Abstract

Results from recent studies of bottom quarks produced in hadron collisions at the CERN Sp̄pS and Fermilab Tevatron collider are reviewed. The measurements of the bottom quark production cross section are compared with the theoretical calculations of Nason, Dawson and Ellis. A new measurement of mixing in the neutral B meson system and the observation of the decays B_{d}^{∘} → J/ΨK^{∗∘} and B_{d}^{±} → J/ΨK^{±} from the CDF experiment are reported. The limits on B meson flavour-changing neutral currents are summarized.

Bottom Physics at Hadron Colliders

Pekka K. Sinervo Department of Physics University of Toronto Toronto, CANADA

M5S 1A7

1 Introduction

The study of bottom quarks provides us with a unique window into the heavy flavour sector of the standard model. The lifetimes and partial widths of bottom hadrons can be directly related to the Cabibbo-Kobayashi-Maskawa matrix elements and the mass of the hypothesized top quark while the production properties of bottom quarks (b-quarks) in high-energy collisions reflect their couplings to the other fermions [1].

Much of our current knowledge of bottom hadrons has come from the CESR and DORIS e^{+}e^{−} colliders, where the production and decay of the Υ(4S) resonance into BB̄ meson pairs provides us with a copious source of B mesons. However, the production rate of bottom hadrons at \overline{p} p colliders is approximately three orders of magnitude higher than what can be currently achieved at e^{+}e^{−} colliders [4]. The large b-quark production cross section at a hadron collider is tempered by the difficulty separating the bottom hadron events from the much larger rate of events arising from the production of light quark and gluon final states. This separation is typically achieved by requiring a distinctive signature or “tag”, such as the presence of an energetic lepton and the associated hadrons that result when a b-quark decays semileptonically. The efficiency of such tagging schemes can be quite low and they tend to restrict the b-quark final states that are experimentally accessible.

The UA1 collaboration at the CERN Sp̄pS collider and the CDF collaboration at the Fermilab Tevatron Collider have been studying bottom quark systems produced in hadron-hadron collisions and have made several recent measurements of b-quark production and decay properties. The UA1 collaboration has accumulated a data sample with an integrated luminosity of 4.7 pb^{−1}, while the CDF experiment has gathered a 4.4 pb^{−1} data set. I will summarize their most recent b-physics results focusing on (i) the measurement of the b-quark production cross section, σ_{b}, (ii) a study of B^{∘}−B̄^{∘} mixing using 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^{−}.

2 The UA1 and CDF Detectors

The muon detection capabilities of the UA1 detector are used throughout their bottom quark studies. The UA1 detector [2] has excellent muon identification, employing a central drift chamber to measure the muon candidate momenta in a dipole magnetic field. This is followed by 9 − 10 interaction lengths of absorber material and a set of chambers outside the aborber that measure the trajectories of muon candidates penetrating through the absorber. A hadronic calorimeter measures the energy flow around the muon candidate. The detector triggers on inclusive muon candidates with muon P_{T} > 6 GeV/c, while the inclusive dimuon trigger accepts events with two muon candidates each with P_{T} > 3 GeV/c.

The CDF detector [3] combines high-resolution charged particle detection in a solenoidal magnetic field with both electromagnetic (EM) and hadronic (HAD) calorimeter coverage out to pseudorapidities (η) of ±4.2. Electrons are identified by using the finelysegmented EM calorimeter to identify electron showers and by requiring a charged track in the central tracking chamber (CTC) matching the position and energy of the EM shower. Muons are identified by requiring the presence of a charged track stub in a set of drift chambers located outside the HAD calorimeter well matched to a CTC track. The CDF collaboration uses events tagged either by requiring an energetic electron candidate with E_{T} > 12 GeV, two muon candidates with P_{T} > 3 GeV/c, or a muon candidate with P_{T} > 3 GeV/c and an electron candidate with E_{T} > 5 GeV in their b-quark studies.

