Measurement of the CP-Violation Parameter sin2beta in B^0_d/B-bar^0_d to J/psi K^0_s Decays

Abstract

We present a measurement of the time-dependent asymmetry in the rate for B-bar^0_d versus B^0_d decays to J/psi K^0_S. In the context of the Standard Model this is interpreted as a measurement of the CP-violation parameter sin(2 beta). A total of 198+-17 B^0_d/B-bar^0_d decays were observed in ppbar collisions at sqrt s = 1.8 TeV by the CDF detector at the Fermilab Tevatron. The initial b-flavor is determined by a same side flavor tagging technique. Our analysis results in sin(2 beta) = 1.8+-1.1(stat)+-0.3(syst).

Introduction

In the Standard Model, charge conjugation - parity (CP) violation can arise from the relationship between the weak interaction and the mass eigenstates of the quarks as described by the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix. The third generation gives the matrix a physical complex phase capable of explaining CP violation.

The decay B0 -> J/psi K0s is particularly interesting because both B0 and B0bar can decay to the same CP final state. There exists both a direct decay path as well as a "mixed" path by which the meson changes (via a box diagram) to its antimeson; the interference of these two paths produces a potentially large CP asymmetry which is cleanly related to the CKM parameter

           Bbar(t) - B(t)
    A(t) = -------------- = sin2beta sin(Delta-m t)
           Bbar(t) + B(t)

                   Vcd Vcb*
    beta = arg ( - -------- )
                   Vtd Vtb*

OPAL has reported, also using a J/psi K0s sample, sin2beta = 3.2(+1.8-2.0)(stat)+-0.5(syst).

Data Sample

The following is a brief summary of the event reconstruction.

J/psi -> mu+mu-

• Run 1abc data (1992-96), triggering on two muons
• both muons:
  • in central muon detectors, with track-matching cuts
  • reconstructed in SVX, Pt > 1.5 GeV/c
  • calorimeter energy > 0.5 GeV
• vertex constraint
• combined mass between 2.8 and 3.4 GeV/c2

K0s -> pi+pi-

• pions within 15cm of J/psi vertex
• SVX information if used and satisfying quality cuts
• unconstrained mass combination between 300 and 850 MeV/c2
• vertex constraint
• vertex-constrained mass within 5sigma of K0s mass
• vertex fit P(chi2) > 0.1%
• Pt(K0s) > 0.7 GeV/c
• Lxy > 5sigma beyond J/psi vertex

B -> J/psi K0s combination

• 4-particle combined fit, with 3D K0s pointing constraint back to J/psi vertex
• Pt(B) > 4.5 GeV/c
• 2D chi2 for particle fit and K0s pointing < 20
• 2D chi2 for pointing B candidate to primary vertex < 4

If there are multiple B candidates in a given event, the one with the lowest 2D chi2 (fit and K0s pointing) is chosen.

The resulting mass distribution is shown here for J/psi K0s with ct>0 and ct>200um. The curve on the first plot is the result of the likelihood fit, which gives 198+-17 B0/B0bar decays for all measured ct's.

Same-side Tagging

After having reconstructed the B0 meson, we select the nearby tracks according to the following criteria:

• reconstructed in SVX
• DeltaR < 0.7
• z0 less than 5cm away from B0's z0
• Pt > 400 MeV/c
• impact parameter with respect to the primary vertex < 3sigma

The "right-sign" SST correlation is between a pi+ and a B0, and a pi- and a B0bar. In the case of a charged B meson, a pi+ is associated with a B-, and a pi- with a B+.

Results

Raw asymmetry

When we apply SST to the J/psi K0s data, we get the following breakdown of tags:

LaTeX source for this table can be found here.

The time-dependent asymmetry plot is given here. We show two fits: the dashed curve represents a simple chisqr fit to the binned asymmetries to the function Asin(Delta-m t). The fit returns A=0.36+-0.19. The solid curve gives the unbinned maximum likelihood fit result, which gives a corresponding amplitude of 0.31+-0.18. In both cases, Delta-m is fixed. The inset plot shows the likelihood scan around the central value. The likelihood fit also incorporates corrections for systematic effects (for instance, detector biases), but these corrections do not change much, as shown by the fact that the two fits give similar results. (Detals of the likelihood function may be found in the PRD submission on mixing, FERMILAB-PUB-98/188-E).

