Primary Authors: P. Garosi, G. Punzi, P. Squillacioti
Introduction
This webpage summarizes the CDF preliminary result for
the measurement of Branching Fractions and CP
Asymmetries of the suppressed (sup)
decay modes B^{-} →
D^{0}π^{-} and B^{-} →
D^{0}K^{-}, with the D^{0}→K^{+}π^{-}, based upon 7
fb^{-1} of data.
This is the first measurement of these modes at a
hadron collider.
A more detailed summary of the results can be found in
arxiv:1108.5765.
Motivation
The branching fractions and CP asymmetries of B^{-}→D^{0}
K^{-} modes allow a theoretically-clean way of measuring the
CKM angle γ. Nowadays γ is the least well-known CKM
angle, with uncertainties of about 10-20 degrees.
In particular the "ADS method" [1][2] makes use of modes where the D^{0}
decays in the Doubly Cabibbo Suppressed (DCS) mode: D^{0}→K^{+}π^{-}.
The large interference between the decays in which B^{-} decays to D^{0}
K^{-} through a Color Allowed b→c transition, followed
by the DCS decay
D^{0}→K^{+}π^{-}, and the decay
in which B^{-} decays to D^{0}K^{-} through a Color Suppressed b→u transition, followed
by the Cabibbo Favored (CF) decay
D^{0}→K^{+}π^{-}, can
lead to measurable CP asymmetries, from which the γ
angle can be extracted.
Since the two final states are the same, we will call both "suppressed decays"
(forming the "suppressed sample"),
while as "favored decay" the B^{-}→D^{0}K^{-},
with the D^{0}→K^{-}
π^{+}.
The ADS method is very powerful, but the corresponding decay is rare and a careful background study must be performed.
The observables of the ADS method are:
- R_{ADS}(K) = (BR(B^{-}→[K^{+}
π^{-}]_{D}K^{-}) + BR(B^{+}→[K^{-}
π^{+}]_{D}K^{+})) ⁄ (BR(B^{-}→[K^{-}
π^{+}]_{D}K^{-}) + BR(B^{+}→[K^{+}
π^{-}]_{D}K^{+}))
- A_{ADS}(K) = (BR(B^{-}→[K^{+}
π^{-}]_{D}K^{-}) - BR(B^{+}→[K^{-}
π^{+}]_{D}K^{+})) ⁄ (BR(B^{-}→[K^{+}
π^{-}]_{D}K^{-}) + BR(B^{+}→[K^{-}
π^{+}]_{D}K^{+}))
- R^{±}(K) = BR(B^{±}→[K^{∓}
π^{±}]_{D}K^{±}) ⁄ BR(B^{±}→[K^{±}
π^{∓}]_{D}K^{±})
R
_{ADS}(K) and A
_{ADS}(K) are related to the γ
angle through these relations:
- R_{ADS}(K) = r_{D}^{2} +
r_{B}^{2} + r_{D}r_{B} cos γ cos(δ_{B}+δ_{D})
- A_{ADS}(K) = 2 r_{B}r_{D} sin γ
sin(δ_{B}+δ_{D}) ⁄ R_{ADS}(K)
where r
_{B} = |A(b→u)/A(b→c)| and
δ
_{B} = arg[A(b→u)/A(b→c)].
r
_{D} and δ
_{D} are the corresponding
amplitude ratio and strong phase difference of the
D meson decay amplitudes.
As can be seen from the expressions above,
A
_{ADS} (max) =
2r
_{B}r
_{D} /
(r
_{B}^{2}+r
_{D}^{2})
is the maximum size of the asymmetry.
For given values of r
_{B}(π) and r
_{D}, sizeable asymmetries may be found also for
B
^{-} → D
^{0}π
^{-} decays,
so we measured also:
- R_{ADS}(π) = (BR(B^{-}→[K^{+}
π^{-}]_{D}π^{-}) + BR(B^{+}→[K^{-}
π^{+}]_{D}π^{+})) ⁄ (BR(B^{-}→[K^{-}
π^{+}]_{D}π^{-}) + BR(B^{+}→[K^{+}
π^{-}]_{D}π^{+}))
- A_{ADS}(π) = (BR(B^{-}→[K^{+}
π^{-}]_{D}π^{-}) - BR(B^{+}→[K^{-}
π^{+}]_{D}π^{+})) ⁄ (BR(B^{-}→[K^{+}
π^{-}]_{D}π^{-}) + BR(B^{+}→[K^{-}
π^{+}]_{D}π^{+}))
- R^{±}(π) = BR(B^{±}→[K^{∓}
π^{±}]_{D}π^{±}) ⁄ BR(B^{±}→[K^{±}
π^{∓}]_{D}π^{±})
Cuts optimization
Data samples are collected through the displaced track trigger that
requires impact parameters in excess of 100 microns and pt>2 GeV/c.
Figs. 1 and 3 show how the B invariant mass distribution for favored and suppressed
samples appears.
While the favored B→Dπ peak clearly appears, the suppressed one is
hidden under the combinatorial background, so the cuts optimization is a crucial step in order to reduce this
background.
It has
been performed on the favored sample, maximizing the figure of merit N_{S}
⁄ (1.5 + √ N_{B}
), where N_{S} is the number of favored B→Dπ signal events, sideband subtracted, in ± 2
σ around the B mass, and N_{B} is the number of favored background events in
the mass window [5.4,5.8] GeV/c^{2}.
