Observation of the B 0 s → X ð 3872 Þ ϕ Decay

Using a data sample of proton-proton collisions at ﬃﬃﬃ s p ¼ 13 TeV, corresponding to an integrated luminosity of 140 fb − 1 collected by the CMS experiment in 2016 – 2018, the B 0 s → X ð 3872 Þ ϕ decay is observed. Decays into J= ψπ þ π − and K þ K − are used to reconstruct, respectively, the X ð 3872 Þ and ϕ . The ratio of the product of branching fractions B ½ B 0 s → X ð 3872 Þ ϕ (cid:2) B ½ X ð 3872 Þ → J= ψπ þ π − (cid:2) to the product B ½ B 0 s → ψ ð 2 S Þ ϕ (cid:2) B ½ ψ ð 2 S Þ → J= ψπ þ π − (cid:2) is measured to be ½ 2 . 21 (cid:3) 0 . 29 ð stat Þ (cid:3) 0 . 17 ð syst Þ(cid:2) % . The ratio B ½ B 0 s → X ð 3872 Þ ϕ (cid:2) = B ½ B 0 → X ð 3872 Þ K 0 (cid:2) is found to be consistent with one, while the ratio B ½ B 0 s → X ð 3872 Þ ϕ (cid:2) = B ½ B þ → X ð 3872 Þ K þ (cid:2) is two times smaller. This suggests a difference in the production dynamics of the X ð 3872 Þ in B 0 and B 0 s meson decays compared to B þ . The reported observation may shed new light on the nature of the X ð 3872 Þ particle. 10.1103/PhysRevLett.125.152001

Using a data sample of proton-proton collisions at ffiffi ffi s p ¼ 13 TeV, corresponding to an integrated luminosity of 140 fb −1 collected by the CMS experiment in 2016-2018, the B 0 s → Xð3872Þϕ decay is observed. Decays into J=ψπ þ π − and K þ K − are used to reconstruct, respectively, the Xð3872Þ and ϕ. The ratio of the product of branching fractions B½B 0 s → Xð3872ÞϕB½Xð3872Þ → J=ψπ þ π − to the product B½B 0 s → ψð2SÞϕB½ψð2SÞ → J=ψπ þ π − is measured to be ½2.21 AE 0.29ðstatÞ AE 0.17ðsystÞ%. The ratio B½B 0 s → Xð3872Þϕ=B½B 0 → Xð3872ÞK 0 is found to be consistent with one, while the ratio B½B 0 s → Xð3872Þϕ=B½B þ → Xð3872ÞK þ is two times smaller. This suggests a difference in the production dynamics of the Xð3872Þ in B 0 and B 0 s meson decays compared to B þ . The reported observation may shed new light on the nature of the Xð3872Þ particle. DOI: 10.1103/PhysRevLett.125.152001 The observed spectrum of cc states below the DD threshold agrees well with theoretical predictions [1,2]. Since the advent of the BABAR and Belle experiments at the B factories and their discovery of several charmonium-like states, the conventional charmonium model above the DD threshold has become the subject of intense discussions. In 2003, the Belle Collaboration observed a new particle in the B þ → J=ψπ þ π − K þ decay [3] named Xð3872Þ and decaying to J=ψπ þ π − , with a very small natural width for a state above the DD threshold. Its world-average mass is 3871.69 AE 0.17 MeV, which is extremely close to thē D 0 D Ã0 threshold of 3872.68 AE 0.07 MeV [4]. With this mass and a total width less than 2 MeV [5,6], the Xð3872Þ particle did not match any of the theoretically predicted charmonium resonances.
