An additional study of multi-muon events produced in {\boldmath $p\bar{p}$} collisions at {\boldmath $\sqrt{s}=1.96$} TeV

We present one additional study of multi-muon events produced at the Fermilab Tevatron collider and recorded by the CDF II detector. We use a data set acquired with a dedicated dimuon trigger and corresponding to an integrated luminosity of 3.9 fb$^{-1}$. We investigate the distribution of the azimuthal angle between the two trigger muons in events containing at least four additional muon candidates to test the compatibility of these events with originating from known QCD processes. We find that this distribution is markedly different from what is expected from such QCD processes and this observation strongly disfavours the possibility that multi-muon events result from an underestimate of the rate of misidentified muons in ordinary QCD events.

This Letter reports on one additional test on the possible origin of multi-muon events observed at the Tevatron.These events were identified in a previous study [1] of a data set acquired with two central (|η| < 0.7) primary (or trigger) muons, each with transverse momentum p T ≥ 3 GeV/c, and with invariant mass larger than 5 GeV/c 2 and smaller than 80 GeV/c 2 .That study shows that many long-standing inconsistencies between measured and predicted properties of the correlated b b production and semileptonic decay at hadron colliders [2][3][4][5] could be explained by the presence of a relevant source of muons which appear to be mostly produced beyond the beam pipe of radius 1.5 cm (this contribution is whimsically referred to as ghost events because they were unnoticed or ignored by previous measurements).Within the large uncertainty of the prediction, mostly based on simulations, the observed rate of ghost events is found to be consistent with being produced by muons arising from in-flight-decays of pions and kaons, or punchthrough of hadronic prongs from K 0 S or hyperon decays.However, a search in ghost events for additional muons with p T ≥ 2 GeV/c and |η| ≤ 1.1 and contained in a cos θ ≥ 0.8 cone around the direction of a primary muon selects a small but significant fraction of events with a large content of muon candidates that appears difficult to account for in terms of known sources with the present understanding of the CDF II detector, trigger, and event reconstruction.
A more recent study by the CDF collaboration [6] has improved the estimate of the contribution of ordinary sources to ghost events.This study addresses in particular the contribution from pion and kaon in-flight-decays.In 1426 pb −1 of data, there are 54437 ± 14171 ghost events and 12169 ± 1319 ghost events with three or more muons which cannot yet be accounted for with ordinary sources.
In this Letter, we investigate the distribution of the azimuthal angle (δφ) between the two primary muons in events in which both primary muons are accompanied by at least one (or two) additional muon candidates in a cos θ ≥ 0.8 cone around their direction, and compare it to those for all QCD sources known to produce dimuon events: b b, cc, and Υ production or events in which one trigger muon is due to hadrons misidentified as muons (cosmic rays are removed from the data sample and the contribution of secondary interactions in the detector volume is negligible [1]).As discussed in Ref. [1], known QCD sources produce a handful of events with four and none with six muon candidates.However, if the unaccounted multimuon events were generated by a gross underestimate of the number of additional muons mimicked by hadrons in ordinary QCD events, the δφ distribution of primary muons in multi-muon events would be similar to that of ordinary QCD events in which the large contribution of next-to-leading order (NLO) terms due to initial and final state radiation results in a broader δφ distribution than that predicted by the Born (LO) approximation.
In fact, the δφ distribution of pairs of b hadrons or jets is traditionally used to determine the relative contribution of NLO to LO terms [7].This type of comparison was also suggested by Ref. [8], in which the excess of multi-muon events is modeled with the decay of two colorless particles produced through the exchange of a heavy object.In such a hypothetical case, their deviation from the back-to-back configuration in the azimuthal angle (δφ = π) is only caused by initial state radiation of the incoming quarks and is expected to be small.
