# Presentation: 801603

## Searches and limit analyses with the Fourier transform

- Alex (+LBL?), Donatella, Franco, Giuseppe, Sandro, Stefano

## Outline

- Quick introduction to the method
- Example
- Task list
- Status:
- “Fitter”
- Samples
- Other pieces (PID, SSKT, Semileptonic sample) in other talks (Paola, Pierlu, Sandro)

## The Method

- We are looking for a periodic signal: Fourier space is the natural tool
- Even Moser and Roussarie mention this!
- They use it to derive the most useful properties of A-scan
- Amplitude approach is approximately equivalent to the Fourier transform
- Amplitude from scan  Re[Fourier]
- Why not go for the real thing?
- Computationally lighter
- As powerful as A-scan
- As is, no need *in principle* for measurements of D,  etc. (however these ingredients add information and tighten the limit)

## Definitions and properties

- Discrete Fourier transform definition
- Given N measurements {tj} 
- Properties:
- Average:
- If f(t) is parent distribution of {tj}
- Normalization:
- Errors:
- Real part:
- NB: Errors can be calculated directly from the data!
-                                                          behaves “as you’d expect”
- While  and its uncertainty are fully data-driven, predicted  requires exactly the same ingredients as the amplitude scan fit

## Properties of ...

- Properties of ...

- Re[]
- contains all the information of the standard amplitude scan
- Amplitude scan properties are only approximate and mostly derived assuming       (Amplitude scan)Re[]
- Re[F] and Re[F] can be computed directly from data!
- b)  Sensitivity is exactly:

- Can we reproduce the A-scan itself?

## Toy Example

- “A-scan” a` la fourier

- 1000 toy events
- ms=18
- S/B=2.
- Dsignal2=1.6%
- Dback2=0.4%
- Background and signal parameterized according to standard analyses
- Histogrammed ct
- Best knowledge on SF parameterization

- No actual fit involved: this method allows to flexibly study systematics!

- Sensistivity:
-   Predicted
-   Measured

## Plans for our method

- Final proof of principle:
-    Process data from last round of analyses and show consistent picture with standard A-scan
- Prove viability of our method:
- Full semileptonic and hadronic samples
- Same taggers and datasets as latest blessed A-scans
- Compare results to our method
- Will be ready on time for winter conferences
- Extend:
- 1fb-1
- All possible modes
- State of the art taggers
- We will have a full analysis by Summer conferences

## Tasks (my view, still being finalized not yet endorsed/discussed)

- Data [Donatella, MDS, Stefano]
- Skimming [Donatella, Marjorie]
- MC
- Ntuples [Johannes, Giuseppe]
- Reco: [Alex, MDS, Stefano]
- Optimize selections [Alex, MDS]
- New channels (new modes, partially reconstructed) [Alex, MDS]
- Basic tools: [Stefano, Alex, MDS, Giuseppe, Johannes]
- PID [Stefano]
- Vertexing (understand resolutions etc.) [Alex, MDS]
- new taggers? (OSKT, SSKT...) [Giuseppe, Johannes]
- Fourier “fitter” [Alex, Franco]
- Toy MC [Alex]
- Tool for data Analysis (from ct, sigma, D, etc. to “the plot”) [Alex]
- Semileptonic Analysis [Alex, Sandro]
- Spring Analysis: reproduce the MIT result
- Summer Anal.:   - full 1 fb-1 indipendent analysis
- Hadronic Analysis (same as 5)
-                    [Alex, Amanda, Giuseppe, Hung-Chung, Stefano]
- Combine Analyses  [Alex]

## Fitter Status

- 

- 

- Pulls Mean vs 

- Pulls  vs 

- “Fitter” fully implemented
- Provided in the same consistent framework:
- Data processing
- Toy MC generation
- Bootstrap extraction
- Combination of several samples

## Dataset Skimming

## Main samples including new data are going to be there in ~week

|  | Files size [evts] |  |  |  | Old Sample |  |  | New Sample |  |  | MIT Yields |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| X |  | WS | 3 |  |  | WS | 3 |  | WS | 3 |  | 3 |
|  |  |  |  |  |  |  |  |  |  |  (90%) | 55142 | 15817 |
| 3 |  |  |  |  |  |  | 
(99%) |  |  |  |  |  |
| K*K | 71 | 62 | 637 |  | - |  |  |  |  |  | 23842 | 6311 |
| KsK | - | - | - |  | - |  |  |  |  |  |  |  |
|  | 134 | 94 | - |  |  |  |  |  |  |  | 10824 |  |
|  |  |  |  |  |  |  |  |  |  |  |  |  |
| K | 370 | 316 | 2038 |  |  |  |  |  |  |  | 842481 | 4611129 |
| K | 18 | - | 100 |  |  |  |  |  |  |  | 137735 | 108943 |
| KK | - | - | - |  |  |  |  |  |  |  |  |  |
|  | - | - | - |  |  |  |  |  |  |  |  |  |
| K3 | - | - | - |  |  |  |  |  |  |  | 101326 | 82035 |
| K | 92 | - | - |  |  |  |  |  |  |  | 960184 | 155745 |
| KK | 90 | - | - |  |  |  |  |  |  |  |  |  |
|  | 42 | - | - |  |  |  |  |  |  |  |  |  |
| K3 | - | - | - |  |  |  |  |  |  |  |  |  |

- 2476 evts
- 270 MB

- 210 evts 25 MB

- BsDsX

- B0D+X

- B0D*(D0)X

- B+D0X

## Conclusions

- This is an AGGRESSIVE PLAN
- We started moving at a good pace
- We need to keep going, faster?
- We want to have
- Preliminary results by spring (me hopes ~march)
- independent results by the summer!
- A joint effort is the only way of getting this through!