3 Bottom Quark Production

The production cross section for heavy quarks has been calculated to next-to-leading order by Nason, Dawson, and Ellis [5]. The results of this calculation are sensitive to approximations made to compute the higher-order diagrams and the light quark and gluon structure functions, as illustrated by the work of G. Altarelli et al. [6]. Thus, the measurement of the total and differential cross section is a consistency check of this calculation. An understanding of heavy quark production as a background to top quark searches provides further motivation to directly measure σ_{b}. Finally, σ_{b} is an important “engineering number” allowing us 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 factories.

Bottom quark production in hadron-hadron collisions is expected to have large contributions from the leading order processes dominated by the gluon fusion reaction gg → b\overline{b}, and higher order diagrams such as “gluon splitting” where a two-gluon final state is produced with one of the gluons fragmenting into a bb̄ system. These processes result in different kinematic configurations for the b and \overline{b}-quark, so that an important test of the theory is provided by the measurement of the differential cross section as a function of such variables as the b-quark transverse momentum (P_{T}). Both the UA1 and CDF collaborations have done this by measuring the rate of events with leptons arising from b-quark production and subsequent semileptonic decay, and inferring from these data the b-quark cross section, taking into account the fragmentation and decay properties of the b-quark.

3.1 UA1 Cross Section Measurement

UA1 has measured the b-quark cross section by studying the rates of

• high-P_{T} muons accompanied by a jet [7],

• dimuon events with large dimuon effective mass [7],

• low-mass, non-resonant dimuon events [7], and

• J/Ψ→ μ^{+}μ^{−} decays [8].

Each measurement is sensitive to a different range of b-quark transverse momenta, and taken together provide both a measure of the total cross section as well as an estimate of the differential cross section as a function of P_{T}. They are presented as differential cross sections integrated above a specific b-quark P_{T} cut and within a specific rapidity (y) interval. A model-dependent extrapolation is made to determine the total b-quark cross section.

3.1.1 Inclusive Muon Sample

The semileptonic decay of a b-quark typically results in a lepton associated with several charged and neutral hadrons. The UA1 collaboration uses this “non-isolated” lepton signature to select muons from b-quark decay and reject muons arising from W and Z boson decay and Drell-Yan production, which typically are well-isolated from other particles in the event. The detailed isolation characteristics of the surviving muon candidates are used to determine the b-quark signal rate relative to the background processes consisting of muons from charm quark (c-quark) semileptonic decays, muon candidates from decays-in-flight of K and π mesons, and fake muon candidates resulting from hadron punch-through and leakage through the absorber.

The muon candidates are selected by requiring a charged track with P_{T} > 10 GeV/c associated with a track stub detected in the outer muon chambers. The quantity

I = \sqrt{(∑ E_{T} /3)^{2} + (∑ p_{T} /2)^{2}}  (1)

is used to characterize the isolation of the candidate, where the sum is taken over all calorimeter towers and tracks within a cone of R = \sqrt{Δη^{2} + Δϕ^{2}} = 0.7. The requirement I > 2 GeV rejects most of the muons from W^{±} and Z^{∘} decay and Drell-Yan production, as these are typically well-isolated from other hadrons in the event. A jet with P_{T} > 10 GeV/c and well separated from the muon candidate is required to further reduce these backgrounds while retaining from 65 to 80% of the b-quark events (this efficiency depends on the b-quark P_{T}). The additional requirement that the transverse mass Figure 1: The isolation distribution of the muons in the UA1 inclusive muon sample.

M_{T} ≡ \sqrt{2P_{T}^{μ}P_{T}^{ν} (1 − cos ϕ^{μν})} be less than 25 GeV/c^{2} further reduces contributions from W^{±} decay (P_{T}^{μ} is the transverse momentum of the muon candidate, P_{T}^{ν} is the missing transverse momentum and ϕ^{μν} is the azimuthal angle between these two momentum vectors). This results in an event sample consisting of ∼ 5000 events.