The resulting values are
Offline cuts on the
tridimensional vertex quality (χ
^{}_{3D}) and on the
B isolation (Isol) are very important handles to suppress combinatorial
background. The B isolation variable is defined as I =
p
_{T}(B) ⁄ (p
_{T}(B)+∑
p
_{T}), where the sum runs over all
tracks contained in a cone in the η-φ
space around the B meson flight direction. We chose two cones, one at
radius 1 and one at radius 0.4, because they produce a
better signal-background separation than using one alone.
The
pointing angle (PA) is defined as the angle between the
3-dimensional momentum of B and the 3-dimensional decay lenght.
Signal events will have small pointing angles, while background events will have larger angles.
To be noted that the cut on L
_{xy}(D)
_{B} is not optimized,
but its value is chosen to reduce the B→three-body physics backgrounds.
Figs. 2 and 4 show the B invariant mass distribution for favored and suppressed samples after the cuts.
Sample composition fit
We performed an extended maximum likelihood fit, that combines mass
and particle identification information, to separate statistically the
B^{-}→DK^{-} contributions from the
B^{-}→Dπ^{-} signals and from the
combinatorial and physics backgrounds.
The dE/dx information is taken from the drift chamber, which provides
about 1.5 σ of K/π separation. We used the "kaoness" (κ) variable in the fit, defined as (dE/dx_{meas} - dE/dx_{pred}(π))
⁄ (dE/dx_{pred}(K) - dE/dx_{pred}(π)). This
variable is indipendent to momentum at the first order.
We fit the two modes (suppressed and favored) simultaneously using a single
likelihood function, to take advantage
of the presence of common parameters to the two modes, as the fraction
of B→D^{*0}π over B→D^{0}π, the slope
and normalization of the combinatorial background and the simulated
models for signals and backgrounds.
Results
We reconstruct the B^{-} →
D^{}π^{-} signal with a statistical significance of 3.6
σ, corresponding to a delta log likelihood -2
ln(L_{0} ⁄ L) , where
L is the likelihood value of the central fit and L_{0} is the
likelihood value obtained fixing the B^{±} →
D^{0}π^{±} yields to zero.
We recontructed the suppressed signals B^{-} →
D^{}K^{-}, with a significance of 3.2 σ,
including systematics. The significance is evaluated
comparing the likelihood-ratio observed in data with the distribution
expected in statistical trial,
generated with different choices of systematic parameters.
The following plots show the B invariant mass distribution for
positive
and negative charges of the suppressed sample:
We measured:
where the systematics contributions can be found in Fig. 17.
The results are in agreement and competitive with B-factories
[3], as can be seen below in the comparison of A_{ADS}(K)
results.
The other results comparisons can be found in Figs. 19-22.
Figures
Below are the eps and gif versions of all figures meant for downloads.
Data Samples.
- Figure 1: favored sample before cuts (.eps)(.gif)
- Figure 2: favored sample after cuts (.eps)(.gif)
- Figure 3: suppressed sample before cuts (.eps)(.gif)
- Figure 4: suppressed sample after cuts (.eps)(.gif)
Mass fit projections.
- Figure 5: favored positive charges (.eps)(.gif)
- Figure 6: favored positive charges log scale (.eps)(.gif)
- Figure 7: favored negative charges (.eps)(.gif)
- Figure 8: favored negative charges log scale (.eps)(.gif)
- Figure 9: suppressed positive charges (.eps)(.gif)
- Figure 10: suppressed positive charges with background
contributions (.eps)(.gif)
- Figure 11: suppressed positive charges log scale (.eps)(.gif)
- Figure 12: suppressed negative charges (.eps)(.gif)
- Figure 13: suppressed negative charges with background contributions (.eps)(.gif)
- Figure 14: suppressed negative charges log scale (.eps)(.gif)
κ fit projections.
- Figure 15: favored positive charges (.eps)(.jpg)
- Figure 16: favored negative charges (.eps)(.jpg)
- Figure 17: suppressed positive charges (.eps)(.jpg)
- Figure 18: suppressed negative charges (.eps)(.jpg)
Results.
- Figure 19: Number of signal events (.jpg) (divided by
charges (.jpg))
- Figure 20: Number of background events (.jpg) (divided by
charges (.jpg))
- Figure 21: Systematic table (.jpg)
- Figure 22: Observables results (.jpg)
- Figure 23: Likelihood ratio for the
B^{-}→DK^{-} significance (.eps)(.gif)
- Figure 24: Likelihood profile of the
B^{-}→DK^{-} fraction vs B^{+}→DK^{+} fraction (.eps)(.gif)
Comparisons with other experiments.
- Figure 25: R_{ADS}(π) (.eps)(.jpg)
- Figure 26: R_{ADS}(K) (.eps)(.jpg)
- Figure 27: A_{ADS}(π)(.eps)(.jpg)
- Figure 28: A_{ADS}(K) (.eps)(.jpg)
References
[1] D. Atwood, I. Dunietz, A. Soni,
"Enhanced CP violation with B→KD(D) modes and
extraction of the Cabibbo-Kobayashi-Maskawa angle γ"
, Phys. Rev. Lett. 78, 3257, (1997).
[2] D. Atwood, I. Dunietz, A. Soni,
"Improved methods for observing CP violation with B→KD and measuring the CKM phase γ.",
Phys. Rev. D 63, 036005, (2001).
[3] http://www.slac.stanford.edu/xorg/hfag.