

 21 Mar 1994

Precision Measurement of the D+

\Lambda

s \Gamma D

+ s Mass Difference

We have measured the vector-pseudoscalar mass splitting M(D

\Lambda +s ) \Gamma M(D+s ) = 144:22 \Sigma

0:47 \Sigma 0:37MeV , significantly more precise than the previous world average. We minimize the systematic errors by also measuring the vector-pseudoscalar mass difference M(D

\Lambda 0) \Gamma

M(D0) using the radiative decay D

\Lambda 0 ! D0fl, obtaining [M(D\Lambda +s ) \Gamma M(D+s )] \Gamma [M(D\Lambda 0) \Gamma

M(D0)] = 2:09 \Sigma 0:47 \Sigma 0:37MeV . This is then combined with our previous high-precision measurement of M(D

\Lambda 0) \Gamma M(D0), which used the decay D\Lambda 0 ! D0ss0. We also measure

the mass difference M(D+s ) \Gamma M(D+) = 99:5 \Sigma 0:6 \Sigma 0:3 MeV, using the OEss+ decay modes of the Ds and D+ mesons.

I. INTRODUCTION Mass splittings between states with the same quark content but different spin configurations give essential information on the nature of the interquark potential. For example, masses of states with orbital angular momentum can be used to probe the contributions to the potential from spin-orbit and tensor forces between the quarks. High-precision measurements of mass splittings between states without orbital excitation (e.g., the pseudoscalar and vector S-states studied in this paper) give information on the relative contributions of chromoelectric and chromomagnetic terms to the Hamiltonian. Comparing the masses of resonant states having the same spin and charge configuration, but differing in the mass of one of the constituent quarks can isolate the effects of individual terms in the interquark potential. Of particular interest here is the vectorpseudoscalar mass splitting for c_s mesons compared with c_d mesons, as these are identical in the flavor SU(3) limit. Differences between them are presumably due to differences in the chromomagnetic contribution to the interquark potential and to the different value of the wave function at the origin, because of the different light quark mass.

Using the decay modes D

\Lambda + ! D+ss0 and D\Lambda 0 ! D0ss0, CLEO II recently produced the definitive

measurements of the mass splittings between the vector and pseudoscalar non-strange charmed mesons: M (D

\Lambda +) \Gamma M (D+), and M (D\Lambda 0) \Gamma M (D0) [?]. These high precision measurements were made possible by:

a) the large data sample accumulated by the CLEO II experiment, b) the CLEO II crystal calorimeter, which allowed us to reconstruct the decay mode D

\Lambda ! Dss0 with high efficiency and good resolution, and c) the

fact that the decay through pion emission is close to threshold, giving excellent precision on the D

\Lambda mass.

Although there were a comparable number of observed events corresponding to the radiative decay D

\Lambda 0 !

D0fl, this mode was not used because the larger Q-value degrades the mass-difference precision relative to the D

\Lambda 0 ! D0ss0 mode. However, having measured the D\Lambda 0 \Gamma D0 splitting to an accuracy of better than 100

KeV using the pionic mode, we can use this to calibrate the mass difference measurement in the radiative mode. This, in turn, can be used to eliminate many systematic errors in our measurements of D

\Lambda +

s ! Dsfl.

II. DETECTOR, DATA SAMPLE, AND EVENT SELECTION The CLEO II detector is a general purpose solenoidal magnet spectrometer and calorimeter. Elements of the detector, and performance characteristics, are described in detail elsewhere [?]. The detector is designed to have high efficiency for triggering and reconstruction of both leptonic and hadronic events. Charged particle momentum measurements are made with three nested coaxial drift chambers consisting of 6, 10, and 51 layers, respectively. These chambers fill the volume r=3 cm to r=1 m, where r is the radial coordinate relative to the beam (z) axis. Eleven of the layers in the main 51-layer drift chamber have sense-wires which are slanted relative to the beam axis to give measurements of the coordinate along z. More precise measurements of the z-coordinate are obtained from cathode pads located at the interfaces of the three tracking chambers. The system achieves a momentum resolution of (ffip=p)2 = (0:0015p)2 + (0:005)2, where p is the momentum, measured in GeV/c. Pulse height measurements in the main 51-layer drift chamber provide dE/dx resolution of 6.5% for Bhabhas, giving good ss=K separation up to momenta of 700 MeV/c. Outside the central tracking chambers are plastic scintillation counters which are used as a fast element in the trigger system and also give particle identification information from time of flight measurements. The scintillation counters have a resolution of 154 ps as measured for hadrons, allowing better than 3oe ss=K separation up to momenta of 1.2 GeV/c.

