Evidence for the Decay D^0 --> K^_pi^+pi^-e^+nu_e
aa r X i v : . [ h e p - e x ] M a y CLNS 07/1994CLEO 07-4
Evidence for the Decay D → K − π + π − e + ν e M. Artuso, S. Blusk, J. Butt, J. Li, N. Menaa, R. Mountain, S. Nisar, K. Randrianarivony, R. Sia, T. Skwarnicki, S. Stone, J. C. Wang, K. Zhang, G. Bonvicini, D. Cinabro, M. Dubrovin, A. Lincoln, D. M. Asner, K. W. Edwards, P. Naik, R. A. Briere, T. Ferguson, G. Tatishvili, H. Vogel, M. E. Watkins, J. L. Rosner, N. E. Adam, J. P. Alexander, D. G. Cassel, J. E. Duboscq, R. Ehrlich, L. Fields, R. S. Galik, L. Gibbons, R. Gray, S. W. Gray, D. L. Hartill, B. K. Heltsley, D. Hertz, C. D. Jones, J. Kandaswamy, D. L. Kreinick, V. E. Kuznetsov, H. Mahlke-Kr¨uger, D. Mohapatra, P. U. E. Onyisi, J. R. Patterson, D. Peterson, J. Pivarski, D. Riley, A. Ryd, A. J. Sadoff, H. Schwarthoff, X. Shi, S. Stroiney, W. M. Sun, T. Wilksen, S. B. Athar, R. Patel, V. Potlia, J. Yelton, P. Rubin, C. Cawlfield, B. I. Eisenstein, I. Karliner, D. Kim, N. Lowrey, M. Selen, E. J. White, J. Wiss, R. E. Mitchell, M. R. Shepherd, D. Besson, T. K. Pedlar, D. Cronin-Hennessy, K. Y. Gao, J. Hietala, Y. Kubota, T. Klein, B. W. Lang, R. Poling, A. W. Scott, A. Smith, P. Zweber, S. Dobbs, Z. Metreveli, K. K. Seth, A. Tomaradze, J. Ernst, K. M. Ecklund, H. Severini, W. Love, V. Savinov, O. Aquines, A. Lopez, S. Mehrabyan, H. Mendez, J. Ramirez, G. S. Huang, D. H. Miller, V. Pavlunin, B. Sanghi, I. P. J. Shipsey, B. Xin, G. S. Adams, M. Anderson, J. P. Cummings, I. Danko, D. Hu, B. Moziak, J. Napolitano, Q. He, J. Insler, H. Muramatsu, C. S. Park, E. H. Thorndike, and F. Yang (CLEO Collaboration) Syracuse University, Syracuse, New York 13244 Wayne State University, Detroit, Michigan 48202 Carleton University, Ottawa, Ontario, Canada K1S 5B6 Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637 Cornell University, Ithaca, New York 14853 University of Florida, Gainesville, Florida 32611 George Mason University, Fairfax, Virginia 22030 University of Illinois, Urbana-Champaign, Illinois 61801 Indiana University, Bloomington, Indiana 47405 University of Kansas, Lawrence, Kansas 66045 Luther College, Decorah, Iowa 52101 University of Minnesota, Minneapolis, Minnesota 55455 Northwestern University, Evanston, Illinois 60208 State University of New York at Albany, Albany, New York 12222 State University of New York at Buffalo, Buffalo, New York 14260 University of Oklahoma, Norman, Oklahoma 73019 University of Pittsburgh, Pittsburgh, Pennsylvania 15260 University of Puerto Rico, Mayaguez, Puerto Rico 00681 Purdue University, West Lafayette, Indiana 47907 Rensselaer Polytechnic Institute, Troy, New York 12180 University of Rochester, Rochester, New York 14627 Dated: May 29, 2007)
Abstract
Using a 281 pb − data sample collected at the ψ (3770) with the CLEO-c detector, we presentthe first absolute branching fraction measurement of the decay D → K − π + π − e + ν e at a sta-tistical significance of about 4.0 standard deviations. We find 10 candidates consistent with thedecay D → K − π + π − e + ν e . The probability that a background fluctuation accounts for this sig-nal is less than 4 . × − . We find B ( D → K − π + π − e + ν e ) = [2 . +1 . − . (stat) ± . × − .This channel is consistent with being predominantly produced through D → K − (1270) e + ν e .By restricting the invariant mass of the hadronic system to be consistent with K (1270), we ob-tain the product of branching fractions B ( D → K − (1270) e + ν e ) · B ( K − (1270) → K − π + π − ) =[2 . +1 . − . (stat) ± . × − . Using B ( K − (1270) → K − π + π − ) = (33 ± B ( D → K − (1270) e + ν e ) = [7 . +4 . − . (stat) ± . ± . × − . The last error accounts forthe uncertainties in the measured K − (1270) → K − π + π − branching fraction. PACS numbers: 13.20.Fc, 12.38.Qk, 14.40.Lb c → se + ν e , the daughter quark is too light for HQET toapply. Nonetheless, this effective theory seems to describe these decays relatively well [1].The