aa r X i v : . [ h e p - e x ] J un RECENT CHARM RESULTS FROM CLEO-C
Istv´an Dank´o(for the CLEO Collaboration)
Rensselaer Polytechnic InstituteTroy, NY 12180, USA
AbstractThe CLEO-c experiment has been collecting data at the charm-threshold re-gion. A selection of recent results on charmed meson and charmonia decaysare presented.
Introduction
The CLEO-c experiment has been taking data at the CESR symmetric e + e − collider at the charm threshold region since 2003. The main goal of the ex-periment is to perform high precision measurements of hadronic branchingfractions, leptonic decay constants, and semileptonic form factors of charmedmesons, together with an extensive study of QCD spectroscopy in the charmo-nium sector in order to provide rigorous constraints on the strong interactiontheory, especially Lattice QCD calculations. If the theoretical calculations sur-vive these tests they can be used to provide much needed theoretical input toextract quark mixing (CKM) matrix elements (e.g. V ub , V td and V ts ), whichremain limited by complications caused by strong interaction dynamics.The selected topics discussed here are the measurement of the absolutebranching fraction of Cabibbo-favored hadronic D , D + , and D s decays; mea-surement of the leptonic decays, D +( s ) → ℓ + ν , and decay constants f D ( s ) ; mea-surement of the D mass; and a study of three-body hadronic decays of χ cJ .Charged and neutral D mesons are produced at the ψ (3770) which pre-dominantly decays to D + D − and D ¯ D with a total cross section of about7 nb. D s mesons are created at around E cm = 4170 MeV, where their pro-duction is dominated by e + e − → D ⋆ ± s D ∓ s with a cross section about 0 . P J ( J = 0 , ,
2) charmonium states are produced in radiative ψ (2 S )decays with a branching fraction of 9% to each. The main advantage of theCLEO experiment compared to B factories and fixed target experiments is thevery clean experimental environment with low multiplicity final states, whicharises from running at or slightly above production thresholds. Background isfurther reduced in e + e − → ψ (3770) → D ¯ D and e + e − → D ⋆s ¯ D s data by fullyreconstructing (tagging) one of the D ( s ) decaying into a hadronic final state. D , D + , D s hadronic branching fractions Precise knowledge of the absolute hadronic branching fractions of the D , D + , D s mesons is important because they are used to normalize the decays of othercharmed mesons and B ( s ) mesons.CLEO measures the absolute branching fraction of three D , six D + ,and six D + s Cabibbo-favored hadronic decays using single tag and double tagevents following a technique pioneered by the MARK-III Collaboration 2). Insingle tag events only one of the D ( s ) or ¯ D ( s ) is reconstructed in a specific finalstate, while in double tag events both D ( s ) and ¯ D ( s ) mesons are reconstructedin one of the hadronic final states. The single and double tag yield can beexpressed as n i = N DD B i ǫ i and n ij = N DD B i B j ǫ ij , where N DD is the numberof D ¯ D , D + D − , or D + s D − s events produced; B i is the branching fraction ofdecay mode i ; ǫ i and ǫ ij are the single and double tag efficiencies. Then thebsolute branching fractions can be obtained from the double and single tagratios and efficiencies as B i = n ij n j ǫ j ǫ ij . (1)Since ǫ ij ≈ ǫ i ǫ j , the branching fraction is nearly independent of the efficiencyof the tagging mode, and many systematic uncertainties cancel in the ratio.There is a difference in the kinematics of D and D s mesons. The D and¯ D mesons produced in e + e − → ψ (3770) → D ¯ D process have the same welldefined energy (and momentum) in the center of mass frame of the colliding e + e − beams ( E D = E beam ). In contrast, a pair of D s mesons is produced in e + e − → D ⋆ ± s D ∓ s followed by the decay D ⋆ ± s → γD ± s (96%) or π D ± s (4%).Therefore, the D s produced