Evidence for Z ± c ( 3900 ) in semi-inclusive decays of b-flavored hadrons

We present evidence for the exotic charged charmoniumlike state Zc±(3900) decaying to J/ψπ± in semi-inclusive weak decays of b-flavored hadrons. The signal is correlated with a parent J/ψπ+π- system in the invariant-mass range 4.2-4.7 GeV that would include the exotic structure Y(4260). The study is based on 10.4 fb-1 of pp collision data collected by the D0 experiment at the Fermilab Tevatron collider. © 2018 authors. Published by the American Physical Society.


I. INTRODUCTION
The charged charmoniumlike state Z AE c ð3900Þ was discovered in 2013 simultaneously by the Belle [1] and BESIII [2] collaborations in the sequential process e þ e − → Yð4260Þ, Yð4260Þ → Z þ c ð3900Þπ − , Z þ c ð3900Þ → J=ψπ þ (charge conjugate processes are implied throughout). Their fits of the Z þ c ð3900Þ signal with an S-wave Breit-Wigner signal shape and an incoherent background gave the signal parameters m ¼ 3894.5 AE 6.6 AE 4.5 MeV, Γ ¼ 63 AE 34 AE 26 MeV and m ¼ 3899.0 AE 3.6 AE 4.9 MeV, Γ ¼ 46 AE 10 AE 20 MeV, respectively. The Z þ c ð3900Þ cannot be a conventional quark-antiquark meson as it is charged and decays via the strong interaction to charmonium. Its minimal quark content is thus ccud.
Since the original observation, the understanding of both the Z þ c ð3900Þ and Yð4260Þ has evolved. The BESIII Collaboration has measured [3] the e þ e − → J=ψπ þ π − cross section at a range of energies from 3.77 to 4.60 GeV and reported that the Yð4260Þ may consist of two states: a narrow state at about 4.22 GeVand a wider one at about 4.32 GeV above a continuum that may also be * Deceased. consistent with a broad resonance near 4.0 GeV. Currently, the "Yð4260Þ" is believed to be composed of two states: a lower-mass narrower state denoted by the Particle Data Group (PDG) [4] as ψð4260Þ with mass m ¼ 4230 AE 8 MeV and width Γ ¼ 55 AE 19 MeV and a higher-mass broader state ψð4360Þ with m ¼ 4368 AE 13 MeV and The Z þ c ð3900Þ is close in mass to Xð3872Þ and also close to the open-charm D ÃD threshold, so it may be a "molecular" state composed of a loosely bound pair of colorless, quark-antiquark pairs containing a charm and a light quark ðcdÞ and ðcuÞ, the isovector analog of the Xð3872Þ. A mass enhancement is also seen in the D ÃD system [5], but the fit for this channel gives a different mass and width compared to that for the J=ψπ þ channel.
The PDG [4] assumes that it is a single resonance decaying to two final states. It lists it as Z c ð3900Þ with m ¼ 3886.6 AE 2.4 MeV and Γ ¼ 28.2 AE 2.6 MeV. The spin and parity are determined to be [6] The presence of Z þ c ð3900Þ in decays of b hadrons is unclear. It is not seen by Belle [7] in the decayB 0 → ðJ=ψπ þ ÞK − nor by LHCb [8] in the decay B 0 → ðJ=ψπ þ Þπ − . On the other hand, the Yð4260Þ may have been seen in the decays B → J=ψππK by BABAR [9], so there could be production of Z þ c ð3900Þ in b-hadron decays through the two-step process H b → Yð4260Þþ anything, Yð4260Þ → Z þ c ð3900Þπ − , where H b represents any hadron containing a b quark. The process may be spread over many channels and thus escape observation in any specific channel.
In this article, we look for the presence of such two-step processes using 10.4 fb −1 of pp collision data collected by the D0 experiment at the Fermilab Tevatron collider.

II. D0 DETECTOR, EVENT RECONSTRUCTION, AND SELECTION
The D0 detector [10] has a central tracking system consisting of a silicon microstrip tracker [11] and a central scintillating fiber tracker, both located within a 1.9 T superconducting solenoidal magnet. A muon system [12] covering pseudorapidity jη det j < 2 [13] is located outside of the central tracking system and the liquid argon calorimeter and consists of a layer of tracking detectors and scintillation trigger counters in front of 1.8 T toroidal magnets, followed by two similar layers after the toroids.
