We report a study of multi-muon events produced at the Fermilab Tevatron collider and recorded by the CDF II detector. In a data set acquired with a dedicated dimuon trigger and corresponding to an integrated luminosity of 2100 pb^-1, we isolate a significant sample of events in which at least one of the muon candidates is produced outside of the beam pipe of radius 1.5 cm. The production cross section and kinematics of events in which both muon candidates are produced inside the beam pipe are successfully modeled by knwon QCD processes which include heavy flavor production. In contrast, we are presently unable to fully account for the number and properties of the remaining events, in which at least one muon candidate is produced outside of the beam pipe, in terms of the same understanding of the CDF II detector, trigger, and event reconstruction. Several topological and kinematic properties of these events are presented in this paper. These events offer a plausible resolution to long-standing inconsistencies related to bb production and decay.

The results have been approved as of July 30, 2008.

A more detailed summary of the results can be found here:

• Analysis
• Measurement of correlated bb production in pp collisions at 1960 GeV:
  PRD 77, 072004 (2008), Public Web Page
• P. Giromini's talk at Fermilab (Joint Experimental-Theoretical Physics Seminar)
• K. Pitts's talk at EFI (HEP Lunch Seminar).

Below are the eps and gif versions of all figures meant for downloads.

• Figure 1 (.eps) (.gif): The projection of the two-dimensional impact parameter distribution of muon pairs onto one of the two axes is compared to the fit result (histogram).
  
• Figure 2 (.eps) (.gif): Efficiency of SVX tight (a) and loose (b) selection in simulated dimuon events due to heavy flavor production (see text). The efficiency is shown as a function of the dimuon invariant mass.
  
• Figure 3 (.eps) (.gif): Two-dimensional impact parameter distributions of muons that pass the (a) tight and (b) loose SVX requirements. Cosmic muons are reconstructed as two back-to-back muons of opposite charge and cluster along the d₁=d₂ diagonal.
  
• Figure 4 (.eps) (.gif): Invariant mass, M, distributions of RS (histogram) and WS (dashed histogram) D⁰ candidates in (a) QCD and (b) ghost events.
  
• Figure 5 (.eps) (.gif): Invariant mass distribution (a) of the dimuon pairs used in the study. The efficiency (b) of the tight SVX requirements as a function of the dimuon invariant mass in the data (bullet) is compared to that in the heavy flavor simulation (circle).
  
• Figure 6 (.eps) (.gif): Two-dimensional impact parameter distribution of dimuons that pass the (a) tight and (b) loose SVX requirements.
  
• Figure 7 (.eps) (.gif): Impact parameter distribution of muons contributed by ghost (bullet) and QCD (histogram) events. Muon tracks are selected with loose SVX requirements. The detector resolution is ≈ 30 μm, whereas bins are 80 μm wide.
  
• Figure 8 (.eps) (.gif): Impact parameter distribution of muons that pass the tight SVX requirements. The line represents the fit described in the text.
  
• Figure 9 (.eps) (.gif): Distribution of Δ (see text) as a function of the distance R of the (a) K and (b) π decay vertices from the beamline. For comparison, the analogous distribution for real muons from heavy flavor decays does not extend beyond Δ=9.
  
• Figure 10 (.eps) (.gif): Impact parameter distributions of simulated CMUP muons (histogram) that pass all analysis requirements, including the loose SVX selection, and arise from (a) pions and (b) kaon in-flight decays. The dashed histograms show the impact parameter of the parent pions and kaons.
  
• Figure 11 (.eps) (.gif): Distributions of (a) the invariant mass of pairs of initial muons and opposite sign tracks and of (b) the impact parameter of initial muons, produced by K⁰_S decays, that pass the loose SVX selection. The solid line represents a fit described in the text. In the impact parameter distribution, the combinatorial background is removed with a sideband subtraction method. For comparison, the vertical scale in (b) is kept the same as in Fig. 7.
  
• Figure 12 (.eps) (.gif): Distributions of the invariant mass of pairs of initial muons and opposite sign tracks produced by Λ decays. We attribute the proton (pion) mass to the track with positive (negative) charge. The solid line represents a fit that uses a Gaussian function to model the signal and a fourth order polynomial to model the combinatorial background.
  
• Figure 13 (.eps) (.gif): Distributions of R, the signed distance of muon-track vertices from the nominal beam line for (a) QCD and (b) ghost events (see text).
  