directly has a well defined energy and momentumin the e + e − center of mass frame, while the secondary D s from the D ⋆s decayhas a much broader momentum distribution around the same value. Thisdifference in kinematics leads to a slightly different selection strategy of D ¯ D and D ± s D ∓ s events.Figure 1: Beam-constrained mass distribution of D ( ¯ D ) candidates in doubletag events summed over all decay modes. In order to identify (tag) the D mesons, we use ∆ E = E D − E beam andthe beam-constrained mass, M bc = p E − ( ~p D ) , where E D and ~p D are theenergy and three-momentum of the reconstructed D meson candidate. Substi-tuting the beam energy for E D improves the mass resolution of D candidatesby an order of magnitude, to about 2 MeV/ c . ∆ E peaks around zero and M bc peaks at the nominal D mass. We require ∆ E to be consistent with zero within3 standard deviations, and extract the number of single and double tags from afit to the one-dimensional and two-dimensional M bc distributions, respectively.Fig. 1 illustrates the beam-constrained mass distribution for double tag eventsummed over all decay modes. In 281 pb − data, we reconstruct 230 ,
000 sin-gle tag and 13 , ±
120 double tag D ¯ D events, and 167 ,
000 single tag and8 , ±
97 double tag D + D − events.The D and D + branching fractions are determined from a simultaneousleast squares ( χ ) fit to all D and D + single and double tag yields. The fitproperly takes into account correlations among all statistical and systematicuncertainties. The preliminary branching fractions based on 281 pb − data arelisted in Table 1 and compared to the 2004 PDG averages 3), which does notinclude our earlier results based on 56 pb − data 4), in Fig. 2.Table 1: Preliminary D and D + branching fractions with statistical and sys-tematic uncertainties. Decay B (%) D → K − π + . ± . ± . D → K − π + π . ± . ± . D → K − π + π − π + . ± . ± . D + → K − π + π + . ± . ± . D + → K − π + π + π . ± . ± . D + → K S π + . ± . ± . D + → K S π + π . ± . ± . D + → K S π + π − π + . ± . ± . D + → K − K + π + . ± . ± . D ⋆ ± s D ∓ s events, we use the beam-constrained mass( M bc = p E − ( ~p D s ) ) and the invariant mass ( M ( D s ) = q E D s − ( ~p D s ) )of the D s (or ¯ D s ) candidate and ignore the γ or π resulting from the D ⋆s decay.The beam-constrained mass is used as a proxy for the momentum of the D s candidates (see Fig. 3). We apply a cut on M bc that selects all of the directly-produced D s and, depending on the decay mode, all or half of the secondary D s . Then the invariant mass of the D s candidate is used as a primary analysisvariable to extract the number of tags. Single tag yields are obtained fromfitting the one dimensional M ( D s ) distributions, while double tag yields aredetermined by counting events in the signal regions in the M ( D + s ) vs. M ( D − s )plane and subtracting backgrounds estimated from sideband regions.For this analysis, we use a binned likelihood hybrid fitter which utilizesGaussian statistics for single tag modes and Poisson statistics for double tagmodes, since the least squares χ fitter used for the D branching fraction mea-surement is not appropriate for the small signals and backgrounds in the D s double tag samples. The preliminary branching fractions based on 195 pb − data are summarized in Table 2 and compared to the 2006 PDG averages 5)igure 2: Ratio of preliminary D hadronic branching fractions to the 2004 PDGaverages (dots). The shaded bars represent the errors in the PDG averages. Figure 3: M bc distribution for D + s → K + K − π + events. The narrow peakat . GeV/ c is due to D s produced directly, while the broad peak between . − . GeV/ c is due to D s from D ⋆s decay. ranching Fraction (%) ’ h + p h + p - p + p + p p + p - K + K + p - K + K + K S K ’ h + p h + p - p + p + p p + p - K + K + p - K + K + K S K PDG 2006 fit -1 CLEO Preliminary, 195 pb