In high-energy pp collisions, the J=ψ can be produced both promptly, either directly or in strong-interaction decays of higher-mass charmonium states, and nonpromptly in weak-interaction b-hadron decays [14][15][16]. The b andb quarks are produced in pairs and fragment into the b-hadron species B þ , B 0 d , B s , b baryons, and B c with the relative branching fractions 0.34, 0.34, 0.10, 0.22, and < 0.01, respectively [4]. Nonprompt J=ψ mesons from H b decays are displaced from the pp interaction vertex by typically several hundred μm as a result of the long b-quark lifetime.
Events used in this analysis are collected with both single-muon and dimuon triggers. We reuse a sample of events, prepared for an earlier study of b-hadron decays, containing a nonprompt J=ψ and a pair of oppositely charged particles consistent with coming from a displaced decay vertex. For this previously used data sample, the event selection requirement that the decay vertex be separated from the primary vertex with a significance of more than 3σ precludes extension of the current study to include the prompt production of Z þ c ð3900Þ and Yð4260Þ. Unless indicated otherwise, we assume the hadrons to be pions and select events in the mass range 4.1 < mðJ=ψπ þ π − Þ < 5.0 GeV that includes the Yð4260Þ states and is high enough for production of the Z þ c ð3900Þ but low enough to exclude fully reconstructed direct decays of b hadrons to final states J=ψh þ h − , where h stands for a pion, a kaon, or a proton. In this study of an inclusive final state, we apply more stringent requirements on the decay-lengthrelated parameters to further suppress combinations where one of the selected particles is produced by the hadronization of partons associated with the primary vertex.
Candidate events are selected by requiring a pair of oppositely charged muons and a charged particle with p T above 1 GeVat a common vertex with χ 2 < 10 for 3 degrees of freedom. Muons must have transverse momentum p T > 1.5 GeV. At least one muon must traverse both inner and outer layers of the muon detector. Both muons must match tracks in the central tracking system. The reconstructed invariant mass mðμ þ μ − Þ must be between 2.92 and 3.25 GeV, consistent with the world-average mass of the J=ψ [4]. To select final states originating from b-hadron decays, the J=ψ þ 1 track vertex is required to be displaced from the pp interaction vertex in the transverse plane by at least 5σ, and the transverse impact parameter [17] significance IP=σðIPÞ of the hadronic track is required to be greater than 2σ.
For accepted J=ψ þ 1 track combinations, another track, with a charge opposite to the first track and with p T > 0.8 GeV, is added to form a common J=ψ þ 2 tracks system. The second track must have an IP significance greater than 1σ, and its contribution to the χ 2 of the J=ψ þ 2 tracks vertex [18] must be less than 6. The cosine of the angle in the transverse plane between the momentum vector and decay path of the J=ψ þ 2 tracks system is required to be greater than 0.9.
For the accepted J=ψ þ 2 tracks combinations, we calculate the J=ψπ þ π − invariant mass by assigning the pion mass to both hadronic tracks. We correct the muon momenta by constraining mðμ þ μ − Þ to the world-average J=ψ meson mass [4]. The sample includes events in which the hadronic pair comes from decays K Ã → Kπ or ϕ → KK. We remove such events by vetoing the mass combinations 0.81 < mðπKÞ < 0.97 GeV, 0.81 <mðKπÞ < 0.97 GeV, and 1.01 <mðKKÞ < 1.03 GeV. We also veto photon conversions by removing events with mðπ þ π − Þ < 0.35 GeV. The K Ã veto rejects about 20% of the phase space while reducing the background by about a factor of 2. The combination of the three vetoes reduces the background by a factor of about 2.5. Multiple candidates per event are allowed, but their rate is negligible.
The transverse decay length distribution of the J=ψπ þ π − system L xy is shown in Fig. 1. With the average resolution of 0.0057 cm, most of the prompt events would be contained at L xy < 0.025 cm. The distribution confirms that prompt background has been strongly suppressed and that the selected J=ψ þ 2 tracks combinations originate predominantly from partially reconstructed vertices of bhadron decays.