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Beyond the time of flight system is the electromagnetic calorimeter, consisting of 7800 thallium doped CsI crystals [?]. The crystal array gives an energy resolution of approximately 4% at 100 MeV and 1.2% at 5 GeV. The central "barrel" region of the detector covers a solid angle of 75% of 4ss. The endcap regions extend the solid angle coverage of the calorimeter to 95% of 4ss, although with poorer energy resolution than the barrel region. The tracking system, time of flight counters, and calorimeter are installed in a 1.5 T superconducting coil. Flux return and tracking chambers used for muon detection are located immediately outside the coil and in the two endcap regions.

A. Data Sample The data sample consists of 1:70fb

\Gamma 1 of e+e\Gamma annihilations collected at CESR at energies just above and

below the \Upsilon (4S) resonance, and on the \Upsilon (4S) resonance itself; the total data sample corresponds to about 2 \Theta 106 produced c_c pairs. All events with 3 or more charged tracks, 1.5 GeV of energy measured in the calorimeter, and having a measured event vertex along the z-coordinate within 5 cm of the known interaction point, are accepted as hadronic event candidates. These events are then used for reconstruction of charmed mesons.

B. Charged Particle and Neutral Particle Selection Our study requires the reconstruction of Ds and D+ in the OEss+ mode (with OE ! K+K

\Gamma ), and D0 in

the K

\Gamma ss+ mode, as well as reconstruction of photons from the radiative transition between the vector and

pseudoscalar states. We impose cuts on candidate tracks, requiring mainly that they come from the primary vertex. Candidate charged and neutral particles must satisfy the requirements listed in Table ??. We impose a ss0 veto on each photon candidate. The ss0 veto is implemented by matching photon candidates with other photon candidates passing the same quality cuts listed in Table ??. If their invariant mass falls within 2.5oe (approximately 12 MeV) of the known ss0 mass and if they give a good kinematic fit to the ss0 hypothesis, these photons are eliminated from further consideration.

III. STUDY OF THE D+S -D+ MASS DIFFERENCE We begin our study by focusing on the reconstruction of the OEss+ decay mode. We require that the two candidate kaons from the OE have particle identification information consistent with that expected for real kaons. There is a large background due to uncorrelated OE and ss+ candidates, which peaks at cos`OE = 1, where `OE is the decay angle of the OE measured in the charmed-meson rest frame with respect to the charmedmeson momentum vector in the lab frame. The cut cos`OE ! 0:8 is effective in reducing this background while retaining 90% of the isotropic signal.

In decays of pseudoscalar charmed mesons into OEss+, the OE is polarized and its decay helicity angle (defined as the angle between one of the daughter kaons and the parent charmed-meson in the OE frame) follows a cos2`helicity distribution. To improve signal-to-noise we require that jcos`helicityj ?0.4. To suppress combinatoric background, we take advantage of the characteristic hard fragmentation function of charmed particles and impose the requirement xp(= pcandidate=pmax) ?0.5. With the above cuts, we obtain the OEss+ invariant mass plot shown in Fig. 1; the mass plot has been fit to two Gaussian signals (representing D+ ! OEss+, and Ds ! OEss+) on top of a smooth background. The fit to the D+ ! OEss+ and Ds ! OEss+ peaks yields approximately 400 and 1400 events, respectively.

We use these fitted signals to determine the mass difference between the Ds and D+ mesons. Although uncertainties in the overall mass scale are on the order of 1-2 MeV, we expect the systematic error in the determination of the difference in masses to be much smaller. Contributions to the overall systematic uncertainty may arise from fitting (which we determine to be 0.25 MeV by varying the fit interval and the background function), and from possible differences between the lab momentum spectra of the OE and ss daughters in the two cases. We probe the latter effect by fitting the mass difference in bins of scaled momentum xp, as shown in Fig. 2. The data are consistent with no variation as a function of xp at the 67% confidence level, and we attribute a systematic error less than 0.1 MeV due to such a dependence. We arrive at a total systematic error of 0.3 MeV, and are therefore able to determine the difference in masses

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3030194-001 FIG. 1. Invariant mass of OEss+ combinations. The smaller peak is the D+ ! OEss+ signal and the larger peak is the D+s ! OEss+ signal.

3030194-002

FIG. 2. Mass difference between D+ and D+s , where both mesons are observed in the OEss+ mode, as a function of scaled momentum xp.

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between the Ds and D+ to be 99.5\Sigma 0.6\Sigma 0.3 MeV. This value compares well with the present Particle Data Group value of 99.5\Sigma 0.6 MeV [?].

IV. DETERMINATION OF THE D

\Lambda +

S -DS MASS DIFFERENCE

With our large sample of D+s ! OEss+, we can make a precise measurement of the D

\Lambda +s -Ds mass difference.

