Measurement of the Relative Branching Fraction of \boldmath $B_{s}^{0} \rightarrow J/ψf_{0}(980), f_{0}(980) \rightarrow \p i^{+}π^{-}$ to B 0 s →J/ψϕ,ϕ→ K + K −
aa r X i v : . [ h e p - e x ] S e p Proceedings of the DPF-2011 Conference, Providence, RI, August 8-13, 2011 Measurement of the Relative Branching Fraction of B s → J/ψf (980) , f (980) → π + π − to B s → J/ψφ, φ → K + K − B. Abbott
Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman, OK, USA
A measurement of the relative branching fraction of B s → J/ψf (980) , f (980) → π + π − to B s → J/ψφ, φ → K + K − is presented. The decay mode B s → J/ψf (980) is an interesting modesince it is a CP-odd eigenstate which could be used in CP-violating studies. Using approximately8 fb − of data recorded with the D0 detector at the Fermilab Tevatron Collider, a relative branchingfraction of 0.210 ± ± I. INTRODUCTION
The CP-violating phase in B s mixing mixing, has been measured [1, 2] using B s → J/ψφ decays. Themeasured absolute value is larger than predicted by the Standard Model (SM) [3], but is statistically consistentwith it. The decay products in B s → J/ψf (980) are in a CP-odd eigenstate and can provide a more directmeasurement of this CP-violating phase. Measuring this CP-violating phase using B s → J/ψf (980) decaysmode can aid in reducing its uncertainty.Based on estimates the relative branching fraction should be large. Using hadronic D + s decays, Stone andZhang [4, 5] estimated the relative width to be: R ≡ Γ( B s → J/ψf (980); f (980) → π + π − )Γ( B s → J/ψφ ; φ → K + K − ) ≈ . . (1)The LHCb collaboration has reported [9] a first measurement of R = 0 . +0 . . − . − . . The Belle col-laboration has made a measurement of the branching fraction B ( B s → J/ψf (980); f (980) → π + π − ) =(1 . +0 . − . (stat . ) +0 . − . (syst . ) +0 . − . (N B ( ∗ )s ¯B ( ∗ )s )) × − [10]. The CDF collaboration has also measured the rel-ative branching fraction and finds R =0.257 ± ± II. RELATIVE BRANCHING FRACTION
To determine an absolute branching fraction, various efficiencies, branching fractions, and cross sections needto be known, as well as the integrated luminosity. However, by measuring a relative branching fraction, severalterms common to both the B s → J/ψf (980) branching fraction and the B s → J/ψφ branching fraction cancelgiving: R = B ( B s → J/ψf (980); f (980) → π + π − ) B ( B s → J/ψφ ; φ → K + K − ) = N B s → J/ψf (980) × ε B s → J/ψφreco N B s → J/ψφ × ε B s → J/ψf (980) reco . (2)All that is required to measure a relative branching fraction are the relative yields and the relative reconstructionefficiencies of the two decay modes, ε B s → J/ψφreco and ε B s → J/ψf (980) reco . III. SELECTION CUTSA. Analysis Cuts
The data set of an integrated luminosity of approximately 8 fb − was divided into four periods correspondingto different detector configurations called RunIIa, RunIIb1, RunIIb2 and RunIIb3.The initial sample of B s → J/ψf (980) was found by first reconstructing J/ψ → µ + µ − candidates by requiringthat two oppositely charged muon candidates with transverse momentum p T > Proceedings of the DPF-2011 Conference, Providence, RI, August 8-13, 2011
Since the D0 detector has a limited ability to separate kaons from pions, all reconstructed tracks not associatedto a
J/ψ are considered for reconstructing f (980) and φ candidates. The tracks are assigned the pion masswhen searching for B s → J/ψf (980) and the kaon mass when searching for B s → J/ψφ . Two tracks with aminimum p T of 300 MeV, having an invariant mass 0.7 GeV < M π + π − < f (980) candidates. Finally, the µ + µ − π + π − candidates wererequired to have a common vertex and have an invariant mass between 5.0–5.8 GeV.Similar requirements were applied to the initial sample of B s → J/ψφ candidates. The only different re-quirements were that 0.91 GeV < M K + K − < µ + µ − K + K − candidates were required to havean invariant mass between 5.0–5.8 GeV. Due to the invariant mass requirements on M π + π − and M K + K − , twotracks cannot be considered both a f (980) and a φ candidate. The final data sample was then formed byapplying the additional requirements: • All runs without optimal performance of muon, silicon microstrip and central fiber trackers are omitted . • All events that only fired a trigger that required muons with a large impact parameter were removed.