The discovery of Xð3872Þ opened a new era of exotic, quarkonium-like spectroscopy. Many new states with unusual properties have been observed, including several charged states [4,7]. At hadron colliders, prompt processes were found to be the dominant Xð3872Þ production mechanism [8][9][10]. The nature of Xð3872Þ, also known as χ c1 ð3872Þ, is still unexplained in spite of the determination of its quantum numbers (J PC ¼ 1 þþ ) [11][12][13]. The studies of the dipion mass spectrum [5,[9][10][11][12][13][14] clearly favor the presence of the intermediate ρ 0 ð770Þ state in the isospin violating Xð3872Þ → J=ψπ þ π − decay. Important information about the Xð3872Þ production in weak decays can be extracted by comparing the branching fractions B½B → Xð3872Þh for different B mesons, where h denotes a light hadron. More measurements of b hadron decays involving Xð3872Þ production would provide important inputs for understanding its internal structure and creation dynamics.
This Letter reports the first observation of the B 0 s → Xð3872Þϕ decay, where Xð3872Þ → J=ψπ þ π − and ϕ → K þ K − decays are used to reconstruct the intermediate resonances, and the measurement of the following ratio of branching fractions: In this expression, N stands for the measured number of signal events in data, and ϵ stands for the efficiency. The J=ψ and ϕð1020Þ (referred to as ϕ throughout the Letter) mesons are reconstructed in the μ þ μ − and K þ K − channels, respectively. The normalization is done via the B 0 s → ψð2SÞϕ decay, with a subsequent ψð2SÞ → J=ψπ þ π − decay. The similarity of the decay topology of the signal and normalization channels results in nearly identical kinematics, leading to the cancellation of many systematic uncertainties in the ratio.
The central feature of the CMS apparatus [15] is a superconducting solenoid of 6 m internal diameter, providing a magnetic field of 3.8 T. Within the solenoid volume are a silicon pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter, and a brass and scintillator hadron calorimeter. Muons are detected in gas-ionization chambers embedded in the steel flux-return yoke outside the solenoid. The analysis uses proton-proton (pp) collision data recorded by the CMS detector during the LHC Run 2 in 2016-2018 at ffiffi ffi s p ¼ 13 TeV, corresponding to an integrated luminosity of 140 fb −1 . Events of interest are selected using a two-tiered trigger system [16]. The first level (L1), composed of custom hardware processors, uses information from the calorimeters and muon detectors to select events at a rate of around 100 kHz within a time interval of less than 4 μs. The L1 trigger used in the analysis requires at least two muons. The second level, known as the high-level trigger, consists of a farm of processors running a version of the full event reconstruction software optimized for fast processing that reduces the event rate to around 1 kHz before data storage. The highlevel trigger algorithm used in the analysis requires two opposite-sign (OS) muons compatible with the dimuon decay of a J=ψ meson at a significant distance from the beam axis, as well as an additional track with transverse momentum p T > 1.2 GeV, compatible with being produced in the dimuon vertex. Simulated event samples for the B 0 s → Xð3872Þϕ and B 0 s → ψð2SÞϕ decays are generated in the analysis. The PYTHIA 8.230 package [17] is used to simulate the production of the B 0 s mesons, which are subsequently decayed with EVTGEN 1.6.0 [18], where the final-state photon radiation is included using PHOTOS 3.61 [19,20]. Generated events are then passed to a detailed GEANT4based simulation [21] of the CMS detector, followed by the same trigger and reconstruction algorithms as used for the collision data. The simulation includes effects from multiple pp interactions in the same or nearby bunch crossings (pileup) with the multiplicity distribution tuned to match the data.
The event selection begins by requiring two OS muons with p T > 4 GeV passing the soft-muon identification criteria [22] and matching those that triggered the event readout. The dimuon mass is required to be compatible with the world-average J=ψ mass [4], m PDG J=ψ . The B 0 s → J=ψK þ K − π þ π − candidates are obtained by combining the selected J=ψ candidate with four high-purity tracks [23] with a total charge of zero that are not matched with the selected muons. At least one of the four tracks is required to have p T > 1.2 GeV and a transverse impact parameter significance greater than 2 to match the trigger requirement. A kinematic vertex fit that constrains the dimuon invariant mass to m PDG J=ψ is performed on the two muons and four tracks. From all reconstructed pp collision vertices, the primary vertex is chosen as the one with the smallest pointing angle, as done in Refs. [24][25][26][27][28][29]. The pointing angle is the angle between the B 0 s candidate momentum and the vector joining the primary vertex and the reconstructed B 0 s candidate decay vertex. Signal events are eventually selected based on the corrected invariant mass mðB 0 are the world-average ψð2SÞ and Xð3872Þ masses, respectively. This approach ensures the independence between the reconstructed B 0 s and J=ψπ þ π − masses and improves the B 0 s mass resolution.