The P_{T} of the muon relative to the jet axis surrounding the lepton candidate, P_{T}^{rel}, is an effective way of discriminating between different sources of non-isolated muons. The decay of a b-quark results in events with larger values of P_{T}^{rel} compared to c-quark decay, while decays-in-flight tend to have relatively smaller P_{T}^{rel} values, as shown in Fig. 1. The fraction of b-quark decay events in the UA1 event sample is determined statistically by fitting the P_{T}^{rel} distribution to the expected contributions from b-quark decay, c-quark decay and decays-in-flight.

The ISAJET Monte Carlo program [9] is used to model the P_{T}^{rel} distributions for Table 1: The rate of muons from b-quark decay as a function of the μ P_{T} for different muon samples. The corresponding b-quark cross sections are also listed and correspond to integrated rates above the indicated P_{T} threshold and for |y| < 1.5.

Channel  P_{T, min} Muon Cross Section b-Quark Cross Section
(GeV/c)  (nb)  (nb)
J/Ψ Events  6  2360 ± 1215
High-Mass Dimuons  6  2660 ± 1330
Low-Mass Dimuons  10  390 ± 170
μ+ jet (10-15 GeV/c)  15  1283 ± 269  120 ± 38
μ+ jet (15-20 GeV/c)  23  180 ± 40  24 ± 8
μ+ jet (20-25 GeV/c)  30  24.3 ± 6.5  4.1 ± 1.4
μ+ jet (25-30 GeV/c)  39  3.2 ± 1.4  0.55 ± 0.30
μ+ jet (30-35 GeV/c)  46  1.1 ± 0.6  0.32 ± 0.20
μ+ jet (35-40 GeV/c)  54  0.14 ± 0.09  0.04 ± 0.03

muons from charm and bottom quark decay. The shape of the P_{T}^{rel} distribution for decays-in-flight is determined using a detector simulation, and the overall normalization of this background is taken from an estimate of the rate of such events using the kinematics of K and π meson decay and the observed distribution of charged hadrons at the Sp̄pS collider. The fitted fraction of events resulting from b-quark decay is 0.33 ± 0.03 ± 0.03, where the second uncertainty comes from the normalization of the decay-in-flight background.

The results of this study are listed in Tab. 1, which shows the efficiency-corrected cross sections for muons from b-quark semileptonic decay for several muon P_{T} bins. These are converted to b-quark cross sections above a given b-quark P_{T} threshold (determined by requiring that 90% of the muons in the P_{T} bin come from b-quarks above this threshold). This technique reduces the sensitivity of the measured cross section to uncertainties in the produced b-quark P_{T} distribution and provides a measure of the P_{T} dependence of the cross section. The systematic uncertainties in this analysis come from uncertainties in the model for b quark fragmentation (±6%); the integrated luminosity (±8%); the detector acceptance (±10%); the branching ratio for b → μ, assumed to be equal to 10.2 ± 1.0%; and the b-quark P_{T} spectrum (±20%).

3.1.2 Bottom Cross Section from Dimuon Events

The non-resonant component of the inclusive dimuon event sample has a contribution from b-quark production and therefore provides an independent measure of σ_{b}. However, the background and signal characteristics change as the dimuon effective mass m_{μμ} Figure 2: The dimuon effective mass distribution for the non-isolated low-mass dimuon events. The shaded region shows the estimated contribution from b-quark same-side sequential decays.

increases, so UA1 chose to perform two separate analyses on the unlike-sign dimuon samples, one using the event sample with 2 < m_{μμ} < 6 GeV/c^{2} and the other using the events with 6 < m_{μμ} < 35 GeV/c^{2}. In both cases, an isolation cut similar to the one employed in the inclusive muon analysis is made requiring that one or both muons be non-isolated. There are 731 and 525 events in the low and high dimuon mass samples, respectively.