Figure 4:
Preliminary D s branching fractions (dots with error bars) comparedto the 2006 PDG averages (shaded bars). in Fig. 4.Table 2: Preliminary D s branching fractions with statistical and systematicuncertainties. Decay B (%) D + → K S K + . ± . ± . D + → K + K − π + . ± . ± . D + → K + K − π + π . ± . ± . D + → π + π + π − . ± . ± . D + → π + η . ± . ± . D + → π + η ′ . ± . ± . D + s → φπ + → K + K − π + , which is one of the largest andeasiest to reconstruct, is frequently used as a reference mode to normalizeother D s decays. However, Dalitz plot analysis of this final state by the E687and FOCUS collaborations has revealed significant signal contribution (from f (980) or a (980)) in the relevant K + K − mass region. Because of this extrasignal the φπ + branching fraction might be ill-measured depending on thespecific choice of (mass and helicity angle) cuts. Therefore, we report thepartial D + s → K + K − π + branching fraction ( B ∆ M ) where the mass of the K + K − system lies within a ± ∆ M (in MeV/ c ) mass range around the φ mass1019 . c ), which is more useful from experimental point of view thanthe φπ + branching fraction. The partial branching fraction with two choicesof ∆ M are B = (1 . ± . ± . B = (2 . ± . ± . D + and D + s leptonic decays and decay constants f D ( s ) In the Standard Model (SM), purely leptonic decays D +( s ) → ℓ + ν ℓ proceedvia the annihilation of the constituent quarks into a virtual W + boson. Thedecay width is proportional to the decay constant, f D ( s ) , which encapsulatesthe strong interaction dynamics in the decay:Γ( D +( s ) → ℓ + ν ) = G F π m M (cid:18) − m M (cid:19) | V cd ( s ) | f D ( s ) , (2) m and M are the mass of the charged lepton and the D ( s ) meson, respectively, G F is the Fermi coupling constant, V cd ( V cs ) is the relevant quark mixing(CKM) matrix element.Knowledge of the decay constants is critical for the extraction of CKMmatrix elements: e.g. the determination of V td and V ts from measurement of B ¯ B and B s ¯ B s mixing is limited by the uncertainty in the calculation of f B and f B s , which currently cannot be measured directly. Experimental measurementof the D meson decay constants ( f D ( s ) ) provide an important test of strong in-teraction theories and validate the most promising calculations involving latticeQCD 6).Since the decay width is a function of m (helicity suppression), the decayrate to τ ν is the largest among the three lepton flavors. Although the D + ( D + s ) decay rate to µν is a factor of 2.65 (9.72) smaller in the SM, it is easierto measure than the decay to τ ν because of the presence of extra neutrino(s)produced by the subsequent decay of the τ . The decay rate to eν is suppressedby about five orders of magnitude which is well below the current experimentalsensitivity. Any deviation from the SM ratios would be an indication of newphysics 7).CLEO has measured the D + → µ + ν branching fraction in 281 pb − datacollected at the ψ (3770) 8). We have fully reconstructed the D − decaying tosix hadronic final states ( K + π − π − , K + π − π − π , K S π − , K S π − π − π + , K S π − π , K + K − π − ), which represent more then 35% of all D decays. Candidates areselected by requiring ∆ E to be consistent with zero within 2 . σ ∆ E , and thenumber of tags in each mode is extracted from a fit to the M bc distribution. Thesum of all tags in the range − . σ M bc < M bc − M D < . σ M bc is 158 , ± , µ + and calculate the missing mass squared M M = ( E beam − E µ + ) − ( − ~p D − − ~p µ + ) , (3)igure 5: The
M M distribution for D + → µ + ν candidate events in data. Theinsert shows the region around zero where the arrows indicate the ± σ signalregion. where ~p D − is the three-momentum of the fully reconstructed D − . The M M distribution for the data is shown in Fig. 5. The peak near zero is mostly dueto D + → µ + ν signal, while the peak at 0 .
