# Presentation: 409748

## Evidence for the exclusive decay 
Bc J/

 Saverio D’Auria 

For the
CDF collaboration

- Evidence for the exclusive decay
- Bc J/
-  _Saverio D’Auria_
- For the
*CDF collaboration*

## Contents

- The Bc meson: what is known, why it is relevant
- The Tevatron and the CDF detector
- The search strategy:“*blind analysis”*
- The results

## ub uc us ud uu

- u_b_ _u_c u_s_ ud u_u_
- d_b_ _d_c d_s_ d_d_
- s_b_ _s_c s_s_
- c_b_ c_c_
- b_b_

- B+ D0 K+ + 
- B0 D+ K0 
- Bs Ds 
- Bc J/
**

- Bc:  the 15th type of meson foreseen by the quark theory:

- Ground state of a *c-*_*b*_ quark combination.

- 1947 Lattes Occhialini Powell: +  +
- 1964 Quark model of mesons: u,d,s
- 1974 J/ discovered: *c*-quark
- 1977 ** discovered: *b*-quark
- 1994 *t*-quark found: too heavy, no bound state
- 1998 Bc observed at CDF: semileptonic decays only

## Why Bc is interesting:

- Together with b the *B*c is the only other meson ground state to have theoretical prediction more precise than experimental mass measurement. Validation of lattice and potential models.
- Spectroscopy of excited states: verify different models.
- Fragmentation: its production rate can shed light on fragmentation mechanism (only heavy quarks involved).
*B*s physics: some *B*s are product of *B*c decays: production rate and branching fraction to *B*s to assess the *B*c contribution to *B*s lifetime and mixing: source of dilution (sameside , instead of K).

**For future experiments:**
* **B**s** mixing: perfect source of tagged B**s.*
-  CP asymmetry measurement in _D_0Ds decay mode.
-  Rare decays.

## Evidence at CDF in ’98

- Observed in Semi Leptonic mode
- only: Bc J/*l *X

- PDG 2004

- Meson made of a *b* and *c* quark

## Slide 6

## Theory can calculate the Bc mass with a very small uncertainty.

- Un-quenched QCD latest calculation of the mass:
-  M(Bc) = (6304 ±12(statsys)+18(discr)) MeV/c2
- arXiv:hep-lat/0411027

- From arXiv:hep-lat/0411027

- 22] I.F. Allison et al. hep-lat/0411027
- 23] W.K. Kwong & J.L. Rosner Phys Rev D 44, 212 (1991)
- 17] H. P. Shannahan et al. Phys. Lett. B 453, 289 (1999)
- 24] E.J. Eichten & C Quigg Phys Rev D 49 5845 (1994)
- 25] N. Brambilla & A. Vairo Phys Rev D 62 094019 (2000)
- 26] N. Brambilla et al. Phys Lett B 513, 381 (2001)

## The CDF detector

## Integrated luminosity on tape to date: 360 pb-1”good runs”

- Integrated luminosity on tape to date: 360 pb-1”good runs”
- Require Silicon, Central Drift Chamber, muon system in good operating conditions. All available data are used in this analysis

- Day ordinal number

## p

## SVX II

- sensors

- Be beampipe

**SVX II**

- Analysis performed in 3D.  First CDF analysis to benefit of L00

**Layer-00**

- 2.3cm

- 4.2cm

- ISL:
-  phi-small angle stereo layer(s)
- SVX:
- 3 phi-z, 2 phi-small angle layers
- L00:
- 1 singlesided layer <r>= 1.6 cm

## L00 performances.

- Measured using impact parameter of prompt tracks
- Fit to:
- Asymptotic resolution,
- Multiple scattering

- Asymptotic resolution:
- beam size accounted for
- Resolution improves from 35.6 to 25.1 m
- Larger improvement at low momentum
- Improves matching of pions to J/ vertex

- In region populated by hybrids

## p

- Tracker
- Central Outer Chamber
- (COT)

## Excellent place to detect a 

- Systematic uncertainty at  sub-MeV/c2 level
- Best single-experiment measurement
- of the mass of b-hadrons.
- Excellent place to detect a
- Fully-reconstructed decay of Bc
_*and to measure its mass*_.

- CDF performances in
*b*-meson mass measurement:

- Mass scale calibrated precisely on J/mass

## The search strategy

## The only meson in which both quarks can decay weakly:

*b*-decays and *c*-decays.
- Choose a decay mode that
-  Has only charged tracks in final state
-  Has a reasonable branching fraction to the final state

- c

- Bc meson

- c

- J/

- *l**l*...