III. FIT RESULTS
Our study is focused on the J=ψπ þ system around the Z þ c ð3900Þ mass. As mentioned above, the production of Z þ c ð3900Þ may occur through a sequential process with an intermediate To test this possibility, we select events in the mass range 4.1 <mðJ=ψπ þ π − Þ < 5.0 GeV. We construct the mass mðJ=ψπ þ Þ by combining the J=ψ with either of the two pion candidates and, following Refs. [1,2], selecting the higher-mass combination. We fit the resulting mðJ=ψπ þ Þ distribution to the sum of a resonant signal represented by a relativistic S-wave Breit-Wigner function with a width fixed to Γ ¼ 28.2 MeV [4] smeared with the D0 mass resolution of σ ¼ 17 AE 2 MeV and a mass that is allowed to vary freely and an incoherent background. Background is mainly due to b-hadron decays to a J=ψ, with a random hadron coming from the same multibody decay. For the background shape, we use Chebyshev polynomials of the first kind. The fitting range is chosen so as to obtain an acceptable fit while avoiding regions where the background function becomes negative.
We perform binned maximum-likelihood fits to the J=ψπ þ mass distribution in six J=ψπ þ π − mass intervals of varying size, chosen to align with the Yð4260Þ states. These intervals, (4.1-4.2), (4.2-4.25), (4.25-4.3), (4.3-4.4), (4.4-4.7), and (4.7-5.0) GeV, contain roughly equal numbers of signal plus background events. In each interval, we represent the background contribution by a Chebyshev polynomial of which the order is chosen to minimize the Aikake Information Criterion (AIC) [19]. For a fit with p free parameters to a distribution in n bins, the AIC is defined as We use fourthorder polynomials in all bins except (4.7-5.0) GeV, where we use a fifth-order polynomial.
As shown in Fig. 2, we see a clear enhancement near the Z þ c ð3900Þ mass for events in the range 4.20 < mðJ=ψπ þ π − Þ < 4.25 GeV, consistent with coming from the ψð4260Þ (recall that the ψð4260Þ mass is 4230 AE 8 MeV [4]), and smaller but finite Z þ C ð3900Þ signals for mðJ=ψπ þ π − Þ ranges between 4.2 and 4.7 GeV. We find no significant signal in the bins 4.1 <mðJ=ψπ þ π − Þ < 4.2 GeV or 4.7 <mðJ=ψπ þ π − Þ < 5.0 GeV. The resulting differential distribution of the signal yield is shown in Fig. 3. We note the presence of a Z þ c ð3900Þ signal with a statistical significance greater than 3σ in the 4.4 < mðJ=ψπ þ π − Þ < 4.7 GeV region above the ψð4360Þ signal [3], indicating some contribution from a non-Yð4260Þ J=ψπ þ π − combination. The measured signal masses are consistent with each other (with a p-value of 0.1).
We then perform a fit to the data in the mass range 4.2 <mðJ=ψπ þ π − Þ < 4.7 GeV. The AIC test gives similar results using the fifth-and fourth-order polynomials as background, while the χ 2 test prefers the fifth-order polynomial (p-value of 0.18 vs 0.066). The fit using the fifth-order polynomial background shown in Fig. 4 yields N ¼ 502 AE 92ðstatÞ signal events, m ¼ 3895.0 AE 5.2ðstatÞ MeV, and a statistical significance of S ¼ 5.6σ. The fit using the fourth-order polynomial gives N ¼608AE82, m¼3895.7AE 4.6MeV, and S ¼ 7.7σ. The statistical significance of the signal is defined as where L max and L 0 are likelihood values for the best-fit signal yield and for the signal yield fixed to zero. In the following, we choose the fit using the fifth-order polynomial as the baseline. A χ 2 test of the fit quality gives the χ 2 over the number of degrees of freedom (ndf) χ 2 =ndf ¼ 36.8=30.

IV. CROSS-CHECKS
In an alternative approach, we perform a simultaneous fit to the four subsamples of the mðJ=ψπ þ π − Þ in the 4.2-4.7 GeV range, allowing for separate free parameters of the fourth-order Chebyshev polynomial background and free signal yields but using a common free signal mass parameter. The fitted mass is 3889.6 AE 9.8 MeV, and the Fits to the three Z þ c ð3900Þ pseudorapidity ranges jηj < 0.9, 0.9 < jηj < 1. To test the sensitivity of the results to the fit quality requirements, we define a control sample by selecting events with the fit quality of the J=ψ þ 1 track vertex in the range 10 < χ 2 < 20. The fitted yield in the control sample is 10 AE 25 events, consistent with no signal.