25 GeV is from D + → ¯ K π + decayswhen a K L escapes detection.The signal region within 2 σ around zero contains 50 events and the totalbackground is estimated to be 2 . ± . +0 . − . events. After background sub-traction and efficiency correction, the measured branching fraction is B ( D + → µ + ν ) = (4 . ± . +0 . − . ) × − . The decay constant obtained from Eq.2 using | V cd | = 0 . ± . D + lifetime (1 . ± .
007 ps) is f D = (222 . ± . +2 . − . ) MeV.We also search for D + → e + ν decay by requiring that the extra track isconsistent with an electron and set a 90% C.L. upper limit of B ( D + → e + ν ) < . × − in the absence of any signal.The branching fraction of D + s → µ + ν and D + s → τ + ν ( τ + → π + ¯ ν ) ismeasured in 314 pb − data collected at e + e − collision energy near 4170 MeV.We fully reconstruct one D − s in eight hadronic decay modes ( K + K − π − , K S K − , ηπ − , η ′ π − , φρ − , π + π − π − , K ⋆ − K ⋆ , ηρ − ). Tags are selected by requiring thebeam constrained mass to be 2 . < M bc < .
067 GeV/ c which is widenough to accepts both direct as well as secondary D s from D ⋆s decay. Thenumber of tags in each mode is extracted from a fit to the invariant massdistribution of the D − s candidates. There is a total of 31 , ±
472 reconstructedtags within 2 . σ (2 σ for the ηρ − mode) of the D s mass. In contrast to thehadronic branching fraction measurement, we select a γ candidate assumed tobe the photon from the D ⋆s → γD s decay, and then calculate the recoil massagainst the D − s tag and the γ : M M ⋆ = ( E cm − E D s − E γ ) − ( ~p cm − ~p D s − ~p γ ) , (4)where E cm ( ~p cm ) the center of mass energy and momentum of the colliding e + e − beam. Regardless whether the D − s candidate is from the D ⋆s decay ornot the recoil mass should peak at the D s mass. We use kinematic constrainsto improve the mass resolutions and remove multiple combinations. The recoilmass spectrum of each decay mode is fitted individually to extract the numberof D ⋆s D s candidates, which result in a total of 18 , ±
426 events within 2 . σ interval around the D s mass. The invariant mass and recoil mass distributionsfor D − s → K + K − π − candidates are shown in Fig. 6.Figure 6: Invariant mass of D − s → K + K − π − tags (left) and the recoil massagainst the same tag and an additional γ (right). Then we require a single additional track in the event with opposite chargeto the D s tag and no additional neutral energy cluster with more then 300MeV. The missing mass is calculated using the energy and momentum of thecandidate track ( E µ , ~p µ ): M M = ( E cm − E D s − E γ − E µ ) − ( ~p cm − ~p D s − ~p γ − ~p µ ) . (5)We consider three cases depending on whether the additional track is consistentwith (i) muon (from D s → µν ), or (ii) pion (from D s → τ ν → πν ¯ ν ), or (iii)lectron (from D s → eν ). The separation between our muon and pion selectionis not complete: the muon selection is 99% efficient for muons (with a 60% fakerate for pions), while the pion selection accepts 40% of pions (with a 1% fakerate for muons). The M M distribution for the three cases is shown on Fig.7. The peak around zero in (i) is mostly due to D s → µν events. In contrast, D s → τ ν → πν ¯ ν events has a longer tail on the positive side due to the extraneutrino. Therefore, we define three signal regions: (A) − . < M M < . in (i) for µν (92 events); (B) 0 . < M M < .
20 GeV in (i) and (C) − . < M M < .
20 GeV in (ii) for πν ¯ ν (31 and 25 events, respectively).The estimated background from sources other than D s → µν or πν ¯ ν decays is3 .