- c

- *l**l*...

- Bs*

| Decay | BR (%) | Final state | BR to Final state |
| --- | --- | --- | --- |
| J/ | 0.13 |  | 7.8 · 10-5 |
| c | 0.20 |  | 1 · 10-4 |
| J/ a1 | 0.13* |  | 3.4 · 10-5 |
| D0 D+ | 1.4 · 10-2 |  | 5 · 10-7 |
| J/ Ds | 0.17 |  | 1.8 · 10-5 |
| Bs  | 16.4 |  | 5 · 10 |

- We have chosen the decay mode:
- 	      Bc J/
- Advantages: we have a good trigger for this mode,
- simple two-body decay, only 3 tracks
- large final branching ratio.

- Kiselev hep-ph/0308214

## The Trigger

- This channel can be studied using the J/ di-muon trigger path

- No lifetime information used
- in this trigger path. Unbiased for lifetime measurement, can go as low as possible in lifetime cuts.

- pT cuts for trigger muons: pT > 1.5 GeV/c
- Trigger on low momentum J/ possible
- Extended muon coverage (CMX) also used

## The decay mode Bc J/

- Same topology as a very well known decay mode of B+ J/

- Experimental difficulties:
- Bc lifetime is shorter than light *b*-mesons (charm decay dominates)  secondary  vertex closer to the primary vertex. Need best spatial resolution (first use of “L00” hits and track-fitted primary vertex position).
- Expected signal > 10 times smaller than the signal in the semileptonic decay.

- Analysis method:
- Reconstruct  vertex
- Constrain  to J/mass
- Attach a third track with pT threshold
- Require
- good vertex 2,
- decay length,
- pointing to primary vertex

## Background

- Large “**prompt**” background from prompt J/ plus track from primary vertex
- Possible background from collinear *b *_*b*_ production (*gluon splitting*).

- 

- 

- Require candidates with decay length >0
- Cut on pT of the “third track”

- B+

- B0

- 

- 

- Require good 3D vertex

## Expected sensitivity calculated with respect to B+ J/,

*It is the same channel used as a reference in the  Run-I observation* .

- All theoretical uncertainties are in the value of R2

- To evaluate the expected signal we use previous measurement and one ratio of *BR*.

## We assumed R2 = 0.06

-  From theoretical predictions
-  From experimental values in light *b*-mesons using simple quark spectator model

- We assumed R2 = 0.06

## The analysis method

- The blind analysis
- The analysis cuts
- The use of Monte Carlo
- The statistical method

## We performed a “blind analysis”:

- Reason: we don’t want to influence the choice of cuts
- based on visual inspection of the result (or, worst, on fit).
- Blinding procedure:
- Within search window substitute the mass value with
- one of two values
- M = 6.0 , if 5.6 < M < 6.4
- M = 6.8 , if 6.4 < M < 7.2
- Search window = PDG mass value ± 2   from 5.6 to 7.2 GeV/c2
- Optimization of cuts based on Monte Carlo simulation of signal
**Assume all candidates in this mass window are background:**
- Fraction of expected signal contribution assumed small.

- Maximize

- S = number of signal events from MC
- B = average number of background events (data) from whole region in a window  ±2- wide (60.4 MeV/c2).

- Balanced score-function for limit and “discovery” (hep-physics/0308063)
- avoid fine-tuning

## Use of Monte Carlo: 

- For relative efficiency with respect to B+  only for sensitivity studies
- For cut optimization.
- Generator: Single b-meson generator using meson pT-y spectrum from Chang et al.
- Full detector simulation, run-dependant conditions for beam position and silicon coverage, full L1 and L2 trigger simulation
- Optimize cuts using measured values for mass (M = 6.4 GeV/c2) and lifetime (c = 0.46 ps), check cut robustness with other values, within range.
- Pythia MC used when underlying event is needed (track-fitted primary vertex)
- Rely on reference sample B+ J/for other quantities.
- Performed checks on reference sample for MC quantities.

## Used the track-fitted primary vertex position:

- Good resolution in *z* as well as in *x-y*

- Beam line

- Exclude candidate tracks
- Algorithm to exclude tracks with large impact parameter.