Due to the limited muon momentum resolution, our selection of the J=ψ mass window passes some non-J=ψ     dimuons while rejecting a fraction of genuine J=ψ's. The non-J=ψ background includes sequential decays b → cμX, c → sμX, and semileptonic b-hadron decays accompanied by a muon track originating from a charged pion or kaon decay in flight. We estimate the fraction of non-J=ψ background in our baseline sample at 9% and the dimuon mass cut efficiency for J=ψ at 94%. A fit to the mðJ=ψπ þ Þ spectrum when the J=ψ mass window is expanded to 2.8-3.4 GeV yields 530 AE 100 Z þ c ð3900Þ signal events, 6% more than in the baseline analysis, in agreement with expectation.

V. SYSTEMATIC UNCERTAINTIES
There are several sources of systematic uncertainties in the baseline measurement of the Z þ c ð3900Þ mass and yield, summarized in Table I. We assign an asymmetric uncertainty of ðþ3; −0Þ MeV to the J=ψπ þ mass scale based on studies of the D0 measured mass shift compared to world-average values in several final states with a similar topology [20].
The estimate of the mass resolution is based on the dependence of the measured and simulated resolution of the released kinetic energy for decays with a similar topology. The variation of the assumed resolution by its uncertainty of AE2 MeV has a negligible effect on the measured Z þ c ð3900Þ mass. We assign an uncertainty on the signal yield equal to half of the difference between the two extreme results.
We assess the effects of the fitting procedure and background shape as half of the difference of the results obtained with the fourth-and fifth-order Chebyshev polynomials. Similarly, we estimate the effect of bin size by comparing the results for 20 and 10 MeV bins.
We assign the uncertainty in the signal model as half of the difference in the results obtained with the relativistic Breit-Wigner shapes with and without the energy dependence of the natural width.
In the analysis, we set the natural width equal to the world-average value. We assign the uncertainty in the mass and yield measurement by repeating the fits with the width altered by AE2.6 MeV [4].

VI. RESULTS
A. Z c ð3900Þ signal yield as a function of mðJ=ψπ + π − Þ Table II lists the Z þ c ð3900Þ fitted signal yields and the measured mass in the six nonoverlapping intervals of the J=ψπ þ π − invariant mass between 4.1 and 5.0 GeV. The Z þ c ð3900Þ width is fixed at Γ ¼ 28.2 MeV for these fits. The measured masses are consistent with each other and with the original results of Refs. [1,2], and thus we conclude that we are observing the same Z þ c ð3900Þ state. We report the results for the range 4.2-4.7 GeV as our best measurement of the mass of the Z þ c ð3900Þ resonance and the signal significance.
Our baseline result above allows the Z þ c ð3900Þ mass to float but fixes its width at the world-average value and thus raises the question of whether the significance of the fit would change if the world-average [4] mass were used. We   The systematic uncertainties are taken into account in the estimate of the significance by convolving the p-value as a function of signal yield with a Gaussian function with a mean corresponding to our measured value and width equal to the systematic uncertainty on the yield. Adding the systematic uncertainty changes the significance for the baseline fit from 5.6σ to 4.6σ.