5, 3 .
5, and 3 . The
M M distribution in data when the additional track is consistentwith muon (i), pion (ii), or electron (iii). We calculate three branching fractions: B ( D + s → µ + ν ) = (0 . ± . ± . B eff ( D + s → µ + ν ) = (0 . ± . ± . B ( D + s → τ + ν ) = (8 . ± . ± . τ ν regions (B)+(C). In thefirst two cases, the D s → τ ν contribution is subtracted assuming the relativeecay rate between µν and τ ν final states is equal to the SM expectation andusing B ( τ → πν ) = (10 . ± . B ( D + s → e + ν ) < . × − .The decay constant is calculated from the most precise branching fraction( B eff ) using Eq. 2 with | V cs | = 0 . D s life time of (500 ± × − s: f D s = (270 ± ±
7) MeV.We also measure D + s → τ + ν with a different technique utilizing the τ + → e + ν ¯ ν decay with a total product branching fraction of about 1 . D − s candidate in the event and require an additionaltrack consistent with an e + but do not attempt to find the γ from the D ⋆s decay.Events with additional tracks and more than 400 MeV total neutral energy inthe calorimeter are vetoed (the typical energy of the γ or π from D ⋆ decay isaround 150 MeV). After analyzing 195 pb − subsample of our data we obtaina preliminary branching fraction B ( D + s → τ + ν ) = (6 . ± . ± . f D s = (278 ± ±
12) MeV.The weighted average of these two results is f D s = (273 ± ±
5) MeV.Combined with our published f D value we find a ratio f D s /f D = 1 . ± . ± .
03. The measured decay constants are consistent with most theoretical mod-els. In particular, recent unquenched Lattice QCD calculations 9) yield f D =(201 ± ±
17) MeV, f D s = (249 ± ±
16) MeV, and f D s /f D = 1 . ± . ± . D mass Precise knowledge of the D mass is not only important for its own sake butit can also help with the interpretation of the X (3872) state. Because of theproximity of the X mass (3871 . ± . c ) to M ( D ) + M ( D ⋆ ), onetheoretical suggestion is that the X (3872) is a bound state of D and ¯ D ⋆ mesons 10). However, it is necessary to measure the D mass with betterprecision than the current PDG average of 1864 . ± . c
5) in order toreach a firm conclusion.CLEO has measured the D mass 11) in e + e − → ψ (3770) → D ¯ D events using the decay D → K S φ followed by K S → π + π − and φ → K + K − .In order to obtain a clean sample of signal events, the ¯ D has been reconstructedusing the same tagging technique described in section 2, imposing loose require-ments on ∆ E and M bc of the candidates. The D → K S φ decay was selectedbecause the final state pions and kaons have small momenta, and therefore theuncertainty in their measurements makes small contribution to the final result.In addition, the mass of the K S candidates can be kinematically constrainedto its well known value.Pions from the K S are required to originate from a displaced vertex andhave a M ( π + π − ) invariant mass in the range 497 . ± . c beforethe mass-constrained kinematic fit. The φ candidates are accepted with a ( K + K − ) invariant mass of 1019 . ±
15 MeV/ c . The mass distribution ofthe D candidates in 281 pb − data is shown in Fig. 8. A likelihood fit usinga Gaussian peak and a constant background yields 319 ± D events anda D mass of 1864 . ± .
150 MeV/ c with a mass resolution of 2 . ± . c (the errors are statistical only). The total systematic error on themass measurement (0 .
095 MeV/ c ) is dominated by uncertainty in detectorcalibration, which is studied using the K S mass in inclusive D → K S X decaysand the ψ (2 S ) mass in exclusive ψ (2 S ) → π + π − J/ψ ( J/ψ → µ + µ − ) events.Figure 8: The invariant mass of D → K s φ candidates in data. Our final D mass with statistical and systematic uncertainties is M ( D ) = 1864 . ± . ± .