A fit of the m_{μμ} distribution for the low-mass dimuon sample is performed to extract the contribution from semileptonic b-quark decays, where the resulting charm system also decays semileptonically (“same-side sequentials”). This fit allows for contributions from same-side sequential b-quark decays, Drell-Yan dimuon production, leptonic decays of light mesons and resonant J/Ψ and Ψ′ decays. The fit estimates the b-quark contribution as 100 ± 27 events. The result of this fit as a function of dimuon effective mass is shown in Fig. 2. This gives an estimated b-quark cross section, integrated above a P_{T} of 10 GeV/c, corresponding to 390 ± 170 nb.

The P_{T}^{rel} distribution for the high mass dimuons is used to separate the fraction of bquark events in the sample from the c-quark and decay-in-flight backgrounds. The fit of this distribution to the b and c-quark contributions yields an overall b-quark fraction of 55±4±1%. A fit of the same-sign P_{T}^{rel} distribution subtracting the expected contribution from decays-in-flight yields a distribution that is consistent with coming only from bquark decays. This is confirmation that the decay-in-flight background rate is correctly calculated, as the like-sign sample is not expected to have a contribution from c-quark decay. This analysis results in a b-quark cross section estimate of 2660 ± 1330 nb for b-quark |y| < 1.5 and P_{T} > 6 GeV/c.

3.1.3 Bottom Cross Section From J/Ψ Decays

The J/Ψ meson is produced in hadron-hadron collisions by both direct charmonium production pp̄ → χ_{c}X followed by the decay χ_{c} → J/ΨX′ and by B meson production followed by the decay B → J/ΨX. A measure of the J/Ψ cross section along with a correction for the fraction due to the former process provides a measure of σ_{b}.

The UA1 collaboration selects J/Ψ candidates by requiring two opposite-sign muon candidates in each event, each with P_{T} > 3 GeV/c. The resulting dimuon effective mass distribution shows a clear J/Ψ signal of ∼ 1250 events on a background of order ∼ 250 events. The decay χ_{c} → J/ΨX can be distinguished from the decay B → J/ΨX by using the isolation properties of the J/Ψ, which in this case is determined from the charged track density as a function of R from the J/Ψ meson direction. This distribution, shown in Fig. 3, is fit to contributions from both χ and B decays, resulting in

\frac{N(B → J/Ψ)}{N(J/Ψ)} = 0.31 ± 0.02(stat) ± 0.12(syst).  (2)

This gives a cross section for J/Ψ mesons from b-quark decays of 1.92 ± 0.15 ± 0.79 nb for J/Ψ’s in the rapidity interval |y| < 2.0 and P_{T} > 5 GeV/c. This corresponds to an integrated b-quark cross section for b-quark P_{T} > 6 GeV/c and |y| < 1.5 of 2360 ± 1215 nb, after correcting for the fraction of J/Ψ’s estimated to come from the cascade decay b → Ψ′X → J/ΨγX (25% of the J/Ψ decays are estimated to come from this source).

3.1.4 Summary of UA1 Cross Section Results

These four methods give estimates of the cross section for inclusive muon and dimuon events from b-quark decay. These muon-level cross sections are converted into b-quark cross sections using the ISAJET Monte Carlo program to determine the relationship between the observed muon rates and the parent b-quark cross sections as a function of b-quark P_{T}, as described in the inclusive muon analysis.

The b-quark cross sections from the different analyses are listed in Table 1 and plotted in Fig. 4. The systematic uncertainties introduced in translating the muon level cross sections to b-quark cross sections comes from the uncertainty in the b-quark Figure 3: The charged track density around the J/Ψ candidates as a function of the separation R from the J/Ψ.

Figure 4: The cross section for pp̄ → bX integrated above b-quark P_{T, min} plotted as a function of P_{T, min}(this does not include the cross section for \overline{b} production). The theoretical calculation of P. Nason et al. is also shown.

fragmentation, the produced b-quark P_{T} spectrum and the branching fraction BR(b → μX).