- Event reconstruction

## Motivation for each cut

- pT of the third track ():
- To cut off  the low-momentum tracks from underlying event
- 3D vertex 2 = 2 () + 2 () + 2 ()
- To ensure good 3-track vertex:
- Significance of the projected decay length: Lxy /(Lxy)
- To select non-prompt candidates
- Contribution to the 3D Vertex due to the third track 2 () :
- To ensure that the third track is correctly assigned to the J/ vertex
- Pointing angle  (in 3D):
- To select fully reconstructed decays
- Impact parameter of reconstructed meson in *x-y* plane:
- As before, very powerful for short decay.
- Upper ct cut:
-  to cut background from long-lived *b*-hadrons

- Cuts optimized using “N-1” iterative process

## “N-1” distributions of quantities on which we cut.

- “N-1” distributions of quantities on which we cut.

- Normalized to unit area
- Shape of signal and background quite different

## “N-1” cut optimization graphs

- “N-1” cut optimization graphs

## Summary of cut values used:

- pT () 		> 1.8 GeV/c
- Lxy/(Lxy) 	      > 4.4
- 2(3D)  		< 9.0
- d0(Bc)  		< 65 m
- pointing angle< 0.4 radians
- 2vtx() 		< 2.6
- ct 		<  750 m

| Cut | MC Efficiency | N-1 data entries | Background rejection |
| --- | --- | --- | --- |
| Lxy/(Lxy) | 42.0% | 11930 | 96.7% |
| pT () | 62.3% | 3043 | 87.1% |
| 2(3D) | 80.5% | 762 | 48.4% |
| Pointing angle | 85.4% | 768 | 48.8% |
| 2vtx() | 92.7% | 565 | 30.4% |
| d0(Bc) | 97.5% | 448 | 12.3% |
| ct | 98.7% | 410 | 4.1% |

- Summary of analysis cuts

## B+ J/

- (efficiency = 60% with respect to cuts used in B+ mass measurement that has 10× more background)
- Using these cuts the relative efficiency from Monte Carlo is

- Based on “standard” values of MC ( i.e. spectrum) and lowest theoretical value for R = 0.008
- we have estimated an expected signal S ranging from 4 to 30 events, as the lifetime varies within the 1- uncertainty

- B+ J/
- Used for
- checking data/MC
- estimating expected significance

- Reference channel

## Background: 390 events survive the cuts. 

- Background: 390 events survive the cuts.
- The expected  resolution varies from 13 to 19 GeV/c2 over the mass range
- The average background ranges from  9 to 20 events in a ±2  region around the mass peak. detector resolution from MC (checked on J/ K).

- Resolution as a function of invariant mass

- Background expected

## What do we expect from Monte Carlo

## Checks on events passing the cuts

*z*-distribution looks ok (no excess from “bulkhead regions)
- Silicon hit use ok

## The statistical method

- In this case standard methods of establishing signal significance (e.g. Poisson probability) fail (Rolke-Lopez, PHYSTAT 2003) At the limit of infinite search window the probability of occurring in a fluctuation is 1.

- We have to set up a way to test
- the hypothesis : “there is a significant peak in one place” against the
*null hypothesis*: “there is no peak in any place in the search window”
- What is fixed in our test: the width of the signal (detector resolution)
- Some definitions:
- “False positive” : mistaking a random fluctuation for a mass peak
- “False negative”: concluding that there is no significant peak, when 		    instead there is signal. (not a mistake, a missed opportunity)
- Philosophical note:
- The real truth is unknown and can be inferred only in the limit of infinite statistics. Practically: more statistics and/or independent tests.

## The statistical method

- Decide in advance on a procedure to search for a peak, i.e define an algorithm and a “significance” or “score function”.
- Decide in advance on a level of acceptable probability for false positive (probability that background fluctuates into a signal): we choose  Pfp = 0.1% this is better than single-sided Gaussian tail > 3 
- Deploy the peak-finder method on a “toy Monte Carlo” distribution, containing only background and no signal, to set-up the statistical test: establish the value of the  “score function” corresponding to  Pfp = 0.1% . This completely defines the test.
- Find the power of the statistical test, i.e. minimum number of real events needed to have only 5% of false negative, using “toy MC”. Useful for establishing limit.
- Apply the same test to the data and find out if it is above or below the threshold determined in step (3).

