Measurements of branching fractions and CP asymmetries in the Doubly Cabibbo Suppressed decay modes B± → D0h± on 7 fb-1

Primary Authors: P. Garosi, G. Punzi, P. Squillacioti


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.


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:

  • RADS(K) = (BR(B-→[K+ π-]DK-) + BR(B+→[K- π+]DK+)) ⁄ (BR(B-→[K- π+]DK-) + BR(B+→[K+ π-]DK+))
  • AADS(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±)
RADS(K) and AADS(K) are related to the γ angle through these relations:
  • RADS(K) = rD2 + rB2 + rDrB cos γ cos(δBD)

  • AADS(K) = 2 rBrD sin γ sin(δBD) ⁄ RADS(K)
where rB = |A(b→u)/A(b→c)| and δB = arg[A(b→u)/A(b→c)]. rD and δD are the corresponding amplitude ratio and strong phase difference of the D meson decay amplitudes.
As can be seen from the expressions above, AADS (max) = 2rBrD / (rB2+rD2) is the maximum size of the asymmetry. For given values of rB(π) and rD, sizeable asymmetries may be found also for B- → D0π- decays, so we measured also:
  • RADS(π) = (BR(B-→[K+ π-]Dπ-) + BR(B+→[K- π+]Dπ+)) ⁄ (BR(B-→[K- π+]Dπ-) + BR(B+→[K+ π-]Dπ+))
  • AADS(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 NS ⁄ (1.5 + √ NB  ), where NS is the number of favored B→Dπ signal events, sideband subtracted, in ± 2 σ around the B mass, and NB 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 quality3D) and on the B isolation (Isol) are very important handles to suppress combinatorial background. The B isolation variable is defined as I = pT(B) ⁄ (pT(B)+∑ pT), 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 Lxy(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/dxmeas - dE/dxpred(π)) ⁄ (dE/dxpred(K) - dE/dxpred(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.


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 AADS(K) results. The other results comparisons can be found in Figs. 19-22.


Below are the eps and gif versions of all figures meant for downloads.


[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).