Measurement of the anomalous like-sign dimuon charge asymmetry with 9 fb of collisions
We present an updated measurement of the anomalous like-sign dimuon charge asymmetry for semi-leptonic -hadron decays in 9.0 fb of collisions recorded with the D0 detector at a center-of-mass energy of TeV at the Fermilab Tevatron collider. We obtain . This result differs by standard deviations from the prediction of the standard model and provides evidence for anomalously large violation in semi-leptonic neutral decay. The dependence of the asymmetry on the muon impact parameter is consistent with the hypothesis that it originates from semi-leptonic -hadron decays.
pacs:13.25.Hw; 14.40.Nd; 11.30.Er
The D0 Collaboration111with visitors from Augustana College, Sioux Falls, SD, USA, The University of Liverpool, Liverpool, UK, SLAC, Menlo Park, CA, USA, University College London, London, UK, Centro de Investigacion en Computacion - IPN, Mexico City, Mexico, ECFM, Universidad Autonoma de Sinaloa, Culiacán, Mexico, and Universität Bern, Bern, Switzerland. Deceased.
We measure the like-sign dimuon charge asymmetry of semi-leptonic decays of hadrons,
in 9.0 fb of collisions recorded with the D0 detector at a center-of-mass energy TeV at the Fermilab Tevatron collider. Here and are the number of events containing two positively charged or two negatively charged muons, respectively, both of which are produced in prompt semi-leptonic -hadron decays. At the Fermilab Tevatron collider, quarks are produced mainly in pairs. Hence, to observe an event with two like-sign muons from semi-leptonic -hadron decay, one of the hadrons must be a or meson that oscillates and decays to a muon of charge opposite of that expected from the original quark charge (). The oscillation ( or ) is described by higher order loop diagrams that are sensitive to hypothetical particles that may not be directly accessible at the Tevatron.
The asymmetry has contributions from the semi-leptonic charge asymmetries and of and mesons Grossman (), respectively:
where is a CP-violating phase, and and are the mass and width differences between the eigenstates of the propagation matrices of the neutral mesons. The coefficients and depend on the mean mixing probability, , and the production rates of and mesons. We use the values of these quantities measured at LEP as averaged by the Heavy Flavor Averaging Group (HFAG) hfag () and obtain
The value of measured by the CDF Collaboration recently cdf-chi0 () is consistent with the LEP value, which supports this choice of parameters. Using the standard model (SM) prediction for and Nierste (), we find
which is negligible compared to present experimental sensitivity. Additional contributions to violation via loop diagrams appear in some extensions of the SM and can result in an asymmetry within experimental reach Randall (); Hewett (); Hou (); Soni (); buras ().
This Article is an update to Ref. PRD () that reported evidence for an anomalous like-sign dimuon charge asymmetry with 6.1 fb of data, at the 3.2 standard deviation level. All notations used here are given in Ref. PRD (). This new measurement is based on a larger dataset and further improvements in the measurement technique. In addition, the asymmetry’s dependence on the muon impact parameter (IP) impact () is studied. The D0 detector is described in Ref. d0-det (). We include a brief overview of the analysis in Sec. II. Improvements made to muon selections are presented in Sec. III; the measurement of all quantities required to determine the asymmetry is described in Secs. IV–X, and the result is given in Sec. XI. Sections XII–XIII present consistency checks of the measurement; Sec. XIV describes the study of the asymmetry’s IP dependence. Conclusions are given in Sec. XV.
The elements of our analysis are described in detail in Ref. PRD (). Here, we summarize briefly the method, emphasizing the improvements to our previous procedure. We use two sets of data: (i) inclusive muon data collected with inclusive muon triggers that provide positively charged muons and negatively charged muons, and (ii) like-sign dimuon data, collected with dimuon triggers that provide events with two positively charged muons and events with two negatively charged muons. If an event contains more than one muon, each muon is included in the inclusive muon sample. Such events constitute about 0.5% of the total inclusive muon sample. If an event contains more than two muons, the two muons with the highest transverse momentum () are selected for inclusion in the dimuon sample. Such events comprise about 0.7% of the total like-sign dimuon sample.