decays induced by the quark level process c → se + ν e are dominated by the twofinal states D → Ke + ν e and D → K ∗ e + ν e . CLEO-c has measured exclusive D semileptonicbranching fractions for all modes observed to date: Ke + ν e , K ∗ e + ν e , πe + ν e , ρe + ν e , and D + → ωe + ν e [2], as well as inclusive D → Xe + ν e branching fractions [3]. The sum of theexclusive branching fractions and the inclusive branching fractions for D meson semileptonicdecays are consistent: P B ( D ) = [6 . ± . ± . P B ( D +excl ) = [15 . ± . ± . B ( D → Xe + ν e ) = [6 . ± . ± . B ( D + → Xe + ν e ) = [16 . ± . ± . D → K (1270) e + ν e . Ingeneral, we expect the decay mediated by the quark level process c → se + ν e to be dominatedby the ground state pseudoscalar and vector daughter mesons. The low available phase spacemakes it less likely to produce heavier mesons, such as P -wave or first radial excitations ofthe s ¯ u and s ¯ d quark states. The lightest excited state is the K (1270). This model predictsthat the partial width Γ( D → K (1270) e + ν e ) is 2% of the total Γ( c → se + ν e ), and thatdecays to other excited resonances are suppressed by at least a factor of 10 more.Little is known about D → K (1270) e + ν e to date. The fixed target experiment E653[5] reported a 90% confidence upper limit of B ( D → K − π + π − µ + ν µ ) < . × B ( D → K − µ + ν µ ). This Letter is the first report on a signal for the decay D → K − π + π − e + ν e .We use a 281 pb − data sample collected at the ψ (3770) with the CLEO-c detector[6, 7]. The three major subsystems of this detector are the charged particle tracking cham-bers, the CsI electromagnetic calorimeter, and a Ring Imaging Cherenkov (RICH) chargedparticle identification system. All these components are critical to an efficient and highlyselective electron and positron identification algorithm. The CsI calorimeter measures theelectron and photon energies with an r.m.s. resolution of 2.2% at E = 1 GeV and 5% at E =100 MeV. One of the key variables for e identification, E/p , uses E , the energy measuredin the calorimeter and p , the momentum measured in the charged particle tracking system.The tracking system is composed of a 6-layer inner drift chamber and a 47-layer main driftchamber. The main drift chamber also provides specific ionization ( dE/dx ) measurementsfor charged particle identification. In addition, charged particles are identified using theRICH detector [8]. Combining information from these detector subsystems, we achieve effi-cient and selective charged particle identification over the entire momentum region relevantfor the decays studied.We use a tagging technique similar to the one pioneered by the Mark III collaboration [9].Details on the tagging selection procedure are given in Ref. [10]. We select events containinga fully reconstructed ¯ D → K + π − , ¯ D → K + π − π , ¯ D → K + π − π + π − , or ¯ D → K S π + π − decay, which we call a tag. (Mention of a specific mode implies the use of the charge3 IG. 1: M bc spectra for (a) ¯ D → K + π − , (b) ¯ D → K + π − π , (c) ¯ D → K + π − π + π − , (d) ¯ D → K S π + π − candidate tags. conjugate mode as well throughout this Letter). Two kinematic variables, namely energydifference, ∆ E ≡ E tag − E beam , and beam-constrained mass, M bc ≡ q E /c − | ~p tag | /c ,are used to select tag candidates, where E beam represents the beam energy and ( E tag , ~p tag )represent the 4-vectors of the ¯ D tag candidate. We first require | ∆ E | to be less than 0.020to 0.030 GeV, depending upon the mode considered. Figure 1 shows the M bc spectra forevents that satisfy the | ∆ E | requirement for the four tagging modes considered. In orderto determine the total number of tags, we fit the M bc distribution with a signal shapecomposed of a Crystal Ball function [11] and a Gaussian, and an ARGUS function [12]parameterizing the background in the fit. The signal window is chosen as 1.858 GeV/ c ≤ M bc ≤ .
