First Measurement of Polarization Amplitudes
We have performed the first measurement of the polarization amplitudes and the first search for CP violation in the charmless B0s → φφ → [K+K-][K+K-] decay, using CDF II data collected by the Two Track Trigger in the period March 2001 → April 2008 which corresponds to an integrated luminosity of 2.9 fb-1.
The B0s → φφ selected decay sample contains approximately 300 signal
events and is the same as in the
branching ratio measurement. Details on events selection are reported in
|Polarization Amplitudes Measurement|
|fT||=|||A|||2 + |Aperp|2||fL||=|||A0|2|
||A0|2 + |A|||2 + |Aperp|2|||A0|2 + |A|||2 + |Aperp|2|
Due to the V-A nature of weak interaction and to the helicity conservation in
QCD, fL >> fT is expected in B decays to two light vector mesons.
This expectation was experimentally confirmed by BaBar and
Belle in tree-dominated transitions
while it was found
fL ≈ fT in
B+ → φK*+ and in B0 → φK*0
where the b → s penguin transition is involved.
This is known as the Polarization Puzzle.
Explanations invoking either New Physics or sub-leading corrections to the Standard Model predictions have been proposed. The B0s → φφ decay proceeds via a b → s penguin transition representing a very interesting decay channel in this experimental and theoretical scenario.
We look at the untagged time-integrated differential decay rate as a function of three angular variables of the final state decay products. This rate depends on the three polarization amplitudes (and their relative phase). Neglecting the tiny CP phase in B0s mixing (as expected in the Standard Model), the rate depends only on three observables: two polarization amplitudes squared |A0|2, |A|||2, and the strong phase δ||. The strength of Aperp can be determined from the normalization condition |A0|2 + |A|||2 + |Aperp|2 = 1.
The fit to the mass and decay product angular distributions is performed in the helicity basis and we define ω=(cosθ1, cosθ2, φ).
Fig: Helicity frame definition of angular variables for a generic decay to V1 V2 with V1 decaying to particles P1, P2 and V2 to Q1, Q2. We take the K+ as P1 and Q1.
The reconstructed mass for signal events is parameterized with a double Gaussian as:
with parameters k and h fixed from Monte Carlo
simulation. The background model for the mass distribution is a simple exponential
and the background fraction
fb is determined from the fit in the B0s candidate mass
range 5.2 < m < 5.6 GeV/c2.
The background model for the angular distributions is parameterized
using the sideband data. The acceptance A(ω) is calculated from Monte Carlo
The time integrated polarization fractions are corrected for the expected lifetime difference for the CP-even and CP-odd B0s mass eigenstates using the world average B0s lifetime and width difference. Since the CDF Two Track Trigger biases the natural decay proper time distribution of the available sample, we study the resulting bias in the polarization measurement with Monte Carlo simulation and account for it as a systematic uncertainty.
We validate this approach by performing a similar measurement using the B0s→ J/ψφ decays, collected via the same trigger, and comparing the obtained results with the current experimental information on the polarization of this decay.
|Table: Fit results with statistical uncertainties||Table: Correlation matrix|
Several systematic uncertainties have been studied with Monte Carlo samples with statistics similar to the our data sample and generated with a model that includes the systematic effect under study. The quoted uncertainty is the shift in the mean value of the fit parameters in 1000 generated pseudo-experiments. The largest effect come from the inclusion of a scalar non-resonant component under the φ meson mass peak. This has been studied generating a B0s → φf0 and a non-resonant B0s → φ(K+K-) sample with branching ratio similar to the equivalent B0 decays. Another important effect is related to the proper time acceptance of the displaced track trigger that introduces a bias in the observed polarization fraction which is dependent on the true value of the B0s width difference ΔΓ. Finally, the effect related to a possible non vanishing CP-violating phase in mixing at a level consistent with the current world average is included.
In the following plot we show the measured polarization fractions f0 versus f||=|A|||2 with the 68% confidence region (orange area) compared with the expectations of the QCD factorization models (Beneke et al., Datta et al.) and the perturbative QCD (Ali et al.) . The cross-bars of the experimental point are statistical and systematic uncertainties added in quadrature; in the QCD factorization cases, f|| has been set to f||=(1-f0)/2 (the dashed line) ±4% (Beneke et al., NPB 774).
|Search for CP violation|
|ATP||=||Γ(TP>0) - Γ(TP<0)|
|Γ(TP>0) + Γ(TP<0)|
Side-bands subtracted distribution of u.
Side-bands subtracted distribution of v.
Fig: Mass distribution of N+ (left) and N- (right) subsamples with fit projections overlaied for u asymmetry.
Fig: Mass distribution of N+ (left) and N- (right) subsamples with fit projections overlaied for v asymmetry.