Bs?ff sensitivity study

1
Bs?ff sensitivity study

• Time dependent angular distribution
• First preliminary results

• Yuehong Xie
• Edinburgh LHCb Group Meeting
• 3 November 2006

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Bs? ff decay rate

• Define q1 and q2 as the polar angles of K in
  their mother f rest frames
• Define j1 and j2 the two azimuzal angles and c
  j2 j1

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Angular functions
4
Time evolvement of Bs
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Time evolvement of anti-Bs
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RooFit procedure

• Implement a PDF according to the obtained 4D
  distribution
• Should also take into account
• flavour tagging
• time resolution
• time acceptance function
• background
• Generate some events for each experiment and fit,
  leaving fs, A//2 and A-2 , d1, d2 as free
  parameters, fixing GL, GH and all experimental
  parameters assuming they can be obtained
  separately
• Critical issue for fit to converge avoid
  numerical integration in gt1D space
• Notice the total rate is a sum of 6 terms. Each
  term can be factorized into angular part and time
  part. The angular term can be integrated
  analytically. Time part is difficult due to
  acceptance function. Use numerical integration
  for time only. Fit converges !

7
Toy study

• Tagging efficiency 60
• 4k signal events, but so far only use 2.4 k
  tagged ignoring the unragged
• wrong tagging fraction 33
• Ignore background
• Fix Dms17.3 ps-1
• Fix GL0.72 ps-1 and GH0.62 ps-1 ( DG/G0.15)
• Input A-2 0.25 and A-2 0.25
• Input d10 and d2p
• Input fs 0.2
• Time resolution 40 fs, but time convolution not
  implemented yet. Only multiply a time dilution
  faction of exp(-(dms sigma_time)2/2)0.787 to
  oscillation terms
• 100 toy experiments

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Result
sfs 0.093-0.004, ltfsgt 0.195-0.006
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Another example untagged fit
sfs 0.23-0.01, ltfsgt 0.22-0.01
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What is next

• Implement time convolution
• Add background
• Use both tagged and untagged
• More toys