The theoretical estimate for b-quark production to next-to-leading order is also shown in Fig. 4, and is in good agreement with the measured values. Extrapolation of the integral b-quark cross section to P_{T, min}= 0 gives a total b-quark cross section for |y| < 1.5 of 12.8_{−5.4}^{+7.0} μb.

3.2 Bottom Quark Production at the Tevatron

The CDF collaboration has measured the b-quark cross section at \sqrt{s} = 1.8 TeV using a sample of inclusive electron events. This measurement differs from the UA1 inclusive muon measurement in several respects: The CDF electron sample is substantially cleaner and so the uncertainty in the background substraction is relatively small. However, the isolation characteristics of the lepton employed in the UA1 analysis to measure the charm quark contribution are not used in the CDF analysis as the correlation between the electron identification efficiency and the isolation of the electron reduce the effectiveness of this technique.

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 those 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 to charged track momentum is required to satisfy 0.75 < E/p < 1.4. There are ∼ 20 000 candidate events, with electron E_{T} above 7 GeV (the sample with E_{T} between 7 and 12 GeV is prescaled).

Energetic photons converting into electron-positron pairs near the interaction region and π^{∘} → γe^{+}e^{−} decays form a significant background. These are reduced by rejecting events that have a second charged track, opposite in sign to the candidate, that along with the electron forms a photon conversion candidate. The remnant conversion background is estimated to be 20±5% of the sample. The background from charged hadrons is estimated to be 15 ± 15%. The E_{T} spectrum of the electron candidates is shown in Fig. 5.

W^{±} and Z^{∘} boson production and charm and bottom decay are expected to be the principle sources of prompt electrons at the Tevatron collider. The contribution from W^{±} production is removed by requiring that the transverse mass in the event (E̸_{T}) be less than 8\sqrt{∑ E_{T}}, where the sum is over all the calorimeter cells in the detector. Z^{∘} decays are removed by rejecting events having a second electron cluster forming a dielectron effective mass greater than 80 GeV/c^{2}.

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 E_{T} Figure 5: The E_{T} spectrum of the CDF inclusive electron sample after the selection decribed in the text. spectrum, the resulting electron E_{T} spectrum would only have contributions from charm and bottom production. The relative contribution of c-quark decays is expected to be small because of the isolation requirements made by the electron identification cuts, and is difficult to measure 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 assumption introduces a systematic uncertainty in the resulting b-quark cross section of +5% and −12% if one assumes a factor of two uncertainty in the ISAJET ratio of charm to bottom quark production cross sections.

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}, P_{T, min}. 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. An uncertainty in the calculation is introduced by the b-quark production P_{T} distribution used in the Monte Carlo calculation. The ISAJET P_{T} distribution for the lowest-order b-quark production process is used as that matches the P_{T} distribution obtained from the higher-order QCD calculation [5]. The uncertainty introduced by this assumption when calculating the b-quark production cross section above a specific P_{T, min} is neglible compared with the other uncertainties.

A summary of the statistical and systematic uncertainties of this analysis is shown in Table 2. The resulting integrated cross sections are listed in Table 3 for three different choices of E_{T} cuts on the candidate electrons, and are plotted in Fig. 6 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 discrepancy is only a few standard deviations because of the relatively large uncertainties, it is rather striking given the good agreement between the measured and predicted values at \sqrt{s} = 630 GeV.

4 B^{∘}−B̄^{∘} Mixing

The observed 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. 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-Kobayashi-Maskawa matrix. A measurement of this mixing, which is expected to differ for B_{s}^{∘} and B_{d}^{∘} mesons, is an important test of the standard model and can be used to set limits on these parameters [10].

The CLEO and ARGUS experiments directly measure the mixing parameter χ_{d} Table 2: The systematic uncertainties in the CDF b-quark production cross section from the inclusive electron analysis.

