

- Most precise determination of *V**cb* comes from *sl* (“inclusive” determination):

- Constrained from pseudo-scalar/vector B and D mass differences

- Alessandro Cerri         CKM Workshop

- 3/15/05

## Motivation (II)

-   Hadronic moments: BXcl, recoil mass M(Xc)

-   Leptonic moments: BXcl, lepton E in B rest frame

-   Photonic moments: Photon energy in b  s 

- (CLEO, DELPHI, BABAR)

- (CLEO)

- (CLEO, DELPHI, BABAR, CDFII)

- Many inclusive observables can be written using the same expansion (same non-perturbative parameters).  The spectral moments:

-  Constrain the unknown non-pert. parameters and reduce |Vcb| uncertainty.
-  With enough measurements: test of underlying assumptions (duality...).

- Alessandro Cerri         CKM Workshop

- 3/15/05

## What is Xc?

- ~25% of semi-leptonic width
-     is poorly known

- Higher mass states: D**

- Semi-leptonic widths (PDG 04):

|  |          Br (%) |
| --- | --- |
| B+  Xc l  |    10.99  0.31 |
| B+  D* l  |      6.04  0.23 |
| B+  D l  |      2.23  0.15 |

- (PDG b/B+/B0 combination, bu subtracted)

- Possible D’D(*) contributions neglected:
-   No BlD’ experimental evidence so far
-   DELPHI limit:
-                    We assume no D’ contribution in our sample

- Alessandro Cerri         CKM Workshop

- 3/15/05

## Combination with D0, D*0

- Take M(D0), M(D*0), sl, 0, *  from PDG 2004 :
- sl, 0, * are obtained combining BR’s for B-, B0 and admixture, assuming the widths are identical (not the BR’s themselves), and using
- f-/f0  = 1.044 ± 0.05
-  (B-)/(B0)  = 1.086 ± 0.017
- Average:
-        BR(B+ **** X0cl+l) = 0.1099 ± 0.0031
-        BR(B+ **** D0l+l)  = 0.0223 ± 0.0015
-        BR(B+ **** D*0l+l) = 0.0604 ± 0.0023

- Alessandro Cerri         CKM Workshop

- 3/15/05

## Monte-Carlo Validation (I)

- MC vs. semileptonic sample:

- Matching ******2** probability for those plots:

| 67% | 74% | 23% |
| --- | --- | --- |
| 43% | 69% | 87% |

- Alessandro Cerri         CKM Workshop

- 3/15/05

## ** Selection

- Based on topology:
-  impact parameter significances w.r.t. primary, B and D vertices

- pT > 0.4 GeV
- R < 1.0

- |d0PV/| > 3.0
- |d0BV/| < 2.5

- |d0DV/| > 0.8
- Lxy BD > 500m

- Cuts are optimized using MC and background (WS) data:

- Additional cuts only for D+:

- Alessandro Cerri         CKM Workshop

- 3/15/05

## 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*

- Alessandro Cerri         CKM Workshop

- 3/15/05

## Vcb measurements

-  Experiment: large statistics on BR(BXc-) and tB and small systematics

- _V_cb_ measurements_

**|V****cb****| from exclusive B decays**** **
-  Large statistics on Bd0D(*)- available and new measurements are coming
-  Present precision (5%) is systematics limited:
-       Experiments: D** states, D’s BR
-       Theory:  form factor extrapolation, corrections to F(1)=1                            			             can be reduced in the future

- |Vcb|excl=(42.1 1.1exp 1.9theo) 10-3

- (PDG 2002, Vcb review)

- |Vcb|incl= (40.4 ± 0.5exp ± 0.5, ± 0.8theo) 10-3

- (PDG 2002, Vcb review)

- Alessandro Cerri         CKM Workshop

- 3/15/05

## D*+ Reconstruction and Yields

- D*+ channels:   Dm*  M(D0*) – M(D0)

- D(*)+ l- (+cc)  yields:

- ~ 28000 events

- Alessandro Cerri         CKM Workshop

- 3/15/05

## MC validation: quantitative

| 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 |

- Alessandro Cerri         CKM Workshop

- 3/15/05

## Impact Parameters in MC

- _Impact Parameters in MC_

- Comparison data/MC for IP:  (worst case)

- Residual corrections:
-  derived from data:
** ***********
-  non-SVT D daughters (pT > 1.5 GeV)
-  corrections from double ratios
-  in pT
-  in m**

- Alessandro Cerri         CKM Workshop

- 3/15/05

## 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

- Alessandro Cerri         CKM Workshop

- 3/15/05

## 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*

- Alessandro Cerri         CKM Workshop

- 3/15/05

## 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

- Alessandro Cerri         CKM Workshop

- 3/15/05

## Efficiency vs m**

- Alessandro Cerri         CKM Workshop

- 3/15/05

## MC/Data corrections

- Dominant source of systematics!
***** reproduces ****** topology but statistics too low:
- Use all *D** candidates
- Cross check on non-triggering *D**0* daughters (helps for pT)

- Alessandro Cerri         CKM Workshop

- 3/15/05

## Background Subtraction 

- Use mass side-bands to subtract combinatorial background.
- Use D*+[****D0+] - to subtract feed-down from D*+[****D+0] - to D+-.
- Use wrong-sign **+ l- combinations to subtract prompt background to **.
- Possible charge asymmetry of prompt background studied with fully reconstructed B’s: 4% contribution at most.