874 GeV/ c . In order to extract the tag yield, we integrate the signal shapewithin this M bc interval. Alternatively, we count tag candidates in the M bc signal windowand subtract the combinatorial background obtained by integrating the background functionfrom the fit. The total number of tags obtained with the former method is [257 . ± . × ; the second method gives [257 . ± . × . The agreement is excellent and weuse the latter number as the total number of tags in our sample. The difference betweenthe two tag yields is included in a systematic uncertainty.In each event where a tag is found, we search for a set of tracks recoiling against the tagthat are consistent with a semileptonic decay. We select tracks that are well-measured andhave a helical trajectory approaching the event origin within a distance of 5 cm (5 mm) alongthe beam axis (in the plane perpendicular to the beam axis). Each track must include at least50% of the main drift chamber wire hits expected for its momentum and have momentumgreater than 50 MeV/ c . We search for a positron among well reconstructed tracks having amomentum of at least 200 MeV/ c , as the electron identification becomes increasingly difficultat low momenta. We also require | cos θ | < .
90, where θ is the angle between the positrondirection and the beam axis. The positron selection criteria are discussed in Ref. [2]. Theyhave an average efficiency of 95% in the momentum region [0 . − .
0] GeV/ c , and 71% in theregion [0 . − .
3] GeV/ c . In addition, we search for a good track consistent with a K − andtwo oppositely charged tracks consistent with pions. Hadron track identification criteria rely4n dE/dx information from the drift chamber for tracks with p < . c . For trackswith p ≥ . c , in addition to dE/dx measurements, information from the RICHdetector [8] is used to improve the K - π discrimination. In the momentum range relevant forthis analysis the K - π misidentification probability is negligible. The e - π misidentificationprobability, determined experimentally with radiative Bhabhas, has an average value of 17%for electron momenta below 0.2 GeV/ c , and is about 1% for higher momenta.As the decay mode that we are investigating is rare, efficient background suppressionis critical to achieve adequate sensitivity. Accordingly, we require that only four chargedtracks be present in the event in addition to those used in the tag reconstruction. Thedominant source of background in this analysis arises from events in which the detectedpositron comes from a γ conversion ( γ → e + e − ), or a π Dalitz decay ( π → e + e − γ ).This background is equally likely to produce ( e + K − ) combinations, which we call right-signevents (RS), and ( e − K − ) combinations, which we call wrong-sign events (WS). Typically, an e + e − pair arising from a conversion γ or a π Dalitz decay has a strong angular correlationwith almost collinear angular orientation of the two particles. For signal events, the openingangle between the e + π − pair tends to be large. We therefore include a requirement thatthe opening angle be greater than 20 ◦ . This requirement eliminates most of the backgroundfrom conversion γ ’s or π Dalitz decays, while reducing the signal efficiency by only 1.7%.In this semileptonic sample, signal candidate events are selected using the missing masssquared
M M defined as M M = ( E beam − X i =1 E i ) /c − ( − ~p tag − X i =1 ~p i ) /c , (1)where ~p tag is the momentum of the fully reconstructed tag, and ( E i , ~p i ) represent the en-ergy and momentum of the four tracks in the D candidate. For signal events the M M distribution is centered at zero, as it represents the invariant mass squared of the missing ν e . According to Monte Carlo simulation of our signal semileptonic channel, the M M dis-tribution has a resolution consistent among the tag modes with a standard deviation ( σ )of 0 . ± . / c ) . Figure 2 shows the measured M M distribution for RSevents in the data as well as the estimated background, derived from GEANT-based MonteCarlo simulation [13] in combination with particle misidentification probabilities derivedfrom data. In addition we estimate the background directly from the WS events in data.We define a signal window as | M M | ≤ .
