Bottom Physics at CDF

The bottom quark provides us with a unique laboratory to study and probe the electroweak sector of the standard model by measuring the decay proporties of hadrons containing one or more b-quarks. The lifetime and partial widths of bottom hadrons can be directly related to the CKM matrix elements and the mass of the unknown top quark. This has prompted an intensive study of bottom hadrons over the last ten years.

The B meson production cross section at a hadron collider is of order 10 μb, which at the Fermilab Tevatron corresponds to 10^{9} events in an 100 pb^{−1} exposure. This enormous production rate is tempered by the difficulties encountered separating the bottom hadron events from the much larger rate of events arising from the production of lighter quark final states. This separation is typically achieved by requiring a distinctive signature or “tag” such as the presence of an energetic lepton accompanied by the hadron activity that results from the semi-leptonic b quark decay. The efficiency of such tagging schemes can be quite low and they restrict the b quark final states that are experimentally available.

Despite these problems, the CDF collaborations have made several measurements of b quark production and decay properties using data acquired in 1988 and 1989. We briefly summarize the most recent results of these studies, focusing on (i) the measurement of the bottom quark production cross section, (ii) a measurement of B^{∘} −B̄^{∘} mixing from a study of electron-muon final states, (iii) reconstruction of B meson exclusive final states, and (iv) the search for the flavour- changing neutral-current decay B → μ^{+}μ^{−}.

0.1 Bottom Quark Production

The production cross section for heavy quarks has been calculated to next-to-leading order by Nason, Dawson, Ellis and Diemov. The results of this calculation are sensitive to several assumptions made to take into account the higherorder corrections and the light quark and gluon structure functions. Thus, the measurement of the total and differential cross section provides a strong consistency check of this calculation. The cross section itself is an important “engineering number,” as it provides us with the ability to predict the productivity of future b quark studies at hadron colliders and compare such experiments with efforts at fixed target facilities and proposed b factory facilities.

The production ofb-quarks in hadron-hadron collisions has large contributions from both the leading order processes, which are dominated by the reaction gg → b\overline{b}, and higher order diagrams such as “gluon splitting,” where a two gluon final state is produced and one of the final state gluons fragments into a b̄b system. The kinematics of the resulting b-quark final states can be used to estimate the relative contributions from the leading-order and higherorder diagrams. However, this requires measurement of not only the total cross Figure 0.1: The E_{T} spectrum of the CDF inclusive electron sample after the selection decribed in the text.

section but the differential cross section as a function of the such variables as the P_{T} of the b-quark.

CDF has measured the total b quark cross section and its dependence on the P_{T} distribution of the b quark using a sample of inclusive electron events. These measurements have been made in a semi-inclusive sense by first measuring the rate of events with leptons arising from b quark production and subsequent semileptonic decay, and then correcting this to a b quark cross section taking into account other sources of leptons and the fragmentation and decay properties of the b quark.

The event sample is selected by requiring an electron candidate in the central pseudorapidity region |η| < 1.0. The shower in the EM calorimeter is required to have transverse profiles consistent with that expected of an electron. The shower leakage into the hadronic calorimeter must be < 4% of the EM shower energy, and candidates with more than one charged track pointing to the calorimeter shower are removed. This latter cut is used to reduce the backgrounds from fake electrons resulting from hadronic shower fluctuations. In order to further reduce backgrounds from charged hadrons overlapping with π^{∘} showers, the ratio of calorimeter energy and charged track momentum is required to satisfy 0.75 < E/p < 1.4. There are ??? candidate events.

A significant background in this sample comes from energetic photons converting into a electron-positron pair near the interaction region and from π^{∘} Dalitz decays. This background is reduced by rejecting events that have a second charged track, opposite in sign to the candidate, that is consistent with a photon conversion. The remnant conversion background is estimated to be 20 ± 5% of the sample. The remnant background from charged hadrons is estimated to be 15 ± 15%. The event sample consists of ??? events. The E_{T} spectrum of the electron candidates is shown in Fig. 0.1.

Sources of prompt electrons at the Fermilab collider are W and Z^{∘} boson production, and charm and bottom decay. The contribution from W production is removed by requiring that the transverse mass in the event E̸_{T} < 8\sqrt{E_{T}}, which effectively requires that the transverse mass be consistent with that expected from heavy flavour decay. The Z^{∘} contribution is removed by rejecting events that have a second electron cluster satisfying much looser electron identification cuts that forms a di-electron invariant mass greater than 80 GeV/c^{2}. The cuts result in an event sample of ?? events.

The P_{T} distribution of the remaining conversion and charged hadron background in the event sample is assumed to be the same as that for the identified conversion electron sample. After statistically subtracting this contribution from the oberved electron P_{T} spectrum, the resulting electron P_{T} spectrum will only have contributions from charm and bottom production. The technique employed in the UA1 analysis to relate the observed lepton and parent quark transverse momentum is used to infer the cross section for b-quark production above a minimum b-quark P_{T}. The ISAJET Monte Carlo program is used to determine this relationship, after tuning the program to reproduce the fragmentation and decay properties of b-quarks as measured at CLEO and ARGUS.