To select the B 0 s → J=ψK þ K − π þ π − candidates, one must choose which two OS tracks are from kaons, with the other two tracks then being associated with pions. Since the decays of interest have narrow intermediate states ϕ → K þ K − and either ψð2SÞ or Xð3872Þ → J=ψπ þ π − , the following criteria are used to assign the tracks for the selected J=ψK þ K − π þ π − candidates: GeV (iv) if more than one of the mass assignments passes the three selections above, the candidate is discarded.
The selected mass windows are wide enough to allow fits to the mass distributions, while maintaining a selection efficiency above 99%.
The selection criteria are optimized using the Punzi figure of merit [30], which does not rely on the signal normalization. Data sidebands are used to estimate the background, and the B 0 s → Xð3872Þϕ simulated sample is used to measure the signal efficiency. The resulting selection criteria are as follows: 2 GeV, and the decay length of the B 0 s candidate in the transverse plane L xy ðB 0 s Þ > 15σ L xy ðB 0 s Þ, where σ L xy is the uncertainty in L xy . Additionally, the cosine of the angle between the transverse momentum of the B 0 s candidate and the displacement vector must satisfy cosð ⃗ p T ; ⃗ L xy Þ > 0.999, and the invariant mass of the two pions is required to be above 0.45[0.70] GeV in the ψð2SÞ½Xð3872Þ channel.
The signal yields of the B 0 s → Xð3872Þϕ and B 0 s → ψð2SÞϕ decays are extracted using a two-dimensional (2D) maximum likelihood fit to the mðJ=ψπ þ π − Þ and mðK þ K − Þ distributions for B 0 s candidates in the range 5.32 < mðB 0 s Þ < 5.42 GeV. The numbers of Xð3872Þϕ and ψð2SÞϕ signal events from the fit are assumed to come solely from the corresponding B 0 s decays. A systematic uncertainty related to this assumption is evaluated below. Figure 1 shows the observed mðJ=ψπ þ π − Þ (upper) and mðK þ K − Þ (lower) invariant mass distributions for the ψð2SÞϕ candidates with 3.60 < mðJ=ψπ þ π − Þ < 3.75 GeV. Overlaid are the projections of the 2D fit function, which consists of the following four components: (i) ðψð2SÞ; ϕÞ, for the signal component (ii) ðbkg; ϕÞ, for events containing genuine ϕ → K þ K − decays and background J=ψπ þ π − combinations (iii) ðψð2SÞ; bkgÞ, for events containing genuine ψð2SÞ → J=ψπ þ π − decays and background K þ K − combinations (iv) (bkg, bkg), for the background in both dimensions. Each component is a product of two one-dimensional functions. For the ϕ → K þ K − signal, a relativistic Breit-Wigner function convolved with the detector mass resolution is used, where the ϕ natural width is fixed to its known value [4]. The mass resolution is determined from simulated event samples to be about 1.3 MeV. The background in the K þ K − mass distribution is modeled with a threshold function multiplied by a first-order polynomial: where x 0 is the threshold value equal to twice the kaon mass and α is a free parameter. The ψð2SÞ → J=ψπ þ π − signal is described with a double-Gaussian (DG) function with all parameters left free. The background in the mðJ=ψπ þ π − Þ distribution is modeled with a modified threshold function: , and β is a free parameter.