095 MeV /c . (6)This gives M ( D ¯ D ⋆ ) = 2 M ( D ) + ∆ M D ⋆ − D = 3871 . ± .
36 MeV/ c ,and leads to a binding energy of the X(3872) as a D ¯ D ⋆ molecule: ∆ E b = M ( D ¯ D ⋆ ) − M ( X ) = +0 . ± . c . The error in the binding energy isnow dominated by the uncertainty in the mass of the X (3872). χ cJ → h + h − h decays In contrast to the 1 −− members of the charmonium states ( J/ψ , ψ (2 S )), thedecays of the χ cJ ( J = 0 , ,
2) states are not well studied. The different decaymechanism of these states (dominated by annihilation into two (virtual) gluonsand contribution from the color-octet mechanism) might provide complimen-ary information on light hadron spectroscopy and possible glueball dynamics12). At CLEO, the χ cJ states are produced in radiative decays of the ψ (2 S )and we study their decays to eight selected three-body hadronic modes: π + π − η , K + K − η , p ¯ pη , π + π − η ′ , K + K − π , p ¯ pπ , π + K − K S , and K + ¯ p Λ. We have mea-sured branching fractions or set upper limits for the first time in most casesusing about 3 million ψ (2 S ) decays 13). As an example, Fig. 9 illustrates theinvariant mass distribution for two of the hadronic final states.Figure 9: The invariant mass distribution for χ cJ → K + ¯ p Λ (left) and χ cJ → π + π − η (right) candidate events in data. We perform a Dalitz-plot analysis of the decays with the highest statis-tics, χ c → π + π − η (228 events), K + K − π (137 events), and π + K − K S (234events) in order to study the two-body resonant substructure. We use a sim-plified model with non-interfering resonances, which is adequate to show thelargest contributions in our small sample. Fig. 10 shows the Dalitz plot andthree projections for χ c → π + π − η and the result of the fit. There are clearcontributions from a (980) ± π ∓ and f (1270) η intermediate states, and a sig-nificant accumulation of events at low π + π − mass which can be described byan S-wave ( σ ) resonance. This mode might offer the best measurement of the a (980) parameters with higher statistics. The decays χ c → K + K − π and π + K − K S are analyzed simultaneously taking advantage of isospin symmetry.We observe contributions from K ⋆ (892) K , K ⋆ (1430) K , a (980) π intermediatestates. It is not clear whether the K ⋆ (1430) is K ⋆ or K ⋆ , and other Kπ and KK resonances can contribute. Addition of κK or non-resonant componentdoes not improve the fit and the significance of their contribution remains under3 standard deviation.More data is required to do a complete partial-wave analysis taking intoigure 10: Dalitz plot and projections of χ c → π + π − η decay. account the χ c polarization properly and including interference among theresonances. I have reported mostly preliminary results for hadronic and purely leptonicdecays of D and D s mesons from the CLEO-c experiment. These results rep-resent substantial improvement over previous measurements. The D + and D hadronic branching fractions are limited by systematic uncertainties of up to3%. The D s hadronic branching fractions are measured with relative uncer-tainties between 6 − f D ( f D ( s ) ) from purely leptonic decays are also statisticslimited with a total relative uncertainty of 8% (4%).I have also presented the most precise measurement of the D mass, anda study of three-body hadronic decays of the χ cJ states.Precision of these and other measurements will improve in the near futurewith more data on the way. CLEO-c has already collected an additional 8 timesmore data on the ψ (2 S ), and we plan to increase the D ¯ D and D ⋆ ± s D ∓ s datasamples by a factor of 2-3 before data taking ends in April 2008. I would like to thank the conference organizers for the invitation and warmhospitality, and acknowledge my colleagues at CLEO and CESR for their hardwork in achieving the results presented in this report. This research was sup-ported by the US National Science Foundation.
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