Source of Uncertainty  Uncertainty in Cross Section
Conversion background  5%
Hadron contamination  15%
Charm production  10%
Electron identification efficiency  10%
Uncertainty from underlying event model  8%
Trigger efficiency  10%
b-quark fragmentation  16%
B semileptonic decay fraction  10%
Integrated luminosity  7%
Total  32%

Table 3: The CDF b-quark production cross section from the inclusive electron analysis. The corresponds to the cross section for b-quark production in the b-quark rapidity interval |y| < 1.0 and P_{T} greater than P_{T, min}.

Electron E_{T} P_{T, min} b-Quark Cross Section
(GeV)  (GeV/c)  (nb)
10-15  15  1220 ± 390
15-20  23  220 ± 70
20-25  32  56 ± 18

Figure 6: The CDF b-quark production cross section integrated above P_{T, min} versus P_{T, min}. The prediction from Nason et al. is shown. defined as

χ_{d} = \frac{Prob(B_{d}^{∘} → B̄_{d}^{∘})}{Prob(B_{d}^{∘} → B_{d}^{∘}) + Prob(B_{d}^{∘} → B̄_{d}^{∘})},  (3)

since only B_{d}^{∘} mesons are 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},  (4)

where f_{d} and f_{s} are the relative fractions of produced B_{d}^{∘} and B_{s}^{∘} mesons. A prediction or measurement of these fractions then allows one to determine both χ_{s} and χ_{d} .

The UA1 collaboration reported the first observation of B^{∘} − B̄^{∘} mixing in 1987 using the ratio of like-sign to unlike-sign dimuon events to obtain χ̄ = 0.121±0.047 [11]. This was followed by observations at ARGUS and CLEO of mixing in the B_{d}^{∘} system [12]. Recently, the ALEPH and L3 experiments at LEP have reported measurements of χ̄ [13]. The newest result from hadron colliders is from CDF, where a measurement of χ̄ has been made using electron-muon events. I will therefore focus on this latest measurement.^{∗}

The cleanest topological tag for B^{∘}-B̄^{∘} production at a hadron collider is the requirement of two leptons in the final state, with a lepton coming from the semileptonic decay of each B^{∘} meson. This signature has relatively small backgrounds, and yet provides a reasonable rate of events. The mixing in the B^{∘} − B̄^{∘} system produces an excess of like-sign dilepton events relative to the number of opposite sign dileptons, so that the ratio

R = \frac{N(l^{+}l^{+}) + N(l^{−}l^{−})}{N(l + l−)}  (5)

can be related to the mixing parameter χ̄. The CDF collaboration has measured R in an event sample selected by requiring an electron and muon candidate. This sample has a factor of two more sensitivity than the comparable dielectron or dimuon data, and does not suffer from backgrounds in the opposite-sign sample arising from Drell-Yan production and J/Ψ and Υ decay.

4.1 Event Selection

The eμ event sample is defined by requiring events that have passed the CDF dilepton 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 charged 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 energy deposition in the calorimeter associated with the charged track is required to be consistent with a minimum-ionizing particle. This selection results in 1340 events.

∗An updated UA1 measurement consistent with their earlier result has been reported after this conference [14].

There are several background contributions 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 inner-most tracking chamber. There are no backgrounds 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.

Two other sources of dilepton events are

pp̄ → bb̄X
\underrightarrow{|}e^{−}cX′
\underrightarrow{|}μ^{+}X′′

where both leptons arise from the sequential decay of the same b-quark, and

pp̄ → bb̄X → b(e^{+}X′)X
\underrightarrow{|}cX′′
\underrightarrow{|}μ^{+}X′′′

where the b̄ decays semileptonically to e^{+}X′. The former decay mode produces dileptons with invariant masses less than the B meson mass. These are rejected by requiring 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 oppositesign events.

4.2 Sources of Di-lepton Event Candidates

The remaining sources of background events are i) fake electron and muon candidates, ii) charm production and semileptonic decay, and iii) sequential bottom quark decay.