From these data we obtain the inclusive muon charge asymmetry and the like-sign dimuon charge asymmetry , defined as
In addition to a possible signal asymmetry , these asymmetries have contributions from muons produced in kaon and pion decay, or from hadrons that punch through the calorimeter and iron toroids to penetrate the outer muon detector. The charge asymmetry related to muon detection and identification also contributes to and . These contributions are measured with data, with only minimal input from simulation. The largest contribution by far is from kaon decays. Positively charged kaons have smaller cross sections in the detector material than negatively charged kaons pdg (), giving them more time to decay. This difference produces a positive charge asymmetry.
where the fraction of reconstructed muons, , in a given interval in the inclusive muon sample is given in Table 1. The fractions of these muons produced by kaons, pions, and protons in a given interval are , , and , and their charge asymmetries are , , and , respectively. We refer to these muons as “long” or “” muons since they are produced by particles traveling long distances before decaying within the detector material. The track of a muon in the central tracker is dominantly produced by the parent hadron. The charge asymmetry of muons results from the difference in the interactions of positively and negatively charged particles with the detector material, and is not related to CP violation. The background fraction is defined as . The quantity is the fraction of muons from weak decays of and quarks and leptons, and from decays of short-lived mesons (). We refer to these muons as “short” or “” muons, since they arise from the decay of particles at small distances from the interaction point. These particles are not affected by interactions in the detector material, and once muon detection and identification imbalances are removed, the muon charge asymmetry must therefore be produced only through CP violation in the underlying physical processes. The quantity in Eq. (7) is the charge asymmetry related to muon detection and identification. The background charge asymmetries , , and are measured in the inclusive muon data, and include any detector asymmetry. The therefore accounts only for muons and is multiplied by the factor .
The like-sign dimuon charge asymmetry can be expressed PRD () as
The quantity is the charge asymmetry of the events with two like-sign muons. The quantity is the fraction of like-sign dimuon events with two muons, is the fraction of like-sign dimuon events with one and one muon. We also define the quantity as the fraction of like-sign dimuon events with two muons. The quantity is the fraction of muons in the interval in the like-sign dimuon data. The quantities () are defined as , where is the number of muons produced by kaons, pions, and protons, respectively, in a interval , with being the number of muons in this interval, with the factor of two taking into account the normalization of these quantities per like-sign dimuon event. The quantity is a sum over muons produced by hadrons:
We also define as
The estimated contribution from the neglected quadratic terms in Eq. (8) is approximately , which corresponds to about 5% of the statistical uncertainty on .
|Bin||Muon range (GeV)|
Equations (7) – (12) are used to measure the asymmetry . The major contributions to the uncertainties on are from the statistical uncertainty on and the total uncertainty on , and . To reduce the latter contributions, we measure the asymmetry using the asymmetry , which is defined as
Since the same physical processes contribute to both and , their uncertainties are strongly correlated, and therefore partially cancel in Eq. (13) for an appropriate choice of the coefficient . The contribution from the asymmetry , however, does not cancel in Eq. (13) because PRD (). Full details of the measurements of different quantities entering in Eqs. (7) – (12) are given in Ref. PRD (). The main improvements in the present analysis are related to muon selection and the measurement of and . These modifications are described in Sections III, IV and V.
Iii Muon selection
The muon selection is similar to that described in Ref. PRD (). The inclusive muon and like-sign dimuon samples are obtained from data collected with single and dimuon triggers, respectively. Charged particles with transverse momentum in the range GeV and with pseudorapidity rapidity () are considered as muon candidates. The upper limit on is applied to suppress the contribution of muons from and boson decays. To ensure that the muon candidate passes through the detector, including all three layers of the muon system, we require either GeV or a longitudinal momentum component GeV. Muon candidates are selected by matching central tracks with a segment reconstructed in the muon system and by applying tight quality requirements aimed at reducing false matching and background from cosmic rays and beam halo. The transverse impact parameter of the muon track relative to the reconstructed interaction vertex must be smaller than 0.3 cm, with the longitudinal distance from the point of closest approach to this vertex smaller than 0.5 cm. Strict quality requirements are also applied to the tracks and to the reconstructed interaction vertex. The inclusive muon sample contains all muons passing the selection requirements. If an event contains more than one muon, each muon is included in the inclusive muon sample. The like-sign dimuon sample contains all events with at least two muon candidates with the same charge. These two muons are required to have an invariant mass greater than 2.8 GeV to minimize the number of events in which both muons originate from the same quark (e.g., , ). Compared to Ref. PRD (), the following modifications to the muon selection are applied:
To reduce background from a mismatch of tracks in the central detector with segments in the outer muon system, we require that the sign of the curvature of the track measured in the central tracker be the same as in the muon system. This selection was not applied in Ref. PRD (), and removes only about 1% of the dimuon events.