The study presented here uses a dimuon data set corresponding to an integrated luminosity of 3.9 fb −1 and selected with the same requirements used in Ref. [1].High precision charged particle tracking is provided by a large central drift chamber surrounding a trio of silicon tracking devices composed of eight layers of silicon microstrip detectors ranging in radius from 1.5 to 28 cm in the pseudorapidity region |η| < 1 [9].The tracking detectors are inside a 1.4 T solenoid which in turn is surrounded by electromagnetic and hadronic calorimeters.Outside the calorimeters, drift chambers in the region |η| ≤ 1.1 provide muon identification.We search events for additional muons using tracks with p T ≥ 2 GeV/c and |η| ≤ 1.1.The rate of additional muons mimicked by hadronic punchthrough is estimated with a probability per track derived by using kaons and pions from D * ± → π ± D 0 with [1,6,10].The difference between observed additional muons and predicted misidentifications is referred to as real muons.
The δφ distribution for all 3.9 M events is shown in Fig. 1. Figure 2 compares to the corresponding heavy flavor simulations the δφ distribution of trigger muons due to b b and cc production.This figure is reproduced from Ref. [10] that has measured σ b→µ, b→µ and σ c→µ,c→µ in a dimuon data set corresponding to a luminosity of 742 pb −1 .In the b b case, the distribution has an average of 2.5 with a rms deviation of 0.8 rad.The long and important tail extending to δφ = 0 is due to NLO terms and the non-perturbative fragmentation function of b quarks.In cc events, because of the smaller quark mass, NLO terms are approximately a factor of three larger and the fragmentation function is much softer.Accordingly, the δφ distribution has a smaller average (2.4 rad) and a larger rms deviation (0.9 rad).
The azimuthal-angle distribution for primary muons produced by Υ(1S) decays is expected to be similar to those for heavy flavors because the final state contains a bleaching gluon recoiling against the Υ meson.This distribution, shown in Fig. 3, is constructed using muon pairs with invariant mass in the range 9.28−9.6GeV/c 2 .As in Ref. [10], the combinatorial background under the Υ(1S) signal is removed with a sideband subtraction technique.
A similar δφ distribution is also expected for those cases in which one muon is mimicked by a track in the jet recoiling against a muon due to a heavy-quark semileptonic decay.Figure 3 shows the δφ distribution of primary muons when one of them is mimicked by pions produced by K 0 S decays.As in Ref. [6], we select K 0 S → π + π − with a π → µ misidentification by combining primary muons with tracks of opposite charge and p T ≥ 0.5 GeV/c.We select pairs consistent to those arising from a common three-dimensional vertex.We also take advantage of the K 0 S long lifetime to suppress the combinatorial background.We further require that the distance between the K 0 S vertex and the event primary vertex, corrected by the K 0 S Lorentz boost, corresponds to ct > 0.1 cm.We select K 0 S candidates with invariant mass in the range 0.47 − 0.52 GeV/c 2 (see Fig. 3 of Ref. [6]), and remove the combinatorial background with a sideband subtraction technique.
In summary, the δφ distributions of primary muons produced by known QCD processes peak at δφ ≃ π, and exhibit a significant tail extending to δφ = 0. Depending on the production mechanism, the mean and rms deviation of these distributions are in the range of 2.4 − 2.5 rad and 0.7 − 0.9 rad, respectively.The δφ distributions in the subset of events in which each trigger muon is accompanied by at least one or at least two additional real muons are shown in Fig. 4.These δφ distributions, with mean of 2.9 rad and rms deviation of 0.2 rad and without any tail below δφ = 2.5 rad, are different from those of primary muons due to all known QCD sources.
In conclusion, as mentioned earlier, within our present understanding of the CDF-detector response no known sources produce events in which each cos θ ≥ 0.8 angular cone around a primary muon contain at least two additional real muons.Had the additional muons been produced by a subtle failure of our method to evaluate the fake-muon contribution, the resulting δφ distribution of primary muons would have been found consistent with those typical of ordinary QCD processes.• cone around their direction.

FIG. 1 :
FIG.1: Distribution of the azimuthal angle δφ between the two trigger muons for all events.

FIG. 2 :
FIG. 2: The distributions (•) of the azimuthal angle δφ between trigger muons due to (left) b b and (right) cc production are compared to the corresponding heavy flavor simulations (•).Distributions are normalized to unit area.

FIG. 3 :FIG. 4 :
FIG.3: Distribution of the azimuthal angle δφ between the two trigger muons produced by Υ decays (left) and for events (right) in which one primary muon is mimicked by a pion produced by an identified K 0 S decay.The combinatorial background underneath the Υ and K 0 S signals has been removed with a sideband subtraction method.