02 (GeV / c ) . There are 10 events in the signalwindow of M M as shown in Figure 2.Another interesting observable is the invariant mass of the K − π + π − hadron system.Figure 3 shows the invariant mass of the K − π + π − system for RS candidate events, comparedwith the expectation from the ISGW2 model [1], which provides the best representationof our data, where the hadronic system forms the K (1270) resonance. The measureddistribution is in reasonable agreement with this model.We have performed several studies to determine possible background sources. A MonteCarlo sample incorporating all the information available on D meson decays and 40 timesbigger than our collected data demonstrates that the dominant background comes fromconversion γ ’s or π Dalitz decays. As the e to π misidentification probability may notbe modeled accurately by our Monte Carlo simulation, the background from Dalitz decaysis evaluated by folding the e spectra from simulated D → K − π + π decays with the e to π misidentification probability derived from a radiative Bhabha data sample. This studypredicts that 1.56 ± IG. 2: Missing mass squared (
M M ) distribution for the RS sample D → K − π + π − e + ν e . Thedashed histogram represents the estimated background. Events with M M within the two arrowsare considered signal candidates.FIG. 3: Invariant mass of the hadronic system in the data for D → K − π + π − e + ν e . The dashedhistogram represents the predicted distribution obtained using a Monte Carlo simulation accordingto the ISGW2 model, assuming all the K − π + π − are K (1270) decay products. The region withinthe two arrows defines the invariant mass range used to select the K − (1270) resonance. K − π + π − invariant mass is applied. A study of the WS data gives one background event, inagreement with the previous estimate. In addition, there are small background componentsfrom the decays D → K − π + π + π − (0 . ± .
1) and D → K − π + π + π − π (0 . ± . D ¯ D contributions at thiscenter-of-mass energy, such as those from the continuum ( e + e − → q ¯ q , where q is a u , d ,or s quark), radiative return production of ψ (2 S ), and e + e − → τ + τ − processes, and we donot find any background from these sources. Summing up all background contributions, we6nd that 1 . ± .
25 (stat) events are consistent with background. We have also studiedthis sample with a requirement on the invariant mass of the
Kππ system optimized forthe decay D → K − (1270) e + ν e , using the variable S/ √ S + B , where S is the number ofsignal events predicted from Monte Carlo simulations and B is the number of estimatedbackground events. For the optimal invariant mass interval, [1150 − c , we find8 candidate events and an estimated background of 1 . +0 . − . (stat) events, with no events inthe WS sample.The reconstruction efficiency depends on the invariant mass of the K − π + π − system( M had ). A larger fraction of the electron spectrum is below the momentum cut of 0 . c for higher M had , and the spin and parity of the final hadronic state influence theelectron spectrum shape as well. For example, the ISGW2 model studies all the P -wave s ¯ u and d ¯ u hadronic final states, as well as the corresponding radial excitations. Among the P -wave states, the / P are identified with the K (1270), and / P are identified with the K (1400). The latter has a much softer electron spectrum, and therefore our efficiency fordetecting it is smaller. We have studied the signal reconstruction efficiency with the ISGW2model, including different mixing percentages of the / P and / P final states, as well asa phase space model for the distribution of the M had . With the Monte Carlo simulationbased on the ISGW2 model, we obtain ǫ = (10 . ± . M had range and ǫ = (10 . ± . K (1270) mass requirement ([1150 − c ).The absolute branching fraction for D → K − π + π − e + ν e is obtained using B ≡ ( N s − N b ) / ( ǫ eff N tag ), where N s is the number of signal events, N b is the number of backgroundevents, N tag is the number of tags, and ǫ eff is the effective efficiency for detecting the semilep-tonic decay in an event with an identified tag. This effective efficiency includes a correctionterm C ≡ ǫ sltag /ǫ tag accounting for the small difference in tag reconstruction efficiency inevents containing the semileptonic signal and in generic D ¯ D events. The average value of C is 1.036. We obtain B ( D → K − π + π − e + ν e ) = (2 . +1 . − . ± . × − , without applyingany invariant mass requirement. If we apply the K (1270) invariant mass requirement, weobtain B ( D → K − (1270) e + ν e ) · B ( K − (1270) → K − π + π − ) = (2 . +1 . − . ± . × − . Thesmaller systematic uncertainty is derived