The relative contribution of charm quark decays to the event sample is expected to be small because of the isolation requirements made by the electron identification cuts, and so it is difficult to measure this rate directly as is done in the UA1 analysis. The CDF group therefore uses the ISAJET prediction for the relative rate of charm and bottom quark decay events passing the event selection. This ratio, predicted to be ???, introduces a systematic uncertainty in the resulting b-quark cross section of +5% and −12% if one assumes an uncertainty in the relative ISAJET charm to bottom quark production cross sections of a factor of two.

An uncertainty in the calculation is introduced by the b-quark P_{T} distribution used in the Monte Carlo calculation. The b-quark P_{T} distribution predicted by ISAJET for the lowest-order production process is used as that matches the P_{T} distribution obtained from the higher- order QCD calculation. The uncertainty introduced by this assumption when calculating the b-quark production cross section above a P_{T}^{b,min} is relatively small.

A summary of the statistical and systematic uncertainties of this analysis is shown in Table ??. The resulting integrated cross sections are listed in Table ?? for three different choices of P_{T} cuts on the candidate electrons, and are plotted in Fig. ?? along with the QCD prediction. One sees that the observed integrated cross sections are all higher than the predicted values by approximately a factor of two. Although this descrepancy is only a few standard deviations because of the relatively large theoretical uncertainties, it is rather striking given the good agreement between the measured and predicted values at \sqrt{s} = 630 GeV.

0.2 B^{∘}−B̄^{∘} Mixing

The physical neutral bottom meson states are expected to be mixtures of the even and odd charge-parity eigenstates of the weak Lagrangian, in analogy with the K^{∘} meson system. This mixing is predicted by the Standard Model to arise from “box diagrams,” such as those shown in Fig. ??. The size of the mixing depends on several fundamental parameters in the standard model, such as the mass of the top quark, the lifetime of the b-quark, and the size of several components of the Cabibbo-Kobi-Maskawa matrix. A measurement of this mixing thus provides an important test of the standard model, and can be used to set limits on these parameters.

The mixing is also predicted to be different for B_{s}^{∘} and B_{d}^{∘} mesons mesons. The CLEO and ARGUS experiments directly measure the mixing parameter χ_{d}, which is defined as

χ_{s} = \frac{Prob(B_{d}^{∘} → B̄_{d}^{∘})}{Prob(B_{d}^{∘} → B_{d}^{∘}) + Prob(B_{d}^{∘} → B̄_{d}^{∘})},  (0.1)

since only the B_{d}^{∘} mesons are easily produced at their centre- of-mass energies. Experiments at hadron collider facilities and LEP can measure a linear combination

χ̄ ≡ f_{d}χ_{d} + f_{s}χ_{s},  (0.2)

where f_{d} and f_{s} are the fractions of B_{d}^{∘} and B_{s}^{∘} mesons produced at these facilities. A prediction or measurement of these fractions then allows one to determine both χ_{s} and χ_{d} by combining the mixing measurements made at the different facilities.

One of the cleanest signatures for B^{∘} − B̄^{∘} production is the requirement of two leptons in the event, one coming from the semi-leptonic decay of each B^{∘} meson. This signature has relatively small backgrounds, and yet provides a reasonable event rate. The mixing in the B^{∘} − B̄^{∘} system produces an excess of like-sign di-lepton events relative to the number of opposite sign di-leptons. The ratio

R = \frac{N(l^{+}l^{+}) + N(l^{−}l^{−})}{N(l + l−)}  (0.3)

can be related to the mixing parameter χ̄ by taking into account all sources of like and unlike-sign di-lepton events. The CDF collaboration has used a di-lepton event sample defined by requiring an electron and muon candidate to make this measurement. This sample has a factor of two more events than the comparable di-electron or di-muon final states, and does not suffer from backgrounds in the opposite-sign sample arising from Drell Yan production.

The eμ event sample is defined by requiring events that have passed the CDF di-lepton trigger, which requires an electromagnetic shower in the CEM with E_{T} > 5 GeV and a muon candidate with P_{T} > 3 GeV/c. The electromagnetic shower is further required to have less than 4% energy leakage into the hadronic calorimeter, transverse shower profiles consistent with an electron shower, and a charged track reconstructed in the CTC that extrapolates to the EM shower position. The ratio of calorimeter energy to track momentum is required to be less than 1.5. The muon candidate is required to have a well-measured CTC track consistent with coming from the primary vertex and having a good match between the CTC track extrapolated to the muon chambers and the muon track stub detected in the μ chambers. The charged track isalso required to have an energy deposition in the calorimeter consistent with a minimum-ionizing particle.