To ensure that the muon candidate can penetrate all three layers of the muon detector, we require either a transverse momentum GeV, or a longitudinal momentum component GeV, instead of GeV or GeV in Ref. PRD (). With this change, the number of like-sign dimuon events increases by 25%, without impacting the condition that the muon must penetrate the calorimeter and toroids, as can be deduced from Fig. 1.
To reduce background from kaon and pion decays in flight, we require that the calculated from the difference between the track parameters measured in the central tracker and in the muon system be (for 4 d.o.f.) instead of 40 used in Ref. PRD (). With this tighter selection, the number of like-sign dimuon events is decreased by 12%.
Compared to the selections applied in Ref. PRD (), the total number of like-sign dimuon events after applying all these modifications is increased by 13% in addition to the increase due to the larger integrated luminosity of this analysis.
The muon charge is determined by the central tracker. The probability of charge mis-measurement is obtained by comparing the charge measured by the central tracker and by the muon system and is found to be less than 0.1%.
The polarities of the toroidal and solenoidal magnetic fields are reversed on average every two weeks so that the four solenoid-toroid polarity combinations are exposed to approximately the same integrated luminosity. This allows for a cancellation of first-order effects related to the instrumental asymmetry D01 (). To ensure such cancellation, the events are weighted according to the number of events for each data sample corresponding to a different configuration of the magnets’ polarities. These weights are given in Table 2. During the data taking of the last part of the sample, corresponding to approximately 2.9 fb of collisions, the magnet polarities were specially chosen to equalize the number of dimuon events with different polarities in the entire sample. The weights in Table 2 are therefore closer to unity compared to those used in Ref. PRD ().
|polarity||polarity||inclusive muon||like-sign dimuon|
Iv Measurement of , ,
The fraction in the inclusive muon sample is measured using decays, with the kaon identified as a muon (see Ref. PRD () for details). The transverse momentum of the meson is required to be in the interval . Since the momentum of a particle is measured by the central tracking detector, a muon produced by a kaon is assigned the momentum of this kaon (a small correction for kaons decaying within the tracker volume is introduced later). The fraction of these decays is converted to the fraction using the relation
where and are the number of reconstructed and decays, respectively. The transverse momentum of the meson is required to be in the interval . We require in addition that one of the pions from the decay be identified as a muon. In the previous analysis PRD () the production of mesons was studied in a sample of events with an additional reconstructed muon, but we did not require that this muon be associated with a pion from decay. The fraction of events containing and/or quarks was therefore enhanced in the sample, which could result in a bias of the measured fraction . This bias does not exceed the systematic uncertainty of and its impact on the value is less than 0.03%. The application of the new requirement ensures that the flavor composition in the selected and samples is the same and this bias is eliminated.
The selection criteria and fitting procedures used to select and determine the number of , and events are given in Ref. PRD (). As an example, Fig. 2 displays the invariant mass distribution and the fitted candidates in the inclusive muon sample, with at least one pion identified as a muon, for GeV. Figure 3 shows the mass distribution and fit to candidates for all candidates with GeV and MeV. Figure 4 shows the mass distribution and the fit result for candidates for all kaons with GeV. The mass distribution contains contributions from light meson resonances decaying to . The most important contribution comes from the decay with . It produces a broad peak in the mass region close to the mass. The distortions in the background distribution due to other light resonances, which are not identified explicitly, can also be seen in Fig. 4. Our background model therefore includes the contribution of and two additional Gaussian terms to take into account the distortions around 1.1 GeV. More details of the background description are given in Ref. PRD ().
The measurement of the fractions and is also performed using the method of Ref. PRD (). The values of and are divided by the factors and , respectively, which take into account the fraction of kaons and pions reconstructed by the tracking system before they decay. These factors are discussed in Ref. PRD (), and are determined through simulation. Contrary to Ref. PRD (), this analysis determines these factors separately for kaons and pions. We find the values:
The uncertainties include contributions from the number of simulated events and from the uncertainties in the momentum spectrum of the generated particles.
