Improving the precision of gamma/phi_3 via CLEO-c Measurements

Abstract

Quantum correlations in $\psi(3770) \to D^0\bar{D}^0$ provide unique access to information about strong phase differences. Precision determination of the CKM phase $\gamma/\phi_3$ via $B \to D K$ decays depends upon constraints on charm mixing amplitudes, measurements of doubly-Cabibbo suppressed amplitudes and relative phases, and studies of correlated charmed meson decays tagged by flavor or CP eigenstates. CP-tagged $D^0 \to K^-\pi^+\pi^-\pi^+$ decays and CP-tagged $D^0 \to K^0_S\pi^+\pi^-$ Dalitz plots are only available at CLEO-c. Using the 818 pb$^{-1}$ CLEO-c data sample produced by the Cornell Electron Storage Ring (CESR) at $\sqrt{s} = 3.77$ GeV, we perform analyses of these decays. We describe the techniques used to measure the $D$-decay parameters, and the CLEO-c impact on measurements of $\gamma/\phi_3$.

Full text

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arXiv:0810.3666v1 [hep-ex] 20 Oct 2008
34thInternational Conference on High Energy Physics, Philadelphia, 2008
Improving the precision of γ/φ3via CLEO-c Measurements
P. Naik (for the CLEO collaboration)
University of Bristol, Bristol BS8 1TL, UK
Quantum correlations in ψ(3770) → D0¯D0provide unique access to information about strong phase differences.
Precision determination of the CKM phase γ/φ3 via B → DK decays depends upon constraints on charm mixing
amplitudes, measurements of doubly-Cabibbo suppressed amplitudes and relative phases, and studies of correlated
charmed meson decays tagged by flavor or CP eigenstates. CP-tagged D0→ K−π+π−π+decays and CP-tagged
D0→ K0
the Cornell Electron Storage Ring (CESR) at√s = 3.77 GeV, we perform analyses of these decays. We describe the
techniques used to measure the D-decay parameters, and the CLEO-c impact on measurements of γ/φ3.
Sπ+π−Dalitz plots are only available at CLEO-c. Using the 818 pb−1CLEO-c data sample produced by
1. INTRODUCTION
1.1. Measuring the CKM Phase γ
Precision measurements of the weak phases that compose the unitarity triangle, α, β and γ, allow us to test the
internal consistency of the Cabbibo-Kaboyashi-Maskawa (CKM) model and search for signatures of New Physics.
The CKM phase γ is only constrained by direct measurements to (67+32
determining the CKM phase γ exploit the interference within B±→ DK±decays, where the neutral D meson is a
D0or¯D0. The most straightforward of these strategies considers two-body final states of the D meson, but additional
information can be gained from strategies that consider multi-body final states. The parameters associated with the
specific final states needed for these analyses can be extracted from correlations within CLEO-c [2] ψ(3770) data.
−25)◦[1]. The most promising methods of
1.2. Determination of the CKM phase γ from B±→ DK±
The interference between decays of the type B±→ DK±provide a theoretically clean method for extracting the
CKM phase γ when the D0and¯D0mesons decay to a common final state, fD. For example, we may write the ratio
of the amplitudes between the suppressed amplitude and the dominant amplitude as:
A(B−→¯D0K−)
A(B−→ D0K−)= rBei(δB−γ),(1)
and we may write a similar ratio for B+→ DK+. The ratio of these amplitudes is a function of the ratio of the
amplitudes’ absolute magnitudes (rB), a CP invariant strong phase difference (δB), and the CKM weak phase γ.
Due to color and CKM suppression, rB∼ 0.1 [1]; therefore, the interference is generally small. A variety of strategies
exist, however, that attempt to resolve this and maximize the achievable sensitivity to γ.
2. The ADS Formalism and D → K−π+
Atwood, Dunietz and Soni (ADS)[3] have suggested considering D decays to non-CP eigenstates as a way of
maximizing sensitivity to γ. Final states such as K−π+, which may arise from either a Cabibbo favored D0decay or
a doubly Cabibbo suppressed¯D0decay, can lead to large interference effects and hence provide particular sensitivity
to γ. This can be observed by considering the rates for the two possible B−processes:
Γ(B−→ (K−π+)DK−) ∝ 1 + (rBrKπ
Γ(B−→ (K+π−)DK−) ∝ r2
D)2+ 2rBrKπ
2+ 2rBrKπ
D cos?δB− δKπ
D cos?δB+ δKπ
D
− γ?,
− γ?,
(2)
B+ (rKπ
D)
D
(3)
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34thInternational Conference on High Energy Physics, Philadelphia, 2008
where rKπ
relative strong phase difference. By considering the other two rates associated with the B+decay, and combining
this with information from decays to the CP-eigenstates K+K−and π+π−, an unambiguous determination of γ can
be made. CLEO-c has recently measured δKπ
D
to be (22+14
reconstructed ψ(3770) → D¯D decays [5].
