Primary authors: A. Di Canto, M. Dorigo, L. Grillo, S. Leo, L. Oakes, E. Pueschel, G. Punzi, M. Rescigno, D. Tonelli, A. B. Wicklund and A. M. Zanetti
This page outlines the measurement of the
B_{s}^{0} mixing phase β_{s}^{J/ψφ}
in flavortagged
B_{s}^{0} → J/ψφ decays,
using the full Run II data set collected by the CDF experiment
at the Fermilab's Tevatron collider corresponding to an integrated
luminosity of about 9.6 fb^{1}.
Further information can be found in arxiv:1208.2967.
We analyze approximately 11000
B_{s}^{0} → J/ψφ decays collected by a lowpt dimuon trigger,
thus almost doubling the statistics of
the previous iteration of the analysis (Phys. Rev. D 85, 072002 (2012)),
and report confidence regions in one and twodimensional β_{s}^{J/ψφ} and
(β_{s}^{J/ψφ}, ΔΓ_{s}) spaces.
The analysis technique and the employed tools reflect closely those reported in the previous analysis.
The oppositeside flavor tagging algorithms have been entirely recalibrated using about 82000 B^{±} → J/ψK^{±}
decays collected in the whole Run II sample, achieving a tagging performance of εD^{2}= (1.39 ± 0.01)%.
The samesidekaon tagging algorithms have only been used in half of the data sample (εD^{2}= (3.2 ± 1.4)%),
since calibration on the full sample has not been completed yet.
This degrades the statistical resolution of the mixing phase measurement by no more than 15%.
From the onedimensional profile likelihood in β_{s}^{J/ψφ}, including systematic uncertainties, we find β_{s}^{J/ψφ} ∈ [π/2, 1.51] ∪ [0.06, 0.30] ∪ [1.26, π/2] at the 68% confidence level,
and β_{s}^{J/ψφ} ∈ [π/2, 1.36] ∪ [0.21, 0.53] ∪ [1.04, π/2] at the 95% confidence level,
in agreement with the value suggested by the CKM hierarchy.
We present 68% and 95% confidence regions
in the β_{s}^{J/ψφ}ΔΓ_{s} plane including systematic uncertainties:
Our data are compatible with the standard model predictions of
β_{s}^{J/ψφ} and ΔΓ_{s} within less than one standard deviation.
Assuming no CP violation (β_{s}^{J/ψφ} fixed at SM value), we
also measure the mean lifetime, the decay width difference, the transversity amplitudes and the strong phase δ_{⊥} :
τ_{s} = 1.528 ± 0.019(stat) ± 0.009(syst) ps,
ΔΓ_{s} = 0.068 ± 0.026(stat) ± 0.009(syst) ps^{1},
A_{0}(0)^{2} = 0.512 ± 0.012(stat) ± 0.018(syst),
A_{}(0)^{2} = 0.229 ± 0.010(stat) ± 0.014(syst),
δ_{⊥} = 2.79 ± 0.53(stat) ± 0.15(syst) rad.
All results are consistent with previous determinations and are amongst the most precise from a
single experiment to date.
From these results we derive also the ratio
ΔΓ_{s}/Γ_{s}=0.1039 ± 0.048(stat) ± 0.018(syst) and, using the world average B^{0} lifetime,
τ(B^{0}_{s})/τ(B^{0}) = 1.006 ± 0.015(stat+syst),
in agreement with theoretical expectations.
The fraction of Swave in the K^{+}K^{} mass range 1.0091.028 GeV/c^{2}
is determined from the angular information to be consistent with zero with O(2%) uncertainty,
which is in agreement with our previous determination
and the LHCb and
ATLAS results,
and inconsistent with the D0 determination.
An auxiliary simultaneous fit of the K^{+}K^{} and J/ψK^{+}K^{}
mass distributions, which includes the full resonance structure of the B^{0} → J/ψKπ,
determines a (0.8 ± 0.2(stat))% K^{+}K^{} Swave contribution, in agreement with the central fit.
The contamination from misidentified B^{0} decays is (8.0 ± 0.2(stat))%,
which is significantly larger than the 12% values derived assuming
only Pwave B^{0} decays. If neglected, this additional B^{0} component
could mimic a larger K^{+}K^{} Swave than present.
Below are all figures meant for download and CDF Likelihood in Root format to be used in combinations with other experimental results.