by the fact that the model dependence can simplybe estimated by varying the form factors in the ISGW2 model. In this case we do notneed to model a broader invariant mass distribution for the K − π + π − system. Note that theprobability for 1.86 background events to fluctuate to 10 or more events, taking into accounta 0.25 event Gaussian uncertainty, is 4 . × − , corresponding to a significance of about 4.0 σ . The result with the K − π + π − mass requirement has similar statistical significance.The systematic uncertainties for the branching fractions are listed in Table I and arequoted as relative to the measured branching fraction. The uncertainty on the tag yield isestimated from varying the background functions. Systematic uncertainties on track findingand hadron particle identification efficiencies are reported in Ref. [10], while electron iden-tification efficiency is reported in Ref. [3]. The sensitivity to the requirement on the e + π − opening angle has been evaluated by repeating the analysis after changing the requirementby ± ◦ . The model dependence of the efficiency is studied using an alternative invariantmass distribution for the hadronic system governed by phase space. In the analysis where weapply a mass requirement on the K − π + π − system, the model dependence of the efficiencyis estimated by varying the form factors in the ISGW2 model, and the corresponding uncer-tainty is found to be 4%. The background uncertainty is derived by changing the measuredfake probabilities within their errors.In summary, we have presented the first measurement of the absolute branching fraction7 ystematic errors (%)Number of tags 0.5 0.5Tracking 1.3 1.3PID Efficiency (hadrons) 1.9 1.9PID Efficiency (electrons) 1.0 1.0Opening angle cut 1.5 1.5 M Kππ cut – 1.7Model dependence 10.0 4.0Background 5.3 5.3Total 11.9 7.5TABLE I: Systematic errors on D → K − π + π − e + ν e branching fraction. The first column appliesto the analysis without K (1270) mass cut, the second to the analysis with the K (1270) mass cutas described in the text. B ( D → K − π + π − e + ν e ) = [2 . +1 . − . (stat) ± . × − . The invariant mass of thehadronic system recoiling against the e + ν e pair is consistent with K − (1270). By requiring M had to be within the [1150 − c mass window, we obtain the product branchingfraction B ( D → K − (1270) e + ν e ) · ( B ( K − (1270) → K − π + π − ) = [2 . +1 . − . stat ± . × − .The statistical significance is about 4.0 standard deviations. Using the K − (1270) decaymodes reported in the PDG [14], we calculate the K − (1270) → K − π + π − branching frac-tion to be (33 ± B ( D → K − (1270) e + ν e ) is[7 . +4 . − . (stat) ± . ± . × − . The last error accounts for the uncertainties inthe measured K − (1270) branching fractions. This channel is found to be 1.2% of the to-tal semileptonic width. The ISGW [4] model predicts this fraction to be about 1%, whilethe ISGW2 model [1] predicts this fraction to be about 2%; hence the measured branchingfraction and K − π + π − invariant mass are consistent with quark model calculations.We gratefully acknowledge the effort of the CESR staff in providing us with excellentluminosity and running conditions. D. Cronin-Hennessy and A. Ryd thank the A.P. SloanFoundation. This work was supported by the National Science Foundation, the U.S. De-partment of Energy, and the Natural Sciences and Engineering Research Council of Canada. [1] D. Scora and N. Isgur, Phys. Rev. D , 2783 (1995) [arXiv:hep-ph/9503486].[2] G. S. Huang et al. [CLEO Collaboration], Phys. Rev. Lett. , 181801 (2005); T. E. Coan etal. [CLEO Collaboration], Phys. Rev. Lett. , 181802 (2005).[3] N. E. Adam et al. [CLEO Collaboration], Phys. Rev. Lett. , 251801 (2006)[arXiv:hep-ex/0604044].[4] N. Isgur, D. Scora, B. Grinstein and M. B. Wise, Phys. Rev. D , 799 (1989).[5] K. Kodama et al. [Fermilab E653], Phys. Lett. B , 260 (1993).[6] G. Viehhauser CLEO III Operation , Nucl. Instrum. Methods A , 146 (2001).[7] R.A. Briere et al. (CLEO-c and CESR-c Taskforces, CLEO Collaboration), Cornell University,LEPP Report No. CLNS 01/1742 (2001) (unpublished).
8] M. Artuso et al. , Nucl. Instrum. Meth. A , 91 (2003) [arXiv:hep-ex/0209009].[9] J. Adler et al. [Mark III Collaboration], Phys. Rev. Lett. , 1821 (1989).[10] Q. He et al. [CLEO Collaboration], Phys. Rev. Lett. , 121801 (2005) [Erratum-ibid. ,199903 (2006)] [arXiv:hep-ex/0504003].[11] T. Skwarnicki et al. [Crystal Ball Collaboration], DESY Preprint F31-86-02 (1986).[12] H. Albrecht et al. [ARGUS Collaboration], Phys. Lett.B , 304 (1989).[13] R. Brun, F. Bruyant, M. Maire, A. C. McPherson and P. Zanarini, CERN-DD/EE/84-1.[14] W. Yao et al. , Journ. of Phys. G , 1 (2006)., 1 (2006).