D
=
?(0.3342 ± 0.0084)% [4] parameterizes the relative suppression between AD0 and A ¯ D0, and δKπ
D, the
−15)◦through a quantum correlated analysis of completely
3. D → K−π+π+π−
3.1. Multi-body Extension to the ADS Method
The ADS formalism can be extended by considering multi-body decays of the D meson. However, a multi-body
D-decay amplitude is potentially different at any point within the decay phase space, because of the contribution
of intermediate resonances. It is shown in Ref. [6] how the rate equations for the two-body ADS method should be
modified for use with multi-body final states. In the case of the B−rates, for some inclusive final state f, Eq. (3)
becomes:
Γ(B−→ (¯f)DK−) ∝¯A2
f+ r2
BA2
f+ 2rBRfAf¯Afcos
?
δB+ δf
D− γ
?
,(4)
where Rf, the coherence factor, and δf
D, the average strong phase difference, are defined as:
A2
f=
?
?|AD0(x)||A ¯ D0(x)|eiζ(x)dx
Af¯Af
|AD0(x)|2dx,
¯A2
f=
?
|A¯ D0(x)|2dx,(5)
Rfeiδf
D =
{Rf∈ R | 0 ≤ Rf≤ 1},(6)
where x represents a point in multi-body phase space and ζ(x) is the corresponding strong phase difference.
3.2. Determining Rfand δf
Dat CLEO-c
It has been shown in Ref. [6] that, double-tagged D0¯D0rates measured at ψ(3770) threshold provide sensitivity
to both the coherence factor, Rf, and the average strong phase difference, δf
wavefunction [7] of the ψ(3770) and then calculating the matrix element for the general case of two inclusive final
states, F and G, the double-tagged rate is found to be proportional to:
D. Starting with the anti-symmetric
Γ(F|G) ∝ A2
F¯A2
G+¯A2
FA2
G− 2RFRGAF¯AFAG¯AGcos(δF
D− δG
D).(7)
From this, one finds three separate cases of interest for accessing both the coherence factor and the average strong
phase difference. These results are summarized in Ref. [8], where CLEO-c has provided a preliminary determination
of RK3π and δK3π
D
for the instance of F = Kπππ using 818 pb−1of data taken at the ψ(3770) resonance. The
resulting constraints on the parameters RK3πand δK3π
D
from these preliminary measurements are shown in Fig. 1. It
is apparent, from Fig. 1, that the coherence across all phase space is low, reflecting the fact that many out of phase
resonances contribute to the Kπππ final state. An inclusive analysis of this final state with the ADS analysis will
therefore have low sensitivity to the phase γ, although the structure of Eq. (4) makes it clear that such an analysis
will allow for a determination of the amplitude ratio rB, which is a very important auxiliary parameter in the γ
measurement.
Shown in Figure 2 are projections of the overall systematic uncertainty on γ at LHCb [9]. The figure demonstrates
how the overall systematic uncertainty on γ improves as additional information from CLEO-c is used in concert with
expected LHCb data samples documented in Reference [10].
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34thInternational Conference on High Energy Physics, Philadelphia, 2008
π
K3
R
00.10.20.3 0.40.50.60.7 0.80.91
(deg.)
π
K3
δ
D
0
50
100
150
200
250
300
350
σ
σ
σ
1
2
3
Best fit
-1
CLEO-c preliminary 818 pb
Figure 1: (Preliminary) resulting limits on RK3π and δK3π
D
at 1σ, 2σ and 3σ levels.
) °
(
π
K
D
δ
-1001020304050
) °
(
γ
σ
4
5
6
7
8
9
10
11
12
13
/hh ADS/GLW
constraint
D
ADS
π
constraint
π
π
LHCb K
+ CLEO-c
+ LHCb K3
+ CLEO-c K3
π
K
δ
Figure 2: Projections of the overall systematic uncertainty on γ at LHCb, estimated for various values of of δKπ
D .
4. D → KSπ+π−
Dalitz plot analyses of the three-body decay D → K0
currently provide the best measurements of the CKM weak phase γ [11, 12]. However, D → K0
analyses are sensitive to the choice of the model used to describe the three-body decay, which currently introduces a
model systematic uncertainty on the determination of γ which is greater than 5◦[11]. For LHCb and future Super-B
factories, this uncertainty will become a major limitation. A model independent approach to understanding the D
decay has been proposed by Giri and further investigated by Bondar [13], which takes advantage of the quantum
correlated D0/¯D0CLEO-c data produced at the ψ(3770) resonance.