Likelihood contours (with β_{s}^{J/ψφ})
 (eps),
(gif): 2D β_{s}^{J/ψφ}ΔΓ likelihood profile with full coverage adjustment
 (eps),
(gif): 1D β_{s}^{J/ψφ} likelihood profile with full coverage adjustment
 (eps),
(gif): 2D β_{s}^{J/ψφ}ΔΓ likelihood profile with nonGaussian error adjustment only (no systematics)
 (eps),
(gif): 1D β_{s}^{J/ψφ} likelihood profile with nonGaussian error adjustment only (no systematics)
 (eps),
(gif): 2D β_{s}^{J/ψφ}ΔΓ likelihood profile with no coverage adjustment
 (eps),
(gif): 1D β_{s}^{J/ψφ} likelihood profile with no coverage adjustment
Likelihood contours (with ϕ_{s}^{J/ψφ})
 (eps),
(gif): 2D ϕ_{s}^{J/ψφ}ΔΓ likelihood profile with full coverage adjustment
 (eps),
(gif): 1D ϕ_{s}^{J/ψφ} likelihood profile with full coverage adjustment
 (eps),
(gif): 2D ϕ_{s}^{J/ψφ}ΔΓ likelihood profile with nonGaussian error adjustment only (no systematics)
 (eps),
(gif): 1D ϕ_{s}^{J/ψφ} likelihood profile with nonGaussian error adjustment only (no systematics)
 (eps),
(gif): 2D ϕ_{s}^{J/ψφ}ΔΓ likelihood profile with no coverage adjustment
 (eps),
(gif): 1D ϕ_{s}^{J/ψφ} likelihood profile with no coverage adjustment
Likelihood contours for new data ONLY (4.4 fb^{1})
 (eps),
(gif): 2D ϕ_{s}^{J/ψφ}ΔΓ likelihood profile with no coverage adjustment
 (eps),
(gif): 2D β_{s}^{J/ψφ}ΔΓ likelihood profile with no coverage adjustment
Coverage adjustment
 (eps),
(gif): Distribution of 1CL for coverage adjustment of tagged 1D likelihood profile
 (eps),
(gif): Distribution of 1CL for coverage adjustment of tagged 2D likelihood profile
Yield
 (eps),
(gif): B_{s} yield
 (eps),
(gif): B_{s} mass distribution with ct>60μm
Auxiliary fit to determine K^{+}K^{} Swave and
B^{0} → J/ψKπ components (ct(B)>60μm and K^{+}K^{} mass in [0.98,1.2] GeV/c^{2})
 (eps),
(gif): J/ψK^{+}K^{} mass distribution with fit projections overlaid
 (eps),
(gif): K^{+}K^{} mass distribution with fit projections overlaid.
Flavor tagging (see also SSKT)
 (eps),
(gif): B^{+/} yield (for OST calibration)
 (eps),
(gif): OST measured vs. predicted dilution for B^{+} decays
 (eps),
(gif): OST measured vs. predicted dilution for B^{} decays
Fit projections
 (eps),
(gif): Bs lifetime projection for all data
 (eps),
(gif): Bs lifetime projection for signal (background subtracted data)
 (eps),
(gif): Bs lifetime projection for background
 (eps),
(gif): Transversityangles projection for all data
 (eps),
(gif): Transversityangles projection for signal (background subtracted data)
 (eps),
(gif): Transversityangles projection for background
Fit projections assuming SM mixing phase
 (eps),
(gif): Bs lifetime projection for all data
 (eps),
(gif): Bs lifetime projection for signal (background subtracted data)
 (eps),
(gif): Bs lifetime projection for background
 (eps),
(gif): Transversityangles projection for all data
 (eps),
(gif): Transversityangles projection for signal (background subtracted data)
 (eps),
(gif): Transversityangles projection for background
Analysis data

We provide below the analysis data for use in combinations and phenomenological fits.
A root file contain the histogram of the bare profilelikelihood ratio (2ΔLogL).
As described in arxiv:1208.2967, the CDF likelihood ratio does not follow a chisquared distribution and cannot
be used for extracting confidence regions with nominal coverage. Another root file contains a statistics in which the value
of a χ^{2}distributed profilelikelihood ratio is assigned to each point in the Δ Γ  ϕ_{s}^{J/ψφ} space,
corresponding to the actual value of CL associated to that point. This statistics can be effectively used as "CDFlikelihood" with nominal coverage.

Each histogram has 32 bins in ϕ_{s}^{J/ψφ} over the interval [3.2, 3.2]
and 48 bins in ΔΓ over the interval [0.3, 0.3].
 (root): No Coverage Corrected Histogram,
need to set level 3.55 and 8.1 to obtain respectively the 68% and 95% CL regions.
 (root): Coverage Corrected Histogram.
Can set the nominal levels 2.3 and 5.99 to obtain respectively the 68% and 95% CL regions.
For sake of semplicity we also provide a root macro to draw the contours at the desired level. Detailed Instruction in the following README file.
 (macro.C): macro to draw contours.
 (README): User instructions.
 (gif): Example of contour in the space Δ Γ  ϕ_{s}^{J/ψφ} following the instructions written in the README file.