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B s → ff sensitivity study

B s → ff sensitivity study. Time dependent angular distribution First preliminary results. Yuehong Xie Edinburgh LHCb Group Meeting 3 November 2006. B s → ff decay rate. Define q 1 and q 2 as the polar angles of K + in their mother f rest frames

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B s → ff sensitivity study

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  1. Bs→ff sensitivity study • Time dependent angular distribution • First preliminary results Yuehong Xie Edinburgh LHCb Group Meeting 3 November 2006

  2. Bs→ ff decay rate • Define q1and q2 as the polar angles of K+ in their mother f rest frames • Define j1and j2 the two azimuzal angles and c= j2+ j1 Yuehong Xie

  3. Angular functions Yuehong Xie

  4. Time evolvement of Bs Yuehong Xie

  5. Time evolvement of anti-Bs Yuehong Xie

  6. 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 >1D 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 ! Yuehong Xie

  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 Dms=17.3 ps-1 • Fix GL=0.72 ps-1 and GH=0.62 ps-1 ( DG/G=0.15) • Input: |A┴|2 =0.25 and |A┴|2 =0.25 • Input: d1=0 and d2=p • 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 Yuehong Xie

  8. Result sfs = 0.093+-0.004, <fs> = 0.195+-0.006 Yuehong Xie

  9. Another example: untagged fit sfs = 0.23+-0.01, <fs> = 0.22+-0.01 Yuehong Xie

  10. What is next • Implement time convolution • Add background • Use both tagged and untagged • More toys Yuehong Xie

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