Consider a Dalitz plot in which we define x = m2
Sπ+π−together with studies of B±→ DK±processes
Sπ+π−Dalitz
KSπ− and y = m2
KSπ+. Both D0→ K0
Sπ+π−and¯D0→ K0
Sπ+π−
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34thInternational Conference on High Energy Physics, Philadelphia, 2008
0 0.511.522.53
0
0.5
1
1.5
2
2.5
3
0
1
2
3
4
5
6
7
Phase Bins
Figure 3: Phase binning based on BaBar model. This plot is symmetric in m2
KSπ− and m2
KSπ+
decays appear on this plot. We then divide the Dalitz plot into regions which are expected to have about the same
relative strong phase difference between the D0and¯D0decays, based on the D0→ K0
BaBar [14], as shown in Figure 3. Assuming the amplitude for the D0→ K0
the bin-averaged cosine, ci, and bin-averaged sine, si, for each bin i as follows:
Sπ+π−decay model from
Sπ+π−process is fD(x,y), we can define
fD(x,y) = |fD(x,y)|eiδD(x,y)
ci =
√FiF¯ ı
(8)
1
?
Di
|fD(x,y)||fD(y,x)|cos(δx,y− δy,x)dxdy(9)
si =
1
√FiF¯ ı
?
Di
|fD(x,y)||fD(y,x)|sin(δx,y− δy,x)dxdy(10)
Using the 818 pb−1ψ(3770) → D0¯D0data sample collected by CLEO-c, we can measure the strong phase
parameters, ci and si, using fully reconstructed D0¯D0pairs with K0
double K0
Sπ+π−vs. flavor states, CP eigenstates, and
Sπ+π−samples.
We may create a CP-tagged sample K0
to decay to states of definite CP (π+π−,K+K−,K0
sample only allows us to measure ci, and not si, in each bin. It can be shown that the bin averaged cosine in each
Sπ+π−events by requiring the neutral D which does not decay to K0
Sπ0π0,K0
Sπ+π−
Sπ+π−
Lπ0,K0
Sπ0,K0
Sη, and K0
Sω). The CP-tagged K0
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34thInternational Conference on High Energy Physics, Philadelphia, 2008
(a)
)
+
π
S
0
(K
2
M
00.511.522.53
)
-
π
0
(K
2
M
S
0
0.5
1
1.5
2
2.5
3
vs. CP-odd Tags vs. CP-odd Tags
-π
+
-π
π
S
π
S
00
KK
+
)
-π
+
π (
2
M
00.2 0.4 0.6 0.811.2 1.4 1.6 1.82
2
Events/0.05 GeV
0
2
4
6
8
10
12
14
16
18
20
22
vs. CP-odd Tags vs. CP-odd Tags
-π
+
-π
π
S
π
S
00
KK
+
(b)
)
+
π
S
0
(K
2
M
00.511.522.53
)
-
π
0
(K
2
M
S
0
0.5
1
1.5
2
2.5
3
vs. CP-even Tags vs. CP-even Tags
-π
+
-π
π
S
π
S
00
KK
+
)
-π
+
π (
2
M
00.2 0.4 0.6 0.811.2 1.4 1.6 1.82
2
Events/0.05 GeV
0
5
10
15
20
25
30
35
40
45
vs. CP-even Tags vs. CP-even Tags
-π
+
-π
π
S
π
S
00
KK
+
Figure 4: (a) CP-odd Tags. (b) CP-even Tags.
of these bins is:
ci=(M+
i/S+− M−
(M+
i/S−)
i/S−)
i/S++ M−
(Ki+ K¯ ı)
2√KiK¯ ı
,(11)
where M+
tagged K0
for which doubly-Cabbibo suppressed decays are considered in evaluation of the systematic error. There are ∼ 800
CP-tagged events in the sample we use to determine ciin each bin, which are shown in Figure 4.
Using the K0
events Mi,jcan be related to the number of flavor-tags for each D decay:
i(M−
Sπ+π−events in each bin. In our analysis, we use hadronic flavor-tags (K−π+,K−π+π0, and K−π+π+π−),
i) is the number of CP even(odd)-tagged K0
Sπ+π−events in each bin and Ki(K¯ ı) is the number of flavor
Sπ+π−vs. K0
Sπ+π−sample, one can extract ciand sisimultaneouly. The number of double-tagged
Mi,j=
1
2ND,¯ DB2
f
(KiK¯ + K¯ ıKj− 2?KiK¯ K¯ ıKj(cicj+ sisj)), (12)
where Bf is the branching ratio of K0
There are ∼ 450 K0
The latest preliminary CLEO results for ciand sifrom both K0
are shown in Table 4.
With the measurements presented here, the systematic uncertainty resulting from our understanding of the D
decays is lowered to ∼ 2◦, which is calculated using the methods reported in Reference [15].
Sπ+π−, and ND,¯ Dis the number of ψ(3770) decays, assuming 100% efficiency.
Sπ+π−events in the sample of K0
Sπ+π−CP-Tags and K0
Sπ+π−vs. K0
Sπ+π−vs. K0
Sπ+π−events.
Sπ+π−vs. K0
Sπ+π−events
5