The values of , and in different muon bins are shown in Fig. 5 and in Table 3. The changes in the muon candidates selection adopted here is the main source of differences relative to the corresponding values in Ref. PRD (). The fractions and are poorly measured in bins 1 and 2, and bins 5 and 6 due to the small number of events, and their contents are therefore combined through their weighted average.
V Measurement of , ,
The quantity is expressed as
where is the ratio of the fractions of muons produced by kaons in like-sign dimuon and in inclusive muon data. For the interval , is defined as
where and are the number of reconstructed mesons identified as muons in the like-sign dimuon and in the inclusive muon samples, respectively. The transverse momentum of the meson is required to be in the interval . The quantities and are the number of muons in the interval . A multiplicative factor of two is included in Eq. (17) because there are two muons in a like-sign dimuon event, and is normalized to the number of like-sign dimuon events.
In the previous analysis PRD (), the quantity was obtained from a measurement of the production rate. Presenting it in the form of Eq. (16) also allows the determination of through an independent measurement of the fraction of mesons in dimuon and in inclusive muon data where one of the pions from decay is identified as a muon. This measurement is discussed below. In addition, Eq. (16) offers an explicit separation of systematic uncertainties associated with . The systematic uncertainty on the fraction affects the two determinations of based on Eqs. (7) and (8) in a fully correlated way; therefore, its impact on the measurement obtained using Eq. (13) is significantly reduced. The systematic uncertainty on the ratio does not cancel in Eq. (13). It is estimated directly from a comparison of the values of obtained in two independent channels.
One way to measure is from the fraction of events in the inclusive muon and like-sign dimuon data,
where and are the number of reconstructed decays, with the kaon identified as a muon in the like-sign dimuon and in the inclusive muon samples, respectively. The transverse momentum of the meson is required to be in the interval . The measurement using Eq. (18) is based on the assumption
which was validated through simulations in Ref. PRD (). The corresponding systematic uncertainty is discussed below.
In Ref. PRD (), the fractions and were obtained independently from a fit of the invariant mass distribution in the like-sign dimuon and inclusive muon sample, respectively. Figure 6 shows the same mass studies as in Fig. 4, but for the like-sign dimuon sample. The fit in both cases is complicated by the contribution from light meson resonances that decay to , producing a reflection in the invariant mass distribution. In addition, the detector resolution is not known a priori and has to be included in the fit. All these complications are reduced significantly or eliminated in the “null-fit” method introduced in Ref. PRD (), which is used in this analysis to measure the ratio .
In this method, for each interval , we define a set of distributions that depend on a parameter :
where and are the number of entries in the bin of the invariant mass distributions in the like-sign dimuon and inclusive muon samples, respectively. For each value of the number of decays, , and its uncertainty, , are measured from the distribution. The value of for which defines . The uncertainty is determined from the condition that corresponding to .
The advantage of this method is that the influence of the detector resolution becomes minimal for close to zero, and the contribution from the peaking background is reduced in to the same extent as the contribution of mesons, and becomes negligible when is close to zero. As an example, Fig. 7 shows the mass distribution for , for all kaons with GeV. This distribution is obtained from the distributions shown in Figs. 4 and 6, using Eq. (20). The contributions of both and , as well as any other resonance in the background, disappear. As a result, the fitting procedure becomes more robust, the fitting range can be extended, and the resulting value of becomes stable under a variation of the fitting parameters over a wider range.
The value of is also obtained from the production rate of mesons in the inclusive muon and dimuon samples. We compute for a given interval , as
where and are the number of reconstructed decays with one pion identified as a muon in the dimuon and the inclusive muon data, respectively. The correction factor is discussed later in this section. The measurement of using Eq. (21) assumes isospin invariance and consequent equality of the ratio of production rates in the dimuon and in the inclusive muon samples of and mesons, i.e.,
Since the charged kaon in Eq. (22) is required to be within the interval , the transverse momentum of the meson in Eq. (21) is also required to be within the interval . We expect approximately the same number of positive and negative pions from decays to be identified as a muon. Therefore, we use both like-sign and opposite-sign dimuon events to measure and we do not use the multiplicative factor of two in Eq. (21). The requirement of having one pion identified as a muon makes the flavor composition in the samples of charged events and events similar.