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 passing the CDF minimum-bias trigger, and is (2.7 ± 0.9) × 10^{−3}. This is a sum of the probability that a real muon track is identified as a μ candidate and the probability that a charged hadron is misidentified as a muon. The product f_{d}N_{t} represents the number of events expected 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 c or b-quark decay. This background calculation has been checked by verifying that it reproduces the background rates observed in the J/Ψ data sample.

The systematic uncertainties in f_{μ} come from the uncertainty in the K/π ratio and P_{T} spectrum of the minimum-bias sample relative to the eμ sample, and are estimated as ±15% and ±20% respectively. This results in an estimated background to heavy quark decays in the eμ sample of 20 ± 10%. 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).  (6)

The mixing parameter χ̄ can be determined from R by accounting for the like- and opposite-sign dilepton events from sequential b-quark decays and charm quark production. The ISAJET Monte Carlo program was used to estimate the remaining contribution of sequential b-quark decays relative to direct dilepton production, and to estimate the relative rate of charm events to bottom quark events in the opposite-sign sample. The latter contribution is small so that the estimated uncertainty of ±100% on the predicted charm quark production cross section introduces a small uncertainty in the mixing parameter. The estimated contributions are listed in Table 4. These estimates predict that R = 0.233 ± 0.051 in the absence of b-quark mixing, in clear conflict with the measured value, and imply a value of

χ̄ = 0.176 ± 0.028(stat) ± 0.025(syst) ± 0.032(MC).  (7)

The systematic uncertainty in χ̄ is dominated by the uncertainty in the background subtraction. The CDF collaboration has investigated the Monte Carlo dependence of this result, including uncertainties in heavy-quark fragmentation and the relative fraction of lowest-order to higher-order b-quark production. A separate systematic uncertainty has been assigned to these model-dependent uncertainties. The collaboration is currently considering ways of reducing this model-dependent uncertainty.

Table 4: The fraction of observed events from b-quark and c-quark decay in the eμ sample predicted by the ISAJET Monte Carlo calculation (normalized to the total number of observed eμ events).

Process  Fraction of Observed Events
b-quark direct decays  0.76
b-quark sequential decays  0.19 ± 0.07
c-quark decays  0.05 ± 0.05

This value for χ̄ can be combined with the measurements of χ_{d} from CLEO and ARGUS to indirectly place bounds on value for χ_{s}. This requires the unmeasured fraction of B_{s}^{∘} and B_{d}^{∘} mesons in the data sample. If one assumes that contributions to the event sample from bottom baryon production is negligible, a B_{u} : B_{d} : B_{s} production ratio of 0.4 : 0.4 : 0.2, and common semileptonic branching ratios for all B mesons, one predicts f_{d} = 0.4 and f_{s} = 0.2. The data for χ_{d} and χ̄ can be then shown plotted together, as is shown in Fig. 7. The mixing measurements are consistent with standard model predictions for χ_{s} and χ_{d} [10], also shown in the figure.

5 Inclusive and Exclusive B Meson Decays

The observation of B mesons through exclusive decay modes provides a direct confirmation of the preceding results, but faces severe combinatorial backgrounds in a hadron collider experiments. These backgrounds can be reduced by considering final states with multiple lepton candidates. The B decay modes resulting in a J/Ψ meson that subsequently decays to two leptons is particularly promising, as a clean J/Ψ signal is readily obtained and there are relatively few other sources of J/Ψ mesons. These features have been exploited in the UA1 b-quark cross section measurement described earlier.

The CDF collaboration has analyzed a sample of ∼ 2500 J/Ψ decays for evidence of the exclusive decays

B^{±} → J/ΨK^{±}  (8)
B^{∘} → J/ΨK^{∗}^{∘}.  (9)

The J/ΨK^{±} candidate events were selected by requiring a J/Ψ candidate with J/Ψ P_{T} > 8 GeV/c as J/Ψ mesons from charm production are expected to have a softer P_{T} spectrum. All charged tracks with P_{T} > 2.0 GeV/c in a 60^{∘} cone around the J/Ψ candidate were considered K^{±} candidates. The invariant J/ΨK^{±} invariant mass is shown plotted in Fig. 8(a) and shows a signal of approximately 12 events above a comparable background.