The previous best measurement of this mass difference was made by the ARGUS collaboration who obtained a value of 142.5\Sigma 0.8\Sigma 1.5 MeV [?]. The statistical precision of their measurement was limited by their small sample of D

\Lambda +

s ! Dsfl events in which the photons converted to e

+e\Gamma pairs. Their systematic precision was

limited by the relatively large uncertainty in the calibration mode D

\Lambda 0 ! D0fl.

The CLEO measurement is made in the following manner. First, we combine D+s candidates with photon candidates and use the resulting D

\Lambda +s ! Dsfl signal to measure the mass-difference \Delta fls =M(D\Lambda +s )-M(D+s ),

where the s subscript on \Delta indicates that we are considering the c_s meson, and the fl superscript indicates that the measurement is made using photon transitions. This raw mass-difference is still susceptible to errors in the overall photon energy calibration1 which may be effectively eliminated as follows. Using the photon transition D

\Lambda 0 ! D0fl, we similarly measure \Delta flu = M (D\Lambda 0) \Gamma M (D0), which allows us to calculate the

difference between the two mass-differences ffiM=\Delta fls \Gamma \Delta flu. This may then be used with the high precision measurement of \Delta ssu (using D

\Lambda 0 ! D0ss0) [?] to obtain \Delta s = \Delta ssu + ffiM .

By imposing the same photon requirements in our measurements of the two radiative transitions under consideration we can extract \Delta s relatively free of uncertainties in the absolute photon energy calibration. This technique is limited largely by differences in fitting the two signals due to the presence of the large D

\Lambda 0 ! D0ss0 feed-down in the D0fl mass-difference plot. There are no hadronic decays of the D\Lambda +s states to

produce such a reflection in the D

\Lambda +s ! Dsfl mass-difference plot.

A. Measurement of \Delta fls As discussed above, we reconstruct D

\Lambda +s 's in the mode D\Lambda +s ! Dsfl. In order to improve the signal-to-noise

we cut on the decay angle `fl of the photon in the D

\Lambda +s frame. Requiring cos`fl ? -0.7 eliminates a significant

background, as is evident from Fig. 3. This requirement is made in addition to the other photon cuts detailed in Table ??.

Figure 4 shows the distribution we obtain for M (OEss+fl) \Gamma M (OEss+). The mass-difference distribution is fit to the sum of a smooth polynomial plus a "Crystal Ball Line Shape"2 around the region of the expected signal.3 The width of the signal and the magnitude of the tail are set at values obtained from Monte Carlo simulations. The mass difference we obtain from this direct measurement is 144.70\Sigma 0.42 MeV, where the error is statistical only.

B. Measurement of \Delta flu and Determination of ffiM We reconstruct D0's in the mode D0 ! K

\Gamma ss+. The mass-difference signal M (D0fl) \Gamma M (D0) is shown

in Fig. 5 with two different fits overlaid. To obtain this mass-difference plot, we used the same photon cuts as in the D

\Lambda +s ! Dsfl analysis. As before, we perform a fit (Fig. 5a) using the Crystal Ball Line shape

function plus a smooth background. We explicitly exclude the low mass enhancement from D

\Lambda 0 ! D0ss0

from the fit region. The mass difference obtained is \Delta flu = 142:61 \Sigma 0:21 MeV (statistical errors only). This

1The photon energy calibration is based on fitting the observed ss0 mass peak over a wide range of ss0 momenta. 2The Crystal Ball Line Shape is a nearly Gaussian distribution with a tail on the low end to take into account

processes which may give an undermeasurement of the true photon energy.

3The enhancement at low mass-difference arises from misidentified D\Lambda + ! D+ss0 events where the D+ decays to a

three-body final state such as K

\Gamma ss+ss+. When one of the final state particles is misidentified, kinematic reflections

can occur in a mass region around the Ds ! OEss+ signal. This has been verified by examining mass-differences using OEss+ combinations from the Ds sideband region.

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3030194-010 FIG. 3. M(OEss+fl)-M(OEss+) vs. cos`fl where `fl is the photon emission angle in the OEss+fl frame relative to the OEss+fl direction in the lab. Transition photon candidates are required to have cos`fl ? -0.7, as described in the text.

3030194-007

FIG. 4. Mass difference between Dsfl and Ds with fit overlaid.

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may be compared with the value obtained from the ss0 transition, \Delta ssu = 142:12 \Sigma 0:05 \Sigma 0:05 MeV, indicating that our overall photon energy calibration is understood to within 0.5% for the photons of interest in this measurement. To test fitting systematics, we perform an additional fit to this mass-difference plot (shown in Fig. 5b), where we explicitly account for the reflection from the hadronic mode. This is detailed further in our discussion of systematic errors.

