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Determining the Coherence Factor, R, of D ® K3 p Decays. Motivation Reminder B ® DK: Access to CKM g Use of DCS D 0 Decays: ‘ADS’ Approach Coherence Factor, R . Status with Preliminary Measurements Reconstruction Efficiencies Background Estimations (Data and MC)

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Determining the Coherence Factor, R, of D ®K3pDecays

  • Motivation Reminder

    • B ® DK: Access to CKM g

    • Use of DCS D0 Decays: ‘ADS’ Approach

    • Coherence Factor, R

  • Status with Preliminary Measurements

    • Reconstruction Efficiencies

    • Background Estimations (Data and MC)

    • Sensitivities: Present Status and Prospects

Andrew Powell (University of Oxford)

On behalf of the UK group

D-Hadronic PTA, CLEO-c Collaboration Meeting, July 9th 2007

gfromB±®DK ±

  • Extraction through interference between b c and b u transitions


  • Requireandto decay to a common final state,f(D)

Common starting point for a variety of methods to extractg

‘ADS’ Strategy: D ® hh

Large interference possible if amplitudes of similar magnitude

f(D) = non-CP Eigenstate(e.g. K+p-)

DCS Decay

CF Decay

Interference is now large when

looking at ‘wrong sign’ decays: (2) & (4)





These + other rates (e.g. D®KK, pp) allow unknowns to be fitted.

‘ADS’ Strategy: D ® Multi-Body

  • Using the same approach, the final state can also be considered.

  • Neglecting the resonant sub-structure for the 4-body decay would mean rate (2) would look like:

where we introduce the additional parameters rDK3p and dDK3p

  • Considering the resonant sub-structure modifies the above by introducing a dilution term (value: 0-1) called the ‘Coherence’ factor, RK3p. dD then becomes an ‘averaged’ strong phase difference, z :

[ Atwood & Soni, Phys Rev D 68 (2003) 033003 ]

  • The above paper details how one could measure RK3p at a charm factory. We are now making first measurements here at CLEO-c …


  • To measure RK3p we need to analyse the following double tagged y(3770)data samples and simply count the events observed:

    • 1)

    • 2)

    • 3)

    • 4)

Opposite Sign Kaon

CP even

CP odd

Same Sign Kaon

Why These Tags?

  • Provides normalisation factor

  • & 3) :

4) :

Therefore, can get separate measurements of


Preliminary K3p vs Tags

Selection Results

MC Reconstruction Efficiencies

  • Since last time, have followed Alexander Scott’s TQCA CBX note (in preparation)and have applied the following:

  • Best candidate according to

  • |DE| cuts and Signal-Box in MBC(K3p) vs MBC(Tag)

(MBC(K3p), MBC(Tag)) = (1.86 : 1.87, 1.86 : 1.87)

eRec (%)






Cut (GeV)




























Non-Peaking Background In Data

As shown last time, Jim Libby has run a selection for these 5 modes over the 281pb-1 data set. Applying the same techniques as quoted in Alexander Scott’s CBX note, Jim has estimated the non-peaking, combinatoric, background from analysing the Mbc sidebands.

  • Definitions:

    • S: signal box

    • A: lower signal Mbc sideband

      • signal mis-reconstruction

    • B: lower tag Mbc sideband

      • tag mis-reconstruction

    • C: lower mispartition Mbc sideband

      • particles swapped between D candidates

      • |Mbc(K3π)−Mbc(Tag)|<3.5 MeV/c2

    • D: non DD combinatoric

      • |Mbc(K3π)−Mbc(Tag)|>5.5 MeV/c2

K3π vs K3π(Opp. Sign)







K3π vs K0S π0

K3π vs K3π (likesign)

The Other Modes …

K3π vs π+π−

K3π vs K+K−

Counting Signal + Non-Peaking Bkg

Assessing the events found for each mode within these defined sideband regions results in the following signal and estimated background numbers:

Avoids double counting

of combinatoric background

In order to determine sources of peaking background, we have looked at the generic DDbar MC…

MC Background Studies

  • As a ‘preliminary’ study, we have run over the 10 x lumi. corresponding to dataset 37 (10 x 111.105pb-1).

  • All results are consistent with Jim’s estimates, except for a notable peaking background seen in the Ksp0 tag from:

  • r+(p+p0)p-

  • p+p-p0

  • r0(p+p-)p0

Observed ratios

(I : II : III) = (10 : 4 : 1)

  • This is a consequence of a relatively loose Ksp0 mass window (30 MeV)

  • Intend to tighten this in future to 10 – 7.5 MeV

  • An additional peaking background has been observed in the K3p tag:

  • No Flight-Significance cut is currently applied. Intend to apply this to reject the Ks background.

  • K*-(Ksp-)K+

  • K*0(K-p+)Ks

RK3p cos(z ) : Sensitivity


With Current Data Set

& Implementation

  • With the current 281pb-1y(3770)sample and using the set of tags currently being investigated we calculate a statistical uncertainty on the quantity RK3p cos(z )as being:

  • This corresponds to the shaded region in parameter space (right).

  • However, this can be improved …

sstat= 0.36

Above plot generated using an “Illustrative” value: RK3p cos(z ) = -0.5

With Final Data Set

& Additional Tags

  • With a (predicted) 750 pb-1y(3770)sample and using the current set of tags along with additional CP tags (including KL) it is possible to further reduce this uncertainty:

  • Further improvements possible by considering ‘pseudo-CP’ tags (K0pp)

sstat~ 0.15

Above plot generated using an “Illustrative” value: RK3p cos(z ) = -0.5

‘Non-Global’ Determination of RK3p cos(z )

  • We expect RK3p to be small when considering events integrated over all the allowable decay phase-space, as we are doing now. (i.e. ‘Global’ measurement).

  • Given this, we intend to investigate considering only those events in localised regions of decay phase-space (i.e. a binned analysis) where a known resonance is dominant (e.g. K* or r).

  • Through intelligent binning, one would expect greater coherence and a value of RK3p much closer to 1. This would then have obvious benefits towards use in ADS type measurements at experiments like LHCb.

  • This is something we intend to perform and most likely conduct in parallel with the ‘global’ measurement of RK3p cos(z ).


  • Determination of RK3p is invaluable for use as an external constraint in ‘ADS’ type g extraction strategies at LHCb.

  • Progress is being made with the current 281pb-1 CLEO-c dataset to measure the quantity RK3p cos(z ).

  • Once further understanding of our backgrounds has been made, a first determination will be possible.

  • Much improved measurements should be achievable by considering additional CP tags and KL as well as Ks.

  • A ‘binned’ analysis is also foreseen to be performed.

  • Not forgetting that the other technique, an amplitude analysis of the four-body final state, will begin in earnest soon.