The LaTeX source of the likelihood fit results table is here.

Systematic effects

Since the measurement depends upon observing a charge asymmetry, other charge-asymmetric effects must be corrected for in this analysis. The most obvious effect is a charge asymmetry, favoring positive tracks, in the tracking chamber due to wire plane geometry. This effect has been parameterized as a function of track pt and the number of primary vertices in the event (a measure of event occupancy). The effect is shown here in an inclusive, flavor-symmetric sample of long-lived J/psi's (Lxy > 200um, which is >90% pure b's). Four sets of points are shown: (1) SST tags, using the J/psi direction as the B direction; (2) SST candidates; (3) SST candidates with an additional cut that they are more than 2sigma inconsistent with the J/psi (B) vertex; and (4) tracks which satisfy the SST criteria except that they are in a DeltaR cone "sideways" from the B. All of them behave similarly, and we use (3) to parameterize the effect for use in the likelihood fitter.

Systematic uncertainties have been calculated by varying the fixed parameters of the likelihood fit by a 1sigma-type shift and observing the resulting shift in Dsin2beta. Detector biases include the effects of the inherent charge asymmetry in the tracking.

A more detailed version of the systematic uncertainties table, along with a discussion of the parameterization of the tracking charge asymmetry, can be found here.

With systematic uncertainties, the value of the raw asymmetry is Dsin2beta = 0.31+-0.18(stat)+-0.03(syst). Studies on the robustness of the asymmetry can be found here.

Value of sin2beta

The raw asymmetry is divided by the dilution to obtain sin2beta. The dilution we use has been extracted from SST dilution measurements from lepton+D(*) and J/psi K*0, along with charged dilution measurements from lepton+D(*) and J/psi K+-. We have used simulation to extrapolate the different measurements to that appropriate for J/psi K0s. (To see plots showing the agreement between Monte Carlo and data, see the Monte Carlo comparison section of the blessed plots page. There are also more details in the PRD submission, FERMILAB-PUB-98/188-E.)

We find D = 0.166+-0.018(data)+-0.013(MC) to be the dilution appropriate for the J/psi K0s sample. The first error is from the combined dilution measurements from data, and the second error is due to the Monte Carlo extrapolation.

The value of sin2beta is then 1.8+-1.1(stat)+-0.3(syst), where the dilution uncertainty has been folded into the systematic uncertainty.

Limit

If we interpret the result in terms of confidence intervals, we find that the frequentist method advocated by G. Feldman and R. Cousins (and now advocated by the PDG as of 1998) is suitable for us. This method is summarized in the 1998 PDG.) We find that this result excludes sin2beta < -0.20 at 95% C.L. The experimental sensitivity (for us, the median exclusion if the true value was sin2beta = 1) is -0.89.

The confidence belts and limit calculation are shown in this Figure. The band represents the "confidence belts" and the vertical line is at our data value. Values of true sin2beta for which our measured value is outside the band are excluded at 95% C.L.

It is interesting to note that since the raw asymmetry is Dsin2beta, then as long as D > 0, the exclusion of sin2beta=0 is independent of our knowledge of D. For this result, sin2beta < 0 is excluded at 90% C.L.

Papers and more plots

Blessed plots and papers

• Submitted to Phys. Rev. Lett. : FERMILAB-PUB-98/189-E
• Submitted to Phys. Rev. D (details on SST mixing): FERMILAB-PUB-98/188-E
• More plots pertinent to this analysis may be found here.

Related Previous Documentation

• Phys. Rev. Lett. 80, 2057 (1998) (Postscript) (Abstract)
  Measurement of the B^0-B-bar^0 Oscillation Frequency Using pi-B Meson Charge-Flavor Correlations in ppbar Collisions at sqrt s = 1.8 TeV