• Figure 14 (.eps) (.gif): Probability that a track with |η| ≤ 1.1 mimics a muon signal in the CMU, CMX, or CMP detectors as a function of the kaon (left) or pion (right) transverse momentum. We have verified that these fake probabilities do not depend on the SVX requirements applied to the tracks.
  
• Figure 15 (.eps) (.gif): Ratio R of total number of OS-SS muon pairs to that of real OS-SS pairs arising from heavy flavor decays as a function of the dimuon invariant mass. We use simulated events generated with the HERWIG Monte Carlo program. The generator parton-level cross sections have been scaled to match the data [PRD 77, 072004 (2008)]. The number of fake muon pairs has been evaluated by weighting simulated hadronic tracks with the probability of mimicking a muon signal as measured with data. Errors are statistical only.
  
• Figure 16 (.eps) (.gif): The invariant mass distribution of (a) OS-SS muon pairs in the data (bullet) is compared to the simulation prediction (circle). One of the two initial muons in the event is combined with an additional muon if their invariant mass is smaller than 5 GeV/c². The difference (b) between data and prediction is also shown.
  
• Figure 17 (.eps) (.gif): The invariant mass distribution of OS-SS muon pairs in the data (bullet) is compared to the simulation prediction (circle). Initial muons are selected using the tight SVX requirements.
  
• Figure 18 (.eps) (.gif): Events with OS initial muon pairs and an additional muon combined with the opposite-charge initial muon. We show the invariant mass, M_μμ, and opening angle, θ, distributions of these combinations for the QCD and ghost contributions.
  
• Figure 19 (.eps) (.gif): Opening angle distributions of dimuon combinations for ghost events. The initial dimuons have same sign charge, and combinations of an additional and initial muons are split according to the charge of the additional muon. The plots are the projection of two-dimensional distributions in which the additional muon is combined with both initial muons.
  
• Figure 20 (.eps) (.gif): Two-dimensional distribution of the impact parameter of additional muons, d_s, versus that of initial muons, d_p, for ghost events. Muons are selected with loose SVX requirements. The QCD contribution has been removed.
  
• Figure 21 (.eps) (.gif): Impact parameter distribution of (a) additional muons found in events in which the initial muons are selected with tight SVX requirements. The same distribution is plotted in (b) with a magnified vertical scale. Additional muons are selected without SVX requirements.
  
• Figure 22 (.eps) (.gif): Sign-coded multiplicity distribution of additional muons found in a cosθ ≥ 0.8 cone around the direction of a primary muon in ghost events before (a) and after (b) correcting for the fake muon contribution. An additional muon increases the multiplicity by 1 when it has the opposite sign and by 10 when it has same sign charge as the initial muon. The background subtracted distribution is also listed in Table X.
  
• Figure 23 (.eps) (.gif): Distribution of the transverse momentum carried by all tracks with p_T ≥ 1 GeV/c contained in a 36.8° cone around an initial muon in (a) QCD and (b) ghost events.
  
• Figure 24 (.eps) (.gif): Distributions of R, the distance of dimuon vertices from the nominal beam line for initial muons with impact parameter (a) smaller and (b) larger than 0.3 cm.
  
• Figure 25 (.eps) (.gif): Muon impact parameter distributions for events containing (top) only two muons or (bottom) more than two muons in a cosθ ≥ 0.8 cone. We call d_p and d_s the impact parameter of initial and additional muons, respectively. The solid lines represent fits to the data distribution with an exponential function. The fit result is shown in each plot.
  
• Figure 26 (.eps) (.gif): Impact parameter distributions of (a) initial muons and (b) tracks of identified K⁰_S decays. The combinatorial background under the K⁰_S signal in Fig. 11 has been removed using a sideband subtraction method.
  
• Figure 27 (.eps) (.gif): Impact parameter distributions of CMUP muons which are accompanied by a D⁰ meson and are selected without (left) SVX or with (right) loose SVX requirements. The bottom plots are magnified views to show distributions at large impact parameters. The contribution of the combinatorial background under the D⁰ signal has been removed with a sideband subtraction method.
  
• Figure 28 (.eps) (.gif): Impact parameter distributions of muons accompanied by a D⁰ meson and selected as the additional muons in this analysis. No SVX requirements are applied. All events (bullet) are compared to RS (circle) and WS (histogram) combinations (see text). The contribution of the combinatorial background under the D⁰ signal has been removed with a sideband subtraction method.
  
