BR and CP Asymmetry for B→Dh DCS

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^- → D⁰π^- and B^- → D⁰K^-, with the D⁰→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^-→D⁰ 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 D⁰ decays in the Doubly Cabibbo Suppressed (DCS) mode: D⁰→K⁺π^-. The large interference between the decays in which B^- decays to D⁰ K^- through a Color Allowed b→c transition, followed by the DCS decay D⁰→K⁺π^-, and the decay in which B^- decays to D⁰K^- through a Color Suppressed b→u transition, followed by the Cabibbo Favored (CF) decay D⁰→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^-→D⁰K^-, with the D⁰→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^-]_DK^-) + BR(B⁺→[K^- π⁺]_DK⁺)) ⁄ (BR(B^-→[K^- π⁺]_DK^-) + BR(B⁺→[K⁺ π^-]_DK⁺))

A_ADS(K) = (BR(B^-→[K⁺ π^-]_DK^-) - BR(B⁺→[K^- π⁺]_DK⁺)) ⁄ (BR(B^-→[K⁺ π^-]_DK^-) + BR(B⁺→[K^- π⁺]_DK⁺))

R^±(K) = BR(B^±→[K^∓ π^±]_DK^±) ⁄ BR(B^±→[K^± π^∓]_DK^±)

R_ADS(K) and A_ADS(K) are related to the γ angle through these relations:

R_ADS(K) = r_D² + r_B² + r_Dr_B cos γ cos(δ_B+δ_D)

A_ADS(K) = 2 r_Br_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_Br_D / (r_B²+r_D²) 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^- → D⁰π^- decays, so we measured also:

R_ADS(π) = (BR(B^-→[K⁺ π^-]_Dπ^-) + BR(B⁺→[K^- π⁺]_Dπ⁺)) ⁄ (BR(B^-→[K^- π⁺]_Dπ^-) + BR(B⁺→[K⁺ π^-]_Dπ⁺))

A_ADS(π) = (BR(B^-→[K⁺ π^-]_Dπ^-) - BR(B⁺→[K^- π⁺]_Dπ⁺)) ⁄ (BR(B^-→[K⁺ π^-]_Dπ^-) + BR(B⁺→[K^- π⁺]_Dπ⁺))

R^±(π) = BR(B^±→[K^∓ π^±]_Dπ^±) ⁄ BR(B^±→[K^± π^∓]_Dπ^±)

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/c².
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^*0π over B→D⁰π, the slope and normalization of the combinatorial background and the simulated models for signals and backgrounds.

Results

We reconstruct the B^- → Dπ^- signal with a statistical significance of 3.6 σ, corresponding to a delta log likelihood -2 ln(L₀ ⁄ L) , where L is the likelihood value of the central fit and L₀ is the likelihood value obtained fixing the B^± → D⁰π^± yields to zero. We recontructed the suppressed signals B^- → DK^-, 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.