The following parameters are free in the fit: numbers of events in the four components, ϕ and ψð2SÞ meson masses, ψð2SÞ resolution parameters, and background parameters of mðK þ K − Þ and mðJ=ψπ þ π − Þ. The fitted yield for the ψð2SÞ þ ϕ component is N½B 0 For the Xð3872Þ mass region, defined as 3.80 < mðJ=ψπ þ π − Þ < 3.95 GeV, the same fit function is used as in the ψð2SÞ channel, but additional constraints are made because of the lower number of signal events. The shape of the Xð3872Þ → J=ψπ þ π − signal is fixed to the one obtained in data for ψð2SÞ → J=ψπ þ π − , with one floating parameter responsible for the resolution scaling. The Xð3872Þ mass is left free in the fit, and the returned value is in agreement with the known mass [4]. The threshold value y 0 is changed to m PDG J=ψ þ 0.7 GeV to account for the different requirement on the dipion invariant mass applied in the Xð3872Þ channel. The invariant mass distributions and the projections of the 2D fit are shown in Fig. 2. Additional projections of the 2D fit in different ranges of mðJ=ψπ þ π − Þ and mðK þ K − Þ are presented in the Supplemental Material [31]. The measured signal yield is N½B 0 s → Xð3872Þϕ ¼ 299 AE 39. The statistical significance of the B 0 s → Xð3872Þϕ signal has been evaluated with the likelihood ratio technique by applying the background-only and signal-plus-background hypotheses. Using the standard asymptotic approximation [32] for the likelihood, since the conditions of the Wilks' theorem [33] are satisfied, the statistical significance of the B 0 s → Xð3872Þϕ signal is over 6 standard deviations (σ) after accounting for the systematic uncertainties discussed later.
To evaluate the background contribution related to the non-B 0 s production of ψð2SÞϕ in the mass range  5.32 < m(ψð2SÞϕ) < 5.42 GeV, the mass distribution of ψð2SÞϕ is studied, as shown in Fig 3 (upper). The background-subtraction technique s Plot [34] is used, together with the 2D fit described above, to subtract backgrounds from the nonresonant K þ K − and J=ψπ þ π − combinations. The observed m(ψð2SÞϕ) distribution is fitted with a DG function for the signal and an exponential for the background, as shown in Fig. 3 (upper). The fit returns a non-B 0 s background contribution of 0.5%. The same procedure is repeated in the Xð3872Þϕ channel, shown in Fig. 3 (lower), and the measured contribution of the non-B 0 s background is 1.7%. Thus, the ratio of the event yields Xð3872Þ=ψð2SÞ changes by 1.2% after accounting for this background from the non-B 0 s production of ψð2SÞϕ and Xð3872Þϕ combinations. The significance of the B 0 s → Xð3872Þϕ signal extracted from the binned fit to the background-subtracted m(Xð3872Þϕ) distribution exceeds 10σ.
The efficiencies for the signal and normalization channels are calculated using the simulated event samples. The total efficiency includes the detector acceptance, trigger, and candidate reconstruction efficiencies. Only the ratio of the efficiencies for the ψð2SÞ and Xð3872Þ decay modes is needed to calculate the ratio R, which eliminates the systematic uncertainties related to the track and muon reconstruction. The obtained efficiency ratio is ϵ B 0 s →ψð2SÞϕ =ϵ B 0 s →Xð3872Þϕ ¼ 1.136 AE 0.026. It is larger than unity due to a tighter requirement on the dipion mass mðπ þ π − Þ > 0.7 GeV applied in the Xð3872Þ channel. The reported uncertainty is related to the size of the simulated samples. The simulated event samples are validated by comparing distributions of variables used in the candidate selection between the background-subtracted data and simulation. As no significant deviation is found, no additional systematic uncertainty in the efficiency ratio is assigned.
Several sources of systematic uncertainty in the measured ratio R are considered. To evaluate the systematic uncertainties related to the choice of the fit model, several alternative functions are tested. Uncertainties related to the choice of the signal and background models are calculated separately.
