The study of the charmed meson decays is getting a renewable interest because it provides a critical input to the CKM-γ measurements. In addition the discovery of new physics can be revealed in the search for the mixing and CP

violation and the large coupling to the light mesons makes charm decays an important probe of light meson spectroscopy. The Dalitz plot technique and a selection of recent experimental results are briefly reviewed

Pappagallo, M.

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DOI 10.1393/ncc/i2009-10453-1Colloquia: IFAE 2009IL NUOVO CIMENTO Vol. 32 C, N. 3-4 Maggio-Agosto 2009Charmed meson decays: Theoretical overview andexperimental resultsM. PappagalloUniversita` di Bari and INFN, Sezione di Bari - Bari, Italy(ricevuto il 19 Settembre 2009; pubblicato online il 13 Novembre 2009)Summary. — The study of the charmed meson decays is getting a renewable in-terest because it provides a critical input to the CKM-γ measurements. In additionthe discovery of new physics can be revealed in the search for the mixing and CPviolation and the large coupling to the light mesons makes charm decays an impor-tant probe of light meson spectroscopy. The Dalitz plot technique and a selectionof recent experimental results are briefly reviewed.PACS 11.80.Et – Partial-wave analysis.PACS 11.30.Er – Charge conjugation, parity, time reversal, and other discretesymmetries.PACS 12.15.Hh – Determination of Kobayashi-Maskawa matrix elements.PACS 13.25.Ft – Decays of charmed mesons.1. – IntroductionThe Dalitz plot analysis is an invaluable technique exploited to study the three-bodydecay. The decay amplitude can be written as the sum of partial waves labeled by theangular momentum quantum number: S-wave, P -wave, D-wave, . . . Analyses typicallyuse an isobar model formulation in which each wave is described by a coherent sum of anumber of quasi–two-body (resonance+bachelor) amplitudes where the bachelor particleis one of the three final-state products, and the resonance decays to the remaining pairby a Breit-Wigner propagator. Sometimes such formalism is believed to be unsuitablefor the S-wave and a K-matrix formalism is preferred. A Model Independent PartialWave Analysis (MIPWA) [1] is an alternative formalism where the S-wave is defined asan interpolation between points in the complex plane. The magnitude and phase of eachpoint are considered floated parameters of a fit.2. – Measurement of CKM γ angleDeterminations of the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements provideimportant tests on the consistency of the standard model and ways to search for newc© Societa` Italiana di Fisica 143144 M. PAPPAGALLOa) b) c) d)Fig. 1. – CP -even tagged K0Sπ+π− Dalitz plot (a), and its m2(π+π−) projection (b). CP -oddtagged K0Sπ+π− Dalitz plot (c), and its m2(π+π−) projection (d) (CLEO-c Collaboration).physics. The angle γ is the less constrained and therefore it is object of accurate measure-ments. The most powerful manner in which to measure the angle γ is with B− → D˜0K−decays. Here, D˜0 is either D0 or D¯0, and both decay to the same final state, and sotheir amplitudes interfere. One of the most promising D˜0 decays for measuring γ usingthis method is D˜0 → K0Sπ+π−(D˜0 → K0SK+K−), because it is Cabibbo favored (CF)for both D0 and D¯0 decays, thus providing large event yields.The B-factory experiments have devoted a great deal of effort to modelling the D˜0 →K0Sπ+π− decay for the purposes of the γ measurement [2,3]. A recent BABAR study hasused a sample of 487 k flavour tagged D∗+ → D0(K0Sπ+π−)π+ events and a sample of69 k flavour tagged D∗+ → D0(K0SK+K−)π+ events. The former sample is fitted byan isobar model involving ten resonances and a K-matrix and LASS parametrization todescribe the π+π− and the K0Sπ contributions, respectively. The