• Figure 29 (.eps) (.gif): Invariant mass distribution (a) of K⁰_S → π⁺π^- candidates. The background subtracted L_xy distribution of K⁰_S mesons (b) is compared to the expectation based on the K⁰_S measured lifetime [PDG].
  
• Figure 30 (.eps) (.gif): Distribution of n_v, the number of reconstructed secondary vertices of opposite sign track pairs in QCD (histogram) and ghost (bullet) events. We use all tracks with p_T ≥ 1 GeV/c contained in a 36.8° cone around the direction of each initial muon.
  
• Figure 31 (.eps) (.gif): Distribution of the distance L_xy of reconstructed secondary vertices due to long-lived decays in (a) QCD and (b) ghost events. The combinatorial background has been removed by subtracting the corresponding negative L_xy distributions. The data correspond to an integrated luminosity of 742 pb^-1.
  
• Figure 32 (.eps) (.gif): Average number of tracks in a 36.8° cone around the direction of a primary muon as a function of ∑p_T, the transverse momentum carried by all the tracks. We use cones containing at least three muons. Data (bullet) are compared to the QCD expectation (blacksquare) based on the few events predicted by the heavy flavor simulation, normalized to the number of initial dimuons in the data and implemented with the probability that hadronic tracks mimic a muon signal. The detector efficiency for these tracks is close to unity.
  
• Figure 33 (.eps) (.gif): Two-dimensional distributions of (a) the invariant mass, M, of all muons and (b) the total number of tracks contained in a 36.8° cone when both cones contain at least two muons. The QCD and fake muon contributions have been subtracted.
  
• Figure 34 (.eps) (.gif): Distributions of invariant mass, M, of all muons contained in (a) the 27990 36.8° cones with two or more muons and (b) in each cone of the 3016 events in which both cones contain two or more muons. The QCD and fake muon contributions have been subtracted.
  
• Figure 35 (.eps) (.gif): Invariant mass distribution of (a) all muons and (b) all tracks for events in which both cones contain at least two muons. The QCD and fake muon contributions are subtracted. The data correspond to an integrated luminosity of 2100 pb^-1.
  
• Figure 36 (.eps) (.gif): Average number of secondary vertices, ⟨n²_v⟩, in one cone as a function of the number of secondary vertices, n¹_v, observed in the recoiling cone. Both cones contain at least two muons.
  
• Figure 37 (.eps) (.gif): Number of COT hits associated with initial muon tracks as a function of the track impact parameter for (a) QCD and (b) ghost events.
  
• Figure 38 (.eps) (.gif): Impact parameter distribution of tracks corresponding to muons from Υ decays. Tracks are not associated with silicon hits. The combinatorial background under the Υ signal has been removed with a sideband subtraction technique. The solid line is a fit to the data with a Gaussian function.
  
• Figure 39 (.eps) (.gif): Distributions of Δx (see text) for (a) initial and (b) additional CMUP muons, and additional (c) CMU or (d) CMP muons in QCD (histogram) and ghost (bullet) events.
  
• Figure 40 (.eps) (.gif): Distributions of χ² (see text) for (a) initial and (b) additional muons in QCD (histogram) and ghost (bullet) events.
  
• Figure 41 (.eps) (.gif): Invariant mass, M, distributions of all muons in a 36.8° cone when (a) both cones contain at least two muons, (b) a cone contains three or more muons, (c) a cone contains three muons, and (d) of muons and tracks for cones containing 5 to 6 tracks and three or more muons. QCD and fake muon contributions have been subtracted.
  
• Figure 42 (.eps) (.gif): Distributions of (a) the invariant mass and (b) the distance L_xy of three-track systems in QCD events.
  
• Figure 43 (.eps) (.gif): Distributions of (a) the invariant mass and (b) the distance L_xy of three-track systems in ghost events.
  
• Figure 44 (.eps) (.gif): Distribution of the distance L_xy of the fit-constrained vertices of muon pairs contained in a 36.8° cone for (a) ghost and (b) QCD events.
  
• Figure 45 (.eps) (.gif): Distribution of the distance L_xy of fit-constrained vertices of three-track systems contained in a 36.8° cone around the direction of an initial muon for (a) ghost and (b) QCD events. We select cases in which angular cones contain only three tracks.
  
• Figure 46 (.eps) (.gif): Distributions of the invariant mass, M, of three-track systems in (a) ghost and (b) QCD events. Systems with distance L_xy ≥ 0.04 cm (bullet) are compared to those with L_xy ≤ -0.04 cm (circle).