The systematic uncertainty in the modeling of the ϕ → K þ K − signal is estimated by varying the ϕ natural width and the mðK þ K − Þ resolution within their uncertainties. The corresponding changes in the ratio R are negligible. The systematic uncertainty in the mðK þ K − Þ and mðJ=ψπ þ π − Þ background model is estimated by testing alternative models. Instead of the baseline model, either a second-order polynomial or a threshold function multiplied by this polynomial is used. The systematic uncertainty in the J=ψπ þ π − signal model is estimated by replacing the DG function with a Student's t-distribution [35] or, for the Xð3872Þ channel, by conservatively scaling the resolution obtained in the ψð2SÞ channel by the ratio of the resolutions of the two channels observed in the simulation.
The systematic uncertainty related to the non-B 0 s background is estimated using the s Plot technique to subtract the contributions from nonresonant K þ K − and J=ψπ þ π − combinations from the mðB 0 s Þ distribution, as described above and shown in Fig. 3. A systematic uncertainty of 1.2% is assigned, based on the fit results to the backgroundsubtracted m(ψð2SÞϕ) and m(Xð3872Þϕ) distributions.
The uncertainty related to the simulation sample size is 2.2%, as evaluated above. Changes in the detector and trigger conditions in the course of the 2016-2018 data taking are shown to have a negligible effect on the measured ratio, as the signal and normalization processes are very similar. The ratio R is found to be stable across different years of data taking, therefore no related systematic uncertainty is assigned.
Table I summarizes the systematic uncertainties described above, together with the total systematic  uncertainty, obtained by adding the effects from the different sources in quadrature. Using Eq. (1), together with the measured signal yields of the B 0 s → Xð3872Þϕ and B 0 s → ψð2SÞϕ decays and the corresponding efficiency ratio, the product of the branching fractions, with respect to that of the B 0 s → ψð2SÞϕ decay, is measured to be R ¼ ½2.21 AE 0.29ðstatÞ AE 0.17ðsystÞ%: Multiplying the measured ratio R by the known branching fractions B½B 0 s → ψð2SÞϕ and B½ψð2SÞ → J=ψπ þ π − [4], we obtain B½B 0 s → Xð3872ÞϕB½Xð3872Þ → J=ψ π þ π − ¼ ð4.14 AE 0.54ðstatÞ AE0.32ðsystÞAE0.46ðBÞÞ × 10 −6 , where the last uncertainty is related to the uncertainties in the aforementioned world-average branching fractions.
This branching fraction product can be compared to similar ones in B 0 and B þ decays [4]: 0.8Þ × 10 −6 . The measured value for B 0 s is consistent with that for B 0 but about two times smaller than the one for B þ : B½B 0 s → Xð3872Þϕ=B½B þ → Xð3872ÞK þ ¼ 0.482 AE 0.063ðstatÞ AE 0.037ðsystÞ AE 0.070ðBÞ. This ratio is significantly lower than the corresponding one for decays to the charmonium state ψð2SÞ of B½B 0 s → ψð2SÞϕ= B½B þ → ψð2SÞK þ ¼ 0.87 AE 0.10 [4]. While this work was in the journal review, an explanation of the observed difference in the decay branching fractions has been proposed [36] within the tetraquark model of the Xð3872Þ state.
In summary, using a data sample corresponding to an integrated luminosity of 140 fb −1 of proton-proton collisions collected by the CMS experiment at ffiffi ffi s p ¼ 13 TeV in 2016-2018, the B 0 s → Xð3872Þϕ decay is observed for the first time. The comparison with similar decays of B 0 and B þ mesons indicates that the Xð3872Þ formation in B meson decays is different from ψð2SÞ formation, suggesting that Xð3872Þ is not a pure charmonium state, supporting similar conclusions derived from other experimental measurements [2,5,[9][10][11][12][13]. This observation may shed new light on the nature of the Xð3872Þ particle.
We congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort. In addition, we gratefully acknowledge the computing centers and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computing infrastructure essential to our analyses. Finally, we acknowledge the enduring support for the construction and operation of the LHC and the CMS detector provided by the following funding agencies: BMBWF and FWF ( PYTHIA 8.2, Comput. Phys. Commun. 191, 159 (2015