The charges of the kaon and the additional muon in a dimuon event can be correlated, i.e., in general . However, the number of events is not correlated with the charge of the additional muon, i.e., . Since the ratio is determined for the sample of like-sign dimuon events, we apply in Eq. (21) the correction factor , defined as
to take into account the correlation between the charges of the kaon and muon. The abbreviation “c.c.” in Eq. (23) denotes “charge conjugate states”. The coefficients are measured in data using the events with a reconstructed decay and an additional muon. To reproduce the selection for the dimuon sample PRD (), the invariant mass of the system, with the kaon assigned the mass of a muon, is required to be greater than 2.8 GeV. The fitting procedure and selection criteria to measure the number of events are described in Ref. PRD (). The values of for different intervals are given in Fig. 8 and in Table 4.
The average muon detection efficiency is different for the inclusive muon and like-sign dimuon samples because of different thresholds used in their triggers. The difference in muon detection efficiency is large for muons with small , but it is insignificant for muons above the inclusive-muon trigger threshold. The ratio in Eq. (21) is measured as a function of the transverse momenta of mesons, , while the ratio is measured in bins of muon . Each bin contains with different values. The muon detection efficiency therefore does not cancel in Eq. (21), and can affect the measurement of . Figure 9 shows the ratio of detection efficiencies in the inclusive muon and dimuon data. To compute this ratio, we select the mesons in a given interval. The distribution of pions produced in the decay with a given is the same in the dimuon and inclusive muon data. Therefore, any difference in this distribution between dimuon and inclusive muon data is due to the detection. We compute the ratio of these distributions, and normalize it such that it equals unity for GeV. The value of this threshold corresponds to the threshold for single muon triggers. Figure 9 presents the average of the ratios for different intervals. The ratio is suppressed for GeV, and is consistent with a constant for GeV. To remove the bias due to the trigger threshold, we measure for events with GeV. As a result, the ratio is not defined for the first two bins in the channel.
The values of obtained through the null-fit method, for different muon bins, are shown in Fig. 10(a) and in Table 5. The values of are contained in Fig. 10(b) and in Table 5. The difference between the values of measured with mesons and with mesons is shown in Fig. 11. The mean value of this difference is
and the /d.o.f. is 1.7/4. We use two independent methods, each relying on different assumptions, to measure the ratio and obtain results that are consistent with each other. The methods are subject to different systematic uncertainties, and therefore provide an important cross-check. As an independent cross-check, the value of obtained in simulation is consistent with that measured in data, see Sec. XIII for details. We take the average of the two channels weighted by their uncertainties as our final values of for GeV and use the values measured in the channel for GeV. These values are given in Table 5 and in Fig. 10(c). As we do not observe any difference between the two measurements, we take half of the uncertainty of as the systematic uncertainty of . This corresponds to a relative uncertainty of 3.0% on the value of . In our previous measurement PRD (), this uncertainty was 3.6%, and was based on simulation of the events.
Using the extracted values of , we derive the values of , and . The computation of is done using Eq. (16), and we follow the procedure described in Ref. PRD () to determine and . The results are shown in Fig. 12 and in Table 6. The fractions and are poorly determined for the lowest and highest because of the small number of events. The content of bins 1 and 2, and bins 5 and 6 are therefore combined.
Vi Systematic uncertainties for background fractions
The systematic uncertainties for the background fractions are discussed in Ref. PRD (), and we only summarize the values used in this analysis. The systematic uncertainty on the fraction is set to 9% PRD (). The systematic uncertainty on the ratio , as indicated in Sec. V, is set to half of the uncertainty on given in Eq. (24). The systematic uncertainties on the ratios of multiplicities and in interactions are set to 4% notation (). These multiplicities are required to compute the quantities , . The ratios and , required to compute the quantities and PRD () are assigned an additional 4% systematic uncertainty. The values of these uncertainties are discussed in Ref. PRD ().
Vii Measurement of ,
We determine the fraction of muons in the inclusive muon sample and the fraction of events with two muons in the like-sign dimuon sample following the procedure described in Ref. PRD (). We use the following value from simulation