There are several background processes that contribute to this event sample. W bosons are rejected by requiring E̸_{T} < 15 GeV. Electrons from photon conversions in the inner part of the tracking system or from Dalitz decays are rejected by vetoing events that have either a second track forming an invariant mass m_{ee} < 0.5 GeV/c^{2}, or that do not have a charged track candidate in the VTPC tracking chamber. However, there are no backgrounds in the sample from Drell- Yan, Z^{∘}, J/Ψ or Υ production due to the requirement that the two leptons come from different generations. This results in 429 like-sign (LS) and 911 opposite-sign (OS) events.

A source of di-lepton events is the semi-leptonic decay of a b-quark followed by the semi-leptonic decay of the resulting charm hadron. This decay mode produces di-leptons with invariant masses less than the mass of the B meson, and are rejected by requiring that m(eμ) > 5.0 GeV/c^{2}. The remaining sequential background is calculated using the ISAJET Monte Carlo, as described below. This results in 346 like-sign and 554 opposite-sign events.

The remaining sources of di-lepton events have to be accounted for to interpret this value of R in terms of χ̄. The relevant sources are i) charm production and semi-leptonic decay, ii) backgrounds from sequential bottom quark decay, and iii) processes generating fake electron and muon candidates.

The ISAJET Monte Carlo program is used to predict the total rate of likesign and opposite-sign events from charm production that satisfy the event selection. The number of events due to fake electron, fake muon and fake electron and muon candidates has been determined by measuring the probability f_{μ} that a charged track passing the track selection requirements also is identified as a muon candidate, and weighting the number of such tracks in the event sample, N_{t}, by this probability. The probability f_{μ} is defined as the ratio of the number of muon candidates divided by the total number of tracks passing the track selection in a sample of events that passed the CDF minimum-bias trigger. This is therefore the sum of the probability that a real muon track is identified as a μ candidate together with the probability that a charged hadron is misidentified as a muon. The product f_{d}n_{t} represents an estimate of the number of expected events coming from sources of muon candidates not associated with heavy flavour decay (i.e. decay-in- flight and punch-through). This estimate also includes events with fake electrons (since n_{t} includes the events that have hadrons and conversions misidentified as prompt electrons) where the muon candidate is from a source other than ¸ or b-quark decay. This results in an estimated background rate of 20 ± 10%, which has been checked by verifying that it reproduces the background rates observed in the J/Ψ data sample. This background contributes equally to the like-sign and opposite-sign samples so that the value of R corrected for background contributions is

R = \frac{346 − 90}{554 − 90} = 0.552 ± 0.049(stat)_{−0.048}^{+0.039}(bkg).  (0.4)

Taking into account the estimated number of opposite-sign events from charm production and decay, we find that this value for R implies

χ̄ == 0.176 ± 0.028(stat) ± 0.025(MC) ± 0.032(MC),  (0.5)

where we have included a systematic uncertainty on this estimate due to the Monte Carlo calculation for the fraction of lowest-order to higher order production, and other uncertainties related to te ISAJET prediction.

0.3 Inclusive and Exclusive B Decays

0.3.1 Exclusive J/ΨK Decays

The J/Ψ sample in the CDF data set is expected to be a large source of B meson decays as one expects J/Ψ mesons to be produced only indirectly via χ_{c} and B meson production and decay. The measures of the fraction of B decays in the J/Ψ sample consistently indicate that approximately two-thirds of our J/Ψ candidates are from B decays. The most direct measure of this is to reconstruct the decay mode

χ_{c} → J/Ψγ  (0.6)

by finding the low-energy photon as a shower in the Electromagnetic calorimeter. The mass difference between the J/Ψγ system and the J/Ψ candidate shows a clear χ_{c} peak. Folding in our estimated reconstruction efficiency and relevant branching ratios, we find that ??? % of the J/Ψ events are attributable to χ_{c} decay.

This has motivated us to attempt to reconstruct specific exclusive B meson decay modes involving a J/Ψ final state. We selected J/ΨK candidate events by requiring a J/Ψ with P_{T} > 8 GeV/c along with a charged track with P_{T} > 3 GeV/c in proximity to the J/Ψ candidate. We also searched for the exclusive decay mode J/ΨK^{±}π^{∓} using a similar event selection, but now requiring charged tracks that form an invariant Kπ mass that is within 50 MeV/c^{2} of the nominal K^{∗}(890) mass. The combined J/ΨK and J/ΨK^{∗} invariant mass distribution is shown in Fig. ??? and shows a clear signal of 35 ± 9 events.

0.3.2 Rare B Meson Decay Modes

CDF also has searched for the rare decay mode

B^{∘} → μ^{+}μ^{−}  (0.7)

by selecting a sample of clean di-muon events using a selection similar to the one employed for the J/Ψ study. The invariant mass distribution in the vicinity of the B^{∘} mass shows no structure and is consistent with a flat background. If we assume that the J/Ψ′ events come entirely from b-quark production, then we can place an upper limit on the b-quark di-muon branching fraction of 1.1×10^{−5}. We are currently repeating this analysis using the b-quark cross section as measured from the exclusive decay mode channels described above.