# Presentation: 223134

## Hadronic Moments in Semileptonic B Decays

- Ramon Miquel
- Lawrence Berkeley National Laboratory
- (for the CDF II Collaboration)

## 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):

- Ramon Miquel      BEACH 04

- 7/2/04

## 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...).

- Ramon Miquel      BEACH 04

- 7/2/04

## What is Xc?

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

- Higher mass states: D**

- Semi-leptonic widths (PDG 03):

|  |          Br (%) |
| --- | --- |
| B+  Xc l  |    10.89  0.26 |
| B+  D* l  |      6.00  0.24 |
| B+  D l  |      2.23  0.15 |

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

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

- Ramon Miquel      BEACH 04

- 7/2/04

## 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**

- Ramon Miquel      BEACH 04

- 7/2/04

## 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**0 l  better, use isospin for missing channels:

- Ramon Miquel      BEACH 04

- 7/2/04

## Event Topology

- 	      D0 *+                 (Br=67.7%)
- 	                K- +             (Br=3.8%)
-                                   K- + - + (Br=7.5%)
-                                    K- + 0     (Br=13.1%)

- _Event Topology_

- Exclusive reconstruction of D**:

-   D**0      D+ **-
- 	      K- + +  (Br=9.1%)

- “D+”

- “D*+”

- Ramon Miquel      BEACH 04

- 7/2/04

## 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

- Ramon Miquel      BEACH 04

- 7/2/04

## 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:
-  e/: pT > 4 GeV
-  other: pT > 0.4 GeV

- Total: ~ 28000 events

- Ramon Miquel      BEACH 04

- 7/2/04

## ** 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 data:

- Additional cuts only for D+:

- Ramon Miquel      BEACH 04

- 7/2/04

## Raw m** Distribution

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

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

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

**Feed-down**

- Ramon Miquel      BEACH 04

- 7/2/04

## 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.
- 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.

- Ramon Miquel      BEACH 04

- 7/2/04

## 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:

- No Fit !

- Ramon Miquel      BEACH 04

- 7/2/04

## Final Results

- Pole mass scheme

- 1S mass scheme

- 0.61

-  0.69

- Ramon Miquel      BEACH 04

- 7/2/04

## Systematic Errors

|  | m1 (GeV2) | m2
(GeV4) | M1
(GeV2) | M2
(GeV4) | 
(GeV) | 1
(GeV2) |
| --- | --- | --- | --- | --- | --- | --- |
| Stat. | 0.16 | 0.69 | 0.037 | 0.25 | 0.075 | 0.055 |
| Syst. | 0.08 | 0.20 | 0.065 | 0.12 | 0.090 | 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 |
| 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 |  |  | 0.062 | 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 |

- Ramon Miquel      BEACH 04

- 7/2/04

## Comparison with Previous Measurements

- Pole mass scheme

- Ramon Miquel      BEACH 04

- 7/2/04

## Summary

- First measurement of hadronic moments in semileptonic B decays performed at a hadron collider.
- Good agreement with HQET and previous determinations.
- Competitive with other experiments. Little model dependency. No assumptions on shape or rate of D** components.
- Increased statistics and improved tracking will lead to substantially more precise results in the near future.

- Ramon Miquel      BEACH 04

- 7/2/04

## BACK-UP SLIDES

## CKM and  Vcb

- | Vcb | = A******2**
- (defines the scale of UT)

- Ramon Miquel      BEACH 04

- 7/2/04

## Vcb measurements

-  Experiment: large statistics on BR(BXc-) and B 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)

- Ramon Miquel      BEACH 04

- 7/2/04

## Lepton + D Reconstruction

- Lepton + D(*)+:
-  D vertex:
-  3D
-  l+D(+*) vertex (“B”):
-  3D
-  Lxy(B) > 500 m
-  Lxy(D/B) > -200 m
-  m(B) < 5.3 GeV

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

- Track Selection:
-  e/: pT > 4 GeV
-  other: pT > 0.4 GeV

- Ramon Miquel      BEACH 04

- 7/2/04

## D*+ Reconstruction and Yields

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

- D(*)+ l(+cc)yields:

- ~ 28000 events

- Ramon Miquel      BEACH 04

- 7/2/04

## Monte-Carlo Validation (I)

- MC vs. semileptonic sample:

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

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

- Ramon Miquel      BEACH 04

- 7/2/04

## Monte-Carlo Validation (II)

- Relative yield prediction K3/K:  (cross-check)

- Rdata = 0.77±0.02
- Rpred = 0.80±0.04
- Rpred/Rdata = 1.04±0.06

-  efficiency for adding tracks understood

- Relative yield prediction K2/K:  (needed for D+/D* normalization)

- 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

-  uncertainties in Br (incl.) and D** spectroscopy (excl.) compromise prediction
-  1. – 0.87 = 13% used as systematics

| Rdata | Rpred | Rpred/Rdata |
| --- | --- | --- |
| 3.71±0.08 | 3.31±0.58 | 0.89±0.16 |
| 3.71±0.08 | 3.23±0.29 | 0.87±0.08 |

- Ramon Miquel      BEACH 04

- 7/2/04

## 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**

- Ramon Miquel      BEACH 04

- 7/2/04

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

- Ramon Miquel      BEACH 04

- 7/2/04

## Combination with D0, D*0

- Take M(D0), M(D*0), sl, 0, *  from PDG 2003 :
- 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  = 1.04 ± 0.08
- (B) / (B0)  = 1.085 ± 0.017
- Results:
-        BR(B+ ****X0c l+ l) = 0.1089 ± 0.0026
-        BR(B+ ****D0 l+ l)  = 0.0223 ± 0.0015
-        BR(B+ ****D*0 l+ l) = 0.0600 ± 0.0024

- Ramon Miquel      BEACH 04

- 7/2/04

## Main Systematics

-  Semileptonic branching ratios when combining D** with D and D*
-  Efficiency corrections from data
-  Use data-corrected efficiency. vs. pure MC efficiency
-  Efficiency corrections from D** Monte-Carlo
-  D** states + NR Goity-Roberts vs. pure phase-space
-  Mass resolution:
-  Dominated by satellite: ± 60 MeV
-  Prompt background scale
-  Charge correlations WS / RS: ± 4%
-  Other: D+/D* normalization, physics, pl* cut, theory...

- Ramon Miquel      BEACH 04

- 7/2/04