latter sample is fittedby a pure isobar model involving only eight resonances. The resulting measurements of γangle suffer of a systematic uncertainties of 5◦ arising from how well the model representsreality. However this model systematic is uncomfortable for future very high statisticsmeasurements (e.g., LHCb, Super-B).The CLEO-c Collaboration employs an alternative and model-independent approachby exploiting the quantum coherence of D0-D¯0 pairs at the Ψ(3770) [4]. Because ofthis quantum correlation, K0Sπ+π− decays recoiling against flavor tags, CP -tags, andD0 → K0Sπ+π− tags, taken together provide direct sensitivity to the strong phase dif-ference. Figure 1 shows the K0Sπ+π− Dalitz plots and the corresponding projectionsmade with the CLEO-c data for CP -even and CP -odd tags. The difference in struc-ture is apparent, for example the absence of the K0Sρ0 peak in the events containing aCP -odd tag. This measurement will result in a substantial reduction in the systematicuncertainty associated with the interference effects between B− → D0(K0Sπ+π−)K−and B− → D¯0(K0Sπ+π−)K−. Such systematic is estimated 1.7◦. It is not related to anymodel and it depends only on the statistic of the CLEO-c data sample.3. – Search for CP violationWithin the Standard Model, the CP -violating effects are predicted to be negligiblysmall in D decays (O(10−5–10−4)). Observation of a larger CP violation will constitutean unambiguous signal of new physics.The BABAR Collaboration searches for time-integrated CP violation in the three-bodysingly Cabibbo suppressed (SCS) decays D0 → π+π−π0 and D0 → K+K−π0 [5]. Thesedecays proceed via CP eigenstates (e.g., ρπ0, φπ0) and also via flavor states (e.g., ρ±π∓,CHARMED MESON DECAYS: THEORETICAL OVERVIEW AND EXPERIMENTAL RESULTS 145K∗±K∓), thus making it possible to probe CP violation in both types of amplitudesand in the interference between them. Four approaches are adopted, three of which aremodel independent. No evidence of CP violation has been found and any CP violationin the SCS charm decays occurs at a rate which is not larger than a few percent.Assuming the validity of the CPT theorem, an alternative approach to test the pres-ence of CP violation is to search for T violation. A T violation effect can come outby measuring a non-zero value of ATviol ≡ 12 (AT − A¯T ), where AT is the T -odd asym-metry. The FOCUS Collaboration measures such asymmetry in the singly Cabibbosuppressed decay D0 → K+K−π+π− [6]. A sample of 828±46 events shows no evidenceof T -violation (ATviol(D0) = 0.010 ± 0.057(stat) ± 0.037(syst)). A precision of 4 · 10−3could be achieved with the BABAR dataset.4. – Scalar meson spectroscopySome puzzles still remain in light meson spectroscopy. The scalar resonances JPC =0++ are too numerous to fit in a single SU(3) octet. This makes still opened the discussionof the existence of broad states close to threshold such as k(800) and f0(600) and of thepossibility that states such as the a0(980) or f0(980) may be 4-quark states, due to theirproximity to the KK¯ threshold.4.1. k(800) and the D+ → K−π+π+ decay . – The D+ → K−π+π+ decay was oncethought to require very large, constant NR amplitudes. Using larger sample, the FermilabE791 Collaboration found that a satisfactory description of these decays requires morestructure. By including S-wave isobar k(800) → K−π+, a much-improved modelling ofthe Dalitz plot was achieved, and the need for a constant NR term was much reduced.Later the E791 Collaboration has redone the Dalitz plot analysis implementing a modelindependent partial wave analyis for the K−π+ S-wave [1]. A significant phase variationis observed over the full range of invariant mass, with the strongest variation near theK∗0 (1430) resonance. The magnitude is largest just above threshold, peaking