J/ψ selection: • Both muons are required to be detected as a track segment in either one or three layers of the muonsystem and be matched to a central track. • At least one muon must be detected as a track segment in three layers of the muon system. • Both muons must have at least one hit in the silicon microstrip tracker. • < M µ + µ − < f (980) ( φ ) selection: • Both pions (kaons) from the f (980) ( φ ) candidate must have at least 2 hits in the central fiber tracker. • Both pions (kaons) from the f (980) ( φ ) candidate must have at least 2 hits in the silicon microstriptracker. • Both pions (kaons) from the f (980) ( φ ) candidate must have at least 8 hits total in the silicon microstriptracker and the central fiber tracker. • The momentum of the leading pion (kaon) from the f (980) ( φ ) candidate must be greater than 1.4 GeV. • f (980) ( φ ) candidate p T must be greater than 1.6 GeV. B s selection: • < M π + π − < J/ψf (980).) • < M K + K − < J/ψφ .) • p T ( B s ) > • Proper decay length [13], L , significance, L/σ ( L ) >
5, where σ ( L ) is the uncertainty on the proper decaylength. B. Boosted Decision Trees
It is known that boosted decision trees (BDT) [14, 15] are a powerful tool for separating signal from back-ground. Signal and background samples are used to train the BDT and a discriminant is determined for eachevent. By making a selection on the value of the BDT discriminant, the signal to background ratio can bevastly improved. We use the Monte Carlo (MC) pythia program [16] to generate B s and the evtgen program[17] to simulate its decay. Two MC background samples were produced: a prompt sample (directly produced J/ψ ) and an inclusive sample (all decay processes B s → J/ψ + X ). A MC signal sample of B s → J/ψf (980)events was then used to train the BDT on both the prompt and inclusive background. A BDT discriminantwas found for both the prompt and inclusive sample and used in the analysis. A total of 36 different kinematicvariables were used to train the BDT consisting of isolation variables, transverse momentum of the daughters roceedings of the DPF-2011 Conference, Providence, RI, August 8-13, 2011 FIG. 1: BDT distribution after training for both signal (blue) and inclusive background (red). and grand-daughters of the B s and vertex quality of the B s and its daughters. Figures 1 and 2 show the BDTdistributions for the training and test samples for the inclusive and prompt background.The BDT cuts were determined only using the 1 fb − of RunIIa data. A narrow window around the nominal f (980) mass was chosen to keep the signal to noise ratio high. Using a mass cut of 0.96–1.0 GeV on the π + π − mass, the BDT cut value was chosen where both S/ √ B and the signal yield were high. In this way, the BDTdiscriminant for both the inclusive and prompt BDT was required to be greater than 0.35. IV. YIELD RESULTS
A clear B s peak is found when the π + π − invariant mass is near the nominal f (980) mass. It is expectedthat the B s signal can be fitted to a Gaussian distribution, which provides a fitted mean mass ( µ ) and width( σ ) for the B s peak. Since backgrounds are large, a cut of ± σ around the fitted B s peak is used to identifythe f (980) mass peak. A clear f (980) mass peak is observed when the µ + µ − π + π − invariant mass is within ± σ of the fitted B s mass, see Fig. 3. To decide on a π + π − mass window to use for this analysis, a fit to the f (980) mass peak is performed. The f (980) has a large width [18] and is just under the KK mass threshold.This changes the line shape from a simple Breit Wigner form, particularly for higher masses and so the π + π − mass distribution is fitted using a functional form based on Flatt´e [19], convoluted with a Gaussian function,that takes into account the opening of the KK threshold. The lineshape found from fitting the f (980) in MCis used to fit the data. A π + π − invariant mass cut of 0.91–1.05 GeV is applied to identify B s → J/ψf (980)and is shown in Fig. 4. The B s → J/ψf (980) mass distribution was fit to a Gaussian signal with a backgroundfunction consisting of a second-degree polynomial and a Gaussian function at lower invariant mass to take intoaccount partially reconstructed B decays.Using identical cuts (except for the cut on the φ mass), a clear J/ψφ peak is found and is shown in Fig. 5.Since the φ peak is so narrow, the backgrounds are much smaller for B s → J/ψφ .An unbinned likelihood fit was used to determine the candidate yields in each sample. The fit to the
J/ψf (980) mass distribution shown in Fig. 4 gives the following results (statistical uncertainties only): B s mass = 5 . ± . σ = 0 . ± . ± B s → J/ψf (980) candidates . The µ + µ − K + K − mass distribution was fit for a B s → J/ψφ signal using a double Gaussian function with asecond-order polynomial background. A fit to the
J/ψφ distribution shown in Fig. 5 gives the following results
Proceedings of the DPF-2011 Conference, Providence, RI, August 8-13, 2011
FIG. 2: BDT distribution after training for both signal (blue) and prompt background (red). (GeV) - π + π M0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 E ve n t s / M e V - π + π M0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 E ve n t s / M e V Run II, Preliminary, 8 fb ∅ D FIG. 3: π + π − invariant mass distribution peaking at the f (980) mass when the J/ψπ + π − mass is ± σ around thefitted B s mass. (statistical uncertainties only): B s mass = 5 . ± . ± B s → J/ψφ candidates . V. EFFICIENCIES
To determine the efficiencies of the analysis, MC signal samples were used. To take into account the effectsof the instantaneous luminosity, the MC samples were overlaid with zero bias data collected during each runperiod. In the generation of both the
J/ψφ and the