## Toy-MC function: 

-     linear background plus broad Gaussian to simulate partially reconstructed decays
- Peak finder:
-      binned likelihood fit
- Fit function:
-       linear for background, plus gaussian for signal.
-       Constraints:
-                      peak position and width are fixed,
-                      number of signal events S is constrained to be S  0
- Step:	10 MeV
- Range: 	-100 + 200 MeV from the sliding peak position. Asymmetric to minimize bias from partially reconstructed decays
- Score function:

## Results of toy-MC experiments

- function for toy MC experiments
- with Strue = 30 , corresponding to a false negative probability of 5%. Signals smaller than 30 counts can still be detected, with smaller probability.

## Decision tree:

- If the score function is in any contiguous region in mass above 3.5 (that means probability of fluctuation < 0.1%) we interpret this as evidence for this decay and we measure the mass.
- If the score function is everywhere below 3.5 we set a limit on
-   *BR* as a function of lifetime.
- If the score function is above 3.5 in more than one location we declare “crisis” and wait for more data to resolve the issue.

## Why did we choose probability for a false positive < 0.1% :

- The expected number of signal events ranges from 4 to 60 events, and is a function of lifetime, pT spectrum, branching ratio.
- With present data sample we have 10 times more J/ K than Run I
- Although not the whole range of values could be excluded, it is a good time to open the box and allow for “evidence”.
- To achieve a probability of “false positive” corresponding to the probability of a 5 Gaussian tail, with the same test would require about > 1 fb-1.
- 	We decided to open the box with these criteria.

## The results

## One significant peak

- less than 0.1% probability that it is a statistical fluctuation.

- ..Let’s measure the mass

## Here is the mass plot.

## Mass = (6287.0 ± 4.8stat.) MeV/c2

- Measure mass of highest significance peak, width is constrained.

- Mass = (6287.0 ± 4.8stat.) MeV/c2

## Systematic Uncertainties:

- The mass resolution has been calibrated using the J/ mass.
- We benefit from other analyses that have pinned down the
- systematic uncertainties to 300 keV for high statistics decay modes.
- Systematic                Value (MeV/c2)
- Background shape: 	0.8
- Momentum scale: 	0.6
- /K dE/dx: 	0.2
- Tracking:	0.2
- pT: 	0.5
- Total:                       	1.1
- Main source of systematic uncertainty is statistics limited.

- from fits, changing background shape.
- Calculation based on other analysis
- To extrapolate from other analysis
- from other analysis
- Additional, to account for different spectrum

## Comparisons and conclusions

## How does this measurement compare with 

- previous determinations of Bc mass (semileptonic decay)
- Factor 100 more precise, due to the fully reconstructed decay.

## How does this measurement compare with 

- theoretical calculations
- General good agreement

- This measurement

## measurement of Bc lifetime: 

- measure properties of the Bc
- measurement of Bc lifetime:
- semileptonic channels
- fully reconstructed channel(s)
- measurement of production times branching fraction
- measure pT spectrum
- add more statistics, when we shall have more data
- branching fraction of other decay channels: J/ a1, Bs ,...
- excited states
- measure spin
- Far future:
- rare decays
- ..... Whole new set of measurements possible

## Conclusions

- We defined a blind procedure to search for, or set limits on, the decay mode      Bc  J/. The criteria was to unblind the analysis when a background fluctuation with probability < 0.1% was achievable.
- Opening the box we found evidence for fully reconstructed Bc decays, with 19 signal events over a background of 10 events.
- Interpreting these events as Bc J/we measure a Bc  mass of:
-                   M(Bc) = (6287.0 ± 4.8 ± 1.1) MeV/c2
- This mass number is in good agreement with the theoretical predictions
- 	 note: predictions not used to determine region to search for signal.
- We shall study further the properties of the Bc also with other channels and more statistics.

## We are grateful to 

- our colleagues of the FNAL accelerator division,
- who provided luminosity,
- to the Fermilab technical staff and to
- the funding agencies for support.

## Fermilab, 9th November, 2004, 3 a.m.

- Aurora Borealis at 42° N

- Fermilab, 9th November, 2004, 3 a.m.

## Q:

- If the search region were the one indicated by theorists, what would the significance of the signal be?
- A: The probability that the 29 events are  a random fluctuation of an average background of 10 is

*Disclaimer: this statistical test is not what we have done*

## Example of 

- Example of
- Data-MC comparison

- = 11.5 MeV/c2

- MC resolution

## Slide 54

## Some checks on candidate events (from peak)

## Slide 56