at about0.725GeV/c2, above which it falls. A shoulder is seen at the mass of the K∗0 (1430), afterwhich the magnitude falls sharply to its minimum value just above 1.5GeV/c2. FinallyE791 states that, at the statistical level, differences between the MIPWA and the isobarmodel result are not found to be significant, and both provide good descriptions of thedata.The CLEO-c Collaboration found the E791 results are not suitable to describe theDalitz plot of its high statistic sample of D+ → K−π+π+ (140 k events) [7]. Bothisobar and MIPWA approach are performed by adding a I = 2 π+π+ contribution whoseparametrization is taken from the scattering experiments. The addition of the I = 2π+π+ S-wave to either the isobar model or the MIPWA approach results the key piecethat gives good agreement with data in both cases. The magnitude plot does not showany peak just above the threshold and the K−π+ S-wave has a almost flat behavior butin the K∗0 (1430) region.4.2. f0(980) and D+s decays. – In Cabibbo favored decays of D+s mesons the primaryc quark converts into an s quark under emission of an external W+ while the s¯ quarkacts as a spectator particle. The most likely decay of the W+ produces a π+ and theremaining ss¯ system hadronizes into resonances, such as f0(980), f0(1370), f0(1500),f2(1270), . . .. Studying the D+s → π+π−π+ and D+s → K+K−π+ decays can explorethe property of these mesons decaying to the π+π− and K+K− systems.146 M. PAPPAGALLO01020300 0.5 1 1.5 2(a)m(π+ π-) (GeV/c2)Amplitude-5-3-113570 0.5 1 1.5 2(b)m(π+ π-) (GeV/c2)Phase (rad)Fig. 2. – Magnitude (a) and phase (b) of the π+π− S-wave (BABAR Collaboration).The BABAR Collaboration reports in a recent paper the Dalitz plot analysis ofD+s → π+π−π+ where a MIPWA approach is used for the π+π− S-wave [8]. Thedecay is dominated by the π+π− S-wave and there is also an important contributionfrom f2(1270). The S-wave shows, in both magnitude and phase (fig. 2), the expectedbehavior for the f0(980) resonance. The S-wave shows further activity in the regionsof the f0(1370) and f0(1500) resonances. The S-wave is small in the f0(600) region,indicating that this resonance has a small coupling to ss¯.The D+s → K+K−π+ decay has been studied by the BABAR [9] and CLEO-c [10]Collaborations as well. The decay is dominated by P -waves: D+s → φπ+ and D+s →K¯∗(892)0K+. The f0(980) contribution is large but affected by big systematic uncertain-ties due to the interference with the f0(1370) whose parameters are not well measured.The D+s → K+K−π+ decay is also suitable to explore the Kπ S-wave. The 〈Y 01 〉 spher-ical moments in the K−π+ system hints a very small S − P interference in low K−π+mass region and therefore the absence of a k(800) contribution. The fit results confirmthe Kπ S-wave is well described by a K∗0 (1430) contribution only.REFERENCES[1] Aitala E. M. et al. (E791 Collaboration), Phys. Rev. D, 73 (2006) 032004.[2] Aubert B. et al. (BABAR Collaboration), Phys. Rev. D, 78 (2008) 034023.[3] Abe K. et al. (Belle Collaboration), [arXiv:0803.3375].[4] Briereit R. A. et al. (CLEO Collaboration), Phys. Rev. D, 80 (2009) 032002.[5] Aubert B. et al. (BABAR Collaboration), Phys. Rev. D, 78 (2008) 051102.[6] Link J. M. et al. (FOCUS Collaboration), Phys. Lett. B, 622 (2005) 239.[7] Bonvicini G. et al. (CLEO Collaboration), Phys. Rev. D, 78 (2008) 052001.[8] Aubert B. et al. (BABAR Collaboration), Phys. Rev. D, 79 (2009) 032003.[9] Pappagallo M. (BABAR Collaboration), [arXiv:0711.4769].[10] Mitchell R. E. et al. (CLEO Collaboration), Phys. Rev. D, 79 (2009) 072008.

Charmed meson decays: Theoretical overview and experimental results

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Charmed meson decays: Theoretical overview and experimental results

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