J/ψf (980) signal MC’s, a preselection requirement of roceedings of the DPF-2011 Conference, Providence, RI, August 8-13, 2011 (GeV) - π + π - µ + µ M5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 E ve n t s / M e V - π + π - µ + µ M5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 E ve n t s / M e V -1 Run II, Preliminary, 8 fb ∅ D FIG. 4: µ + µ − π + π − mass distribution peaking at the B s mass when the π + π − mass is between 0.91 and 1.05 GeV (GeV) - K + K - µ + µ M5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 E ve n t s / M e V - K + K - µ + µ M5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 E ve n t s / M e V ∅ D -1 Preliminary, 8 fb
FIG. 5: µ + µ − K + K − mass distribution peaking at the B s mass from 8 fb − of data Proceedings of the DPF-2011 Conference, Providence, RI, August 8-13, 2011
TABLE I: The reconstruction efficiency for B s → J/ψφ and B s → J/ψf (980) for various running periods.Sample total reconstruction efficiency B s → J/ψφ
RunIIa 0.0231 ± B s → J/ψφ
RunIIb1 0.0191 ± B s → J/ψφ
RunIIb2 0.00636 ± B s → J/ψf (980) RunIIa 0.0191 ± B s → J/ψf (980) RunIIb1 0.0146 ± B s → J/ψf (980) RunIIb2 0.00529 ± ε B s → J/ψφreco ε B s → J/ψf reco
RunIIa 1.21 ± ± ± p T > φ ( f (980)). Since the p T distributions for thepions and kaons may be different, the preselection efficiencies of this cut must be determined. To determine thepreselection cut efficiencies, two additional MC sets were also generated with no p T cuts on the pions (kaons).By comparing these two results, the preselection cut efficiencies were determined.We found that the reconstruction efficiencies depended heavily on the MC sample used since the instantaneousluminosity was different for the various run periods, therefore we determined the reconstruction efficiencies foreach run range separately. The instantaneous luminosities for runs taken during RunIIb3 were similar to theinstantaneous luminosities for runs taken during RunIIb2 so the reconstruction efficiencies found from RunIIb2were used for RunIIb3. Table I shows the results on the efficiency analysis using MC signal samples. TableI shows that the absolute reconstruction efficiencies vary in each run period, however Table II show that therelative reconstruction efficiencies are relatively stable. However, the differences in the relative reconstructionefficiency is considered a systematic uncertainty on R . VI. SYSTEMATIC UNCERTAINTY STUDIESA. B s → J/ψπ + π − background studies One possible peaking background that affects the B s → J/ψf (980) yield measurement is the non-resonant B s → J/ψπ + π − background. This background was studied by measuring the B s yields in π + π − invariant massless than the f (980) mass. The π + π − mass distribution from B s → J/ψπ + π − background where the π + π − are non-resonant should have a much broader distribution, so determining the B s yield for lower π + π − masseswill allow a determination of the contamination in the f (980) signal region.In determining the π + π − mass window to study, it is important to choose a window where one does notexpect other resonances (i.e., B s → J/ψK ∗ ). The π + π − mass window of 0.8–0.9 GeV was chosen since in thismass range there should not be any B s → J/ψK ∗ events. In fitting the distribution for any possible signal, thesignal µ and σ are constrained to be the values found from the fit to the B s mass in the f (980) signal region.The fit yields 80 ±
75 events, giving no statistically significant evidence of any B s → J/ψπ + π − non-resonantbackground, so no correction was applied. B. Analysis cut variation
To cross check that the results do not vary with the exact value of the analysis cuts, the choice for eachanalysis cut was varied around its nominal value. This is an important test since the selection criteria was roceedings of the DPF-2011 Conference, Providence, RI, August 8-13, 2011 TABLE III: Fractional change due to varying the exact choice of analysis cuts on the relative branching fractionCut ε ( J/ψφ ) ε ( J/ψf ) event yield B s → J/ψφ event yield B s → J/ψf effect on R BDT inc > > > > p T ( B s ) > p T ( B s ) > p T ( f (980)) > p T ( f (980)) > π /K p T > π /K p T > L/σ ( L ) > L/σ ( L ) > B s → J/ψf (980) yieldNominal fit (Gaussian signal + second order polynomial background with fit range 5.1–5.8 GeV) 498 ± ± ± ± ± ± determined with 1 fb − data from RunIIa, and it is important to verify that this did not introduce a bias intothe measurement. Table III shows the results from this study. As can been seen from the table, the value of R does not depend significantly on the exact choice of selection requirement. C. Fitting cross checks
Due to large backgrounds arising from combinatorics and partially reconstructed B decays, there are signifi-cant uncertainties in the exact background shape. Therefore different parameterizations were used to describethe background and different fit regions were used to fit the data. The background polynomial was changedfrom a second-degree polynomial to a third-degree polynomial. The fit range was changed from the nominal5.1–5.8 GeV and finally a different functional form for the background was used by changing the backgroundshape to a polynomial plus an exponential.As can be seen from Table IV, there is a fairly large variation in the number of signal events for B s → J/ψf (980), indicating that the background shape is difficult to model. This fitting systematic gives the largestsystematic uncertainty on R . A study was performed using same-sign pions and forming the mass distributionfrom µ + µ − π ± π ± . However, it was found the the same sign pion distribution did not describe the measuredbackground and so could not be used to help constrain the background shape. A similar study of varying thefitting choices was performed on the B s → J/ψφ sample, however since the backgrounds are much smaller andeasier to describe the event yield numbers changed by less than 1%.A summary of the uncertainties on the BR are summarized in Table V.