B. Normalization to B 0 d → J=ψK Ã We normalize the Z þ c ð3900Þ → J=ψπ þ signal in the parent J=ψπ þ π − mass range of 4. 2-4.7 GeV to the number of events of the decay B 0 d → J=ψK Ã . The latter are required to satisfy the same stringent kinematic and quality cuts as applied to the J=ψπ þ π − except that the K Ã veto is replaced with the requirement that at least one K AE π ∓ pair be within the K Ã mass window. If two such pairs are present, we select the K AE π ∓ combination with mass closer to the K Ã mass. We fit the distribution to a sum of a signal described by a double Gaussian function and a quadratic polynomial background. We find the number of B 0 d decays NðB 0 d Þ¼ 5900 AE 116 ðstatÞ and obtain the ratio of the observed number of events 502=5900 ¼ 0.085 AE 0.019 where the uncertainty is a sum in quadrature of the statistical and systematic uncertainties (0.016 and 0.011, respectively). Since the two processes have the same topology and the kinematic restrictions assure a uniform track finding efficiency, we assume that the efficiency factors cancel out in the ratio. The invariant-mass J=ψKπ distribution and the fit results are shown in Fig. 5. Figure 6 shows a comparison of the decay length distribution of the Z þ c ð3900Þ signal events, obtained by fitting mðJ=ψπ þ Þ in bins of the decay length, and that of the B 0 d signal from the B 0 d → J=ψK Ã decay. The mean TABLE II. Z þ c ð3900Þ signal yields and mass measurements, fit quality, and statistical significance S in intervals of mðJ=ψπ þ π − Þ. The six measurements in nonoverlapping subsamples are dominated by statistical uncertainties. There is a common asymmetric þ3, −0 MeV mass uncertainty. The last row shows a summary result that includes statistical and systematic uncertainties. lifetime of a b-hadron admixture averaged over all b species is similar to the B 0 d lifetime, and the momentum distributions are similar. We therefore expect the decay length distribution of the two states to show general agreement. The distributions show exponential behavior N ∼ e −L xy =Λ in the region above L xy ¼ 0.025 cm where the efficiency is constant, with consistent coefficients of Λ ¼ 0.098 AE 0.030 and 0.130 AE 0.004 cm for the Z þ c ð3900Þ and B 0 d , respectively, supporting the claim that the signal events come from b-hadron decays. The turnover at low L xy occurs because some events of which the L xy resolution is small can pass the 5σ significance cut for lower values of L xy . Figure 7 compares the p T distribution of the J=ψπ þ π − system in Z þ c ð3900Þ events and the p T distribution of B 0 d in the J=ψK Ã channel. The two distributions are similar, as expected for decay products of b hadrons. The average p T of the former (12.5 GeV) is lower than the average p T of B 0 d (13.6 GeV) because the J=ψπ þ π − system carries less than 100% of the parent b-hadron's momentum.
C. Search for the Z + c ð3900Þ in the decayB 0 d → J=ψπ + K − As mentioned in Sec. I, the Belle Collaboration [7] did not see a significant signal of the Z þ c ð3900Þ in the decaȳ B 0 → J=ψπ þ K − . Their amplitude analysis confirmed the Z c ð4430Þ and led to an observation of a new resonance, Z c ð4200Þ. We have studied the J=ψπ þ mass in events consistent with this decay, excluding the events consistent with the decayB 0 d → J=ψK Ã .F i g u r e8(a) shows the scatter plot of mðJ=ψπ þ Þ vs mðJ=ψπ þ K − Þ. There is no indication of the Z þ c ð3900Þ, and the spectrum of mðJ=ψπ þ Þ above 4 GeV is consistent with the resonance structures observed in Fig. 8 of Ref. [7].F i g u r e8(b) shows the mðJ=ψπ þ Þ distribution in a limited range and a fit allowing for a Z þ c ð3900Þ signal and a quadratic background. The fit gives an upper limit of 90 signal events at 90% C.L. Normalizing to the 5900 events of the B 0 d → J=ψK Ã decay, we obtain an upper limit on the ratio of the two processes of 0.015, to be compared to a limit of 0.0011 obtained by Belle.

VII. SUMMARY AND CONCLUSIONS
In summary, our study of the semi-inclusive decays of b hadrons H b → J=ψπ þ π − þ anything reveals a Z AE c ð3900Þ signal that is correlated with the J=ψπ þ π − system in the invariant-mass range 4.2-4.7 GeV that would include the neutral charmoniumlike states ψð4260Þ and ψð4360Þ [4]. There is an indication that some events arise from H b decays to an intermediate J=ψπ þ π − combination with mass above that of the ψð4360Þ, with subsequent decay to Z AE c ð3900Þπ ∓ .  The measured mass of the Z AE c ð3900Þ resonance is m ¼ 3895.0 AE 5.2ðstatÞ þ4.0 −2.7 ðsystÞ MeV. The significance, including systematic uncertainties, is 4.6 standard deviations. We confirm the conclusion of Ref. [7] that there is no significant production of the Z þ c ð3900Þ in the decaȳ B 0 d → J=ψπ þ K − . We set an upper limit on the rate of the process B 0 d → Z þ c ð3900ÞK − relative to B 0 d → J=ψK Ã at 0.015 at the 90% C.L. With the present data sample, we have no sensitivity to prompt production of the Z AE c ð3900Þ in pp collisions.