- Alessandro Cerri         CKM Workshop

- 3/15/05

## BACK-UP: details on systematics

## Systematics

- Input parameters
- D(*)+ Masses, in combining D(*) with D** mM [PDG errors]
- BR (BD+/D*+ mM) [PDG errors]
- Experimental
- Detector resolution [re-smear satellite sample by full resolution: 60MeV]
- Data/MC Efficiency discrepancies [measure Pt and m dependency on control sample, probe different fit models]
- Decay models in MC [full kinematic description vs pure phase space]
- Pl* cut correction [repeat measurement at various Pl* thresholds]
- Backgrounds
- Scale [charge correlation WS/RS from fully reconstructed B: 4%]
- Optimization Bias [repeat optimization procedure on bootstrap copies of the sample]
- Physics background [vary 100%]
- BXc [estimate / yield and kinematic differences using MC]
- Fake leptons [no evidence in WS D+l+, charge-correlated negligible]

- Alessandro Cerri         CKM Workshop

- 3/15/05

## Data-based study

- a

- Optimize

- Cuts!

- Selection

- m1a,m2a

- Selection

- m1unb,m2unb

- -

- Bias!

- Data

- Bootstrap

- =bias
- =(bias fluctuation)(statistical uncertainty)

- Extract a bootstrap sample a of the data
- Optimize  get new set of cuts
- Evaluate bias with respect to the parent distribution (initial data) with new cuts
- We can repeat this 50 times and obtain 50 independent estimates of the bias(es)
- CPU intensive
-     [~5 hours/(bootstrap+optimization+“fit”)]
- Mean of those estimates is an unbiased estimator of the bias
-   (as long as the data is a good
-    representation of the ideal distribution)
-  is a convolution of:
- Intrinsic fluctuation of bias
- Statistical fluctuation of a after cuts

- Alessandro Cerri         CKM Workshop

- 3/15/05

## Physics Background

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

- ~7%

- ~7%

- ~1

- Other modes

- Alessandro Cerri         CKM Workshop

- 3/15/05

##  Background

- A problem if observed m** distributions are different!
- Two possible sources of difference:
- Kinematics: different m** distribution to begin with because
-                        m()/m(B) >> m(e/)/m(B)
- Different reconstruction efficiency
- Study with generator-level MC + smearing + trigger & reco. parameterization
- Conclusion:
- [BlD**]/[BlD**]2%
- Difference in m** acceptance is ~10% and
-       mass-independentirrelevant
- m()/m(B) matters only for the nonresonant component which is in MC 13% of the overall distribution I.e. 13%x2% 0.003small
- [(m1,m2)(0.01 GeV2,0.065 GeV4)] is evaluated on the above montecarlo, the overall BKG systematics is (0.02,0.1))
**B********lD********** Not a Significant Source of Systematics**

- Alessandro Cerri         CKM Workshop

- 3/15/05

## Fake Correlated Leptons

- For background which is sign correlated the nastiest source is D**(-)+X where we mismatch + as a fake lepton:

|  | C=D0 | C=D*0 | C=D1*0 |
| --- | --- | --- | --- |
| Cl | 2.2% | 6.5% | 0.56% |
| C | 0.5% | 0.5% | 0.15% |
| C | 1.3% | 1% | <0.14% |
| ... | ... | ... | ... |

- Decreasing efficiency AND BR

- Assuming:
- An average efficiency equal to the one for signal
- Overall BR(BD**(-)+X) is at most 3xBR(BD**(-)l+X)
- From Run I + Run II studies from Masa, e+ fakes are about 1.6% in total for this trigger
- We get a fake count of ~2.4% the signal
- Kinematic m** bias much smaller than for the  background case
- Similar fake rate
******As negligible (or more favorable) than ******

- Alessandro Cerri         CKM Workshop

- 3/15/05

## One fit to combine them all, one fit to find them!...( )

- One fit to combine them all, one fit to find them!...( )

- Fit based on Bauer et al. (hep-ph/0210027)
- Fit (,1) in the pole scheme to moments vs pl* cut
- Not including all the CLEO points
- Including BELLE’s (thanks to the BELLE folks for privately providing the correlations)

- Alessandro Cerri         CKM Workshop

- 3/15/05

## Statistical Weight

- All

- All but BABAR

- All but CDF

- All but BELLE

- All but CLEO

- All but DELPHI

- Alessandro Cerri         CKM Workshop

- 3/15/05

## Statistical Weight

- All

- All but BABAR

- All but CDF

- Only BABAR

- Only CDF

- Same fit as previous page, but excluding single experiments
- CDF contribution is significant

- Alessandro Cerri         CKM Workshop

- 3/15/05