Proceedings of the DPF-2011 Conference, Providence, RI, August 8-13, 2011
TABLE V: Statistical and systematic uncertainties in branching fraction ratio, R Source UncertaintyStatistical 0.149Systematic from fitting 0.150Systematic from different MC samples 0.0858
VII. FINAL BRANCHING FRACTION RATIO
The decay B s → J/ψf (980) is an interesting decay mode since it can allow a measurement of the CP-violatingphase in B s mixing.A measurement of the relative branching fraction using approximately 8 fb − of data yields: R = B ( B s → J/ψf (980); f (980) → π + π − ) B ( B s → J/ψφ ; φ → K + K − ) = 0 . ± .
032 (stat) ± .
036 (syst) . The relative branching fraction of B s → J/ψf (980) , f (980) → π + π − to B s → J/ψφ, φ → K + K − should belarge enough to allow a measurement of the CP-viiolating phase in B s mixin using the decay B s → J/ψf (980).An analysis to measure φ s using the decay B s → J/ψf (980) is currently being pursued. [1] V.M. Abazov et al. , (D0 Collaboration) Phys. Rev. Lett. , 241801 (2008), arXiv:0802.2255 [hep-ex] and .[2] D. Tonelli (CDF Collaboration), arXiv:0810.3229[hep-ex], T Aaltonen et al., (CDF Collaboration), Phys Rev. Lett. , 161802 (2008), arXiv:0712.2397 [hep-ex].[3] A. Lenz and U. Nierste, JHEP 0706 (2007) 072.[4] S. Stone, L. Zhang, arXiv:0909.5442v2 [hep-ex].[5] S. Stone and L. Zhang, Phys. Rev. D , 074024 (2009) [arXiv:0812.2832].[6] K.M. Eckland et.al (CLEO Collaboration), Phys. Rev. D , 052009 (2009), arXiv:0907.3201v2 [hep-ex].[7] I. Adachi et al., (Belle Collaboration) arXiv:0912.1434 [hep-ex].[8] R. Louvot (Belle Collaboration) arXiv:1009.2605 [hep-ex].[9] R. Aaij et al., (LHCb Collaboration) Phys. Lett. B et al., Phys. Rev. Lett. , 121802 (2011).[11] T. Aaltonen et al. (CDF Collaboration), arXiv:1106.3682 [hep-ex], submitted to Phys. Rev. D.[12] A. Chandra, S. Dugad, D. Zieminska, D0 Note 4697.[13] The proper decay length is defined as L xy ( M B s /p T ), where p T is the transverse momentum of the B s , M B s is theworld average mass of the B s , and L xy is the transverse distance between the primary vertex and the four trackvertex of the B s candidate. Primary vertices are determined by using the beamspot as a contraint and finding thevertex which contains the most tracks. Then using the other tracks not associated with the first primary vertex,but still beam constrained, search for a second primary vertex. This process is then repeated until no additionalprimary vertices are found. If there is more than one primary vertex in an event, the primary vertex nearest the J/ Ψ candidate is selected.[14] L. Breiman et al ., Classification and Regression Trees, (Wadsworth,Stamford, 1984).[15] A. H¨ocker et al ., arXiv:physics/0703039 [physics.data-an] (2007).[16] T. Sj¨ostrand et al ., Comput. Phys. Commun. , 238 (2001).[17] D.J. Lange, Nucl. Instrum. Methods Phys, Res. A , 152 (2001).[18] K. Nakamura et al ., (Particle Data Group), J. Phys. G , 075021 (2010).[19] J.B. Gay et alet al