Figure 7: The regions of χ_{d} and χ_{s} preferred by the CDF mixing measurements, along with the combined CLEO/ARGUS measurements for χ_{d}. The standard model prediction is shown as the shaded region.

Figure 8: The effective J/ΨK^{±} mass distribution is shown in (a), the effective J/ΨK^{∗} mass distribution is shown in (b), and the combined mass distribution is shown in (c).

The J/ΨK^{∗} candidates are selected using the the same J/Ψ sample and requiring two oppositely charged tracks that have an invariant Kπ mass within 50 MeV/c^{2} of the nominal K^{∗}(890) mass. Only the three highest P_{T} tracks in the event are considered in order to reduce the combinatorial backgrounds. A small K^{∗} signal is evident on a large background, and the resulting J/ΨK^{∗} invariant mass spectrum is plotted in Fig. 8(b). A small signal at the mass of the B meson is evident.

The invariant mass distribution for both channels is shown in Fig. 8(c), and a fit to this signal employing a Gaussian lineshape for the signal and a smooth background results in an estimated rate of 35 ± 9 events. Although this is a modest signal, it represents the world’s largest sample of observed B → J/ΨX_{s} events. An estimate of the b-quark production cross section from this signal is expected to yield a measurement that is completitive with the measurements described earlier.

5.1 Upper Limits on B → μ^{+}μ^{−}

The standard model predicts the flavour-changing decays

B → μ^{+}μ^{−} and B → μ^{+}μ^{−}X_{s}  (10)

to occur at a branching ratio of 10^{−9} − 10^{−8} (X_{s} is a strange meson) [15], whereas a branching ratio significantly larger than this would require an extension to the minimal standard model. For this reason, both UA1 and CDF have searched for these decay modes.

The UA1 analysis [16] of the exclusive μ^{+}μ^{−} decay mode is made by selecting events with two muon candidates and then searching for a B meson signal in the dimuon invariant mass spectrum, shown in Fig. 9. There is no apparent signal, allowing the UA1 collaboration to place the 90% confidence level upper limit on the B → μ^{+}μ^{−} branching ratio of

BR(B → μ^{+}μ^{−}) < 8.3 × 10^{−6} (UA1).  (11)

The CDF collaboration, using a similar analysis, sets a limit

BR(B → μ^{+}μ^{−}) < 3.2 × 10^{−6} (CDF).  (12)

The UA1 study also places an upper limit on dimuon decay mode involving strange mesons by requiring in addition to the two muons two charged tracks consistent with a K^{∗}(890). There is again no evidence for a signal, which allows the collaboration to set a limit

BR(B^{∘} → μ^{+}μ^{−}K^{∗}) < 2.3 × 10^{−5} (UA1).  (13)

These limits are substantially more restrictive than earlier results obtained at e^{+}e^{−} colliders.

Figure 9: The UA1 dimuon effective mass distribution in the direct search for B → μ^{+}μ^{−}.

6 Future Bottom Physics at pp̄ Colliders

The B physics program at the CERN Sp̄pS collider is now drawing to a close, but at the same time the bottom physics program at the Fermilab Tevatron is on the threshold of a potential “golden era.” The results discussed in this report illustrate the potential of B physics at hadron colliders.

Both the CDF and D0 collaborations expect to obtain run data samples an order of magnitude larger than the existing data sets in the 1991 Tevatron. In addition, these detectors will have excellent b-quark tagging capabilities, provided by the new CDF silicon vertex detector and the good D0 muon identification. It is reasonable to expect significant new b-physics results from these collaborations in the next several years.

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