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
b

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

- Analysis
- Measurement of correlated
b
b 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).

- 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 d
_{1}=d_{2}diagonal.

- Figure 4 (.eps)
(.gif):
Invariant mass, M, distributions of RS (histogram) and
WS (dashed histogram) D
^{0}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 K
^{0}_{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/c
^{2}. 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 K
^{0}_{S}decays. The combinatorial background under the K^{0}_{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 D
^{0}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 D^{0}signal has been removed with a sideband subtraction method.

- Figure 28 (.eps)
(.gif):
Impact parameter distributions of muons accompanied
by a D
^{0}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 D^{0}signal has been removed with a sideband subtraction method.

- Figure 29 (.eps)
(.gif):
Invariant mass distribution (a) of K
^{0}_{S}→ π^{+}π^{-}candidates. The background subtracted L_{xy}distribution of K^{0}_{S}mesons (b) is compared to the expectation based on the K^{0}_{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,
⟨n
^{2}_{v}⟩, in one cone as a function of the number of secondary vertices, n^{1}_{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 χ
^{2}(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).