Comparing the mass differences obtained from Fig. 5a and Fig. 4, we determine ffiM=\Delta fls \Gamma \Delta flu = 2.09\Sigma 0.47 MeV as summarized in Table ??. Combining this value with \Delta ssu gives \Delta s = 144:22\Sigma 0.47 MeV. The errors quoted in both numbers are statistical errors only.

C. Systematic Errors Systematic uncertainties arise from sources which affect \Delta fls and \Delta flu differently and therefore introduce shifts in ffiM . To the extent that the D

\Lambda +s and D\Lambda 0 fragmentation functions are different, photon energy

calibration uncertainties can introduce systematic shifts, although the good agreement between \Delta flu and \Delta ssu indicates that the photon energy scale is relatively well-understood. As is evident from Figs. 4 and 5, the background shapes are different in the two cases and there are therefore additional uncertainties arising from signal extraction systematics.

We have studied possible biases using Monte Carlo simulations. Given input values of M (D

\Lambda 0) \Gamma M (D0)

and M (D

\Lambda +s ) \Gamma M (D+s ) we are able to recover values which are consistent with the input numbers after

processing the Monte Carlo data through our analysis software. For the D

\Lambda +

s ! Dsfl transition, for example,inputting a mass difference between D \Lambda +s and Ds of 142.60 MeV, we recover a value of 142.55\Sigma 0.15 MeV.

We have investigated the dependence of the measured mass-difference on the photon energy and on the momentum of the D

\Lambda +s , which is correlated with the photon energy. Figure 6 demonstrates that the

dependence of the measured mass-difference on transition photon energy is not large. Figure ?? shows the measured mass difference as a function of the scaled momentum xp of the D

\Lambda +s . The plot is consistent with

no variation of mass difference with momentum. We therefore attribute no additional systematic error to such sources.

There is also an uncertainty of \Sigma 0.5% in the absolute photon energy calibration which results in an error of \Sigma 0.7 MeV in \Delta fls and \Delta flu as shown in Table II. However the contribution to ffiM=\Delta fls \Gamma \Delta flu is only \Sigma 0.02 MeV since the systematic errors essentially cancel each other.

Although systematics due to uncertainties in the overall energy calibration largely cancel, fitting systematics remain. For the signal parameterization, we have checked that variations of signal shape produce shifts in both \Delta fls and \Delta flu which track each other and therefore cancel in the value of ffiM . The presence of the low mass enhancement due to the hadronic decay D

\Lambda 0 ! D0ss0 can distort the shape of the background4

in the case of the calibration mode D

\Lambda 0 ! D0fl. We have done a variety of fits using different assumptions

for the photon line shape plus the possible background shapes in order to quantify the extent to which the hadronic decay can change the value of the mass difference we derive. Such a distribution is shown as the overlaid histogram in Fig. 5b. In this case, we have fit our observed signal to a sum of three pieces: a) a mass-difference background (whose shape is obtained from Monte Carlo studies) due to feed-down from D

\Lambda 0 ! D0ss0, ss0 ! flfl, where one of the ss0 daughter photons is reconstructed and the second is not detected

in the calorimeter, b) a signal representing D

\Lambda 0 ! D0fl, whose shape was also determined by Monte Carlo

simulation, and c) a mass-difference background, obtained from M (K

\Gamma ss+fl) \Gamma M (K\Gamma ss+), where the K\Gamma ss+

combination is taken from the D0 sideband regions. This gives a good fit to the data, indicating that we are able to account for the various components of the observed mass-difference plot. From this fit (Fig. 5b), we obtain a value of the mass difference \Delta flu of 142.75\Sigma 0.24 MeV. This compares well with the mass difference of 142.61\Sigma 0.21 MeV obtained from Fig. 5a. We assign a systematic error contribution of 0.3 MeV to the measurement of \Delta flu and 0.2 MeV to \Delta fls , and conservatively assume the errors are totally uncorrelated in determining the contribution to the overall systematic error in ffiM .

The results of these measurements are summarized in Table ??.

4Note, however, that the hadronic mode is kinematically prohibited from producing background in the region of the D

\Lambda 0 ! D0fl mass-difference signal.

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3030194-003 3030194-006 FIG. 5. D

\Lambda 0 - D0 mass difference distribution. a) Shows a fit to the signal expected from true D\Lambda 0 ! D0fl plus

a smooth background, as done with D

\Lambda +s ! Dsfl, and b) shows a fit to contributions arising from true D\Lambda 0 ! D0fl,

D

\Lambda 0 ! D0ss0, and random photon plus fake D0 combinations, as described in text.

3030194-004

FIG. 6. D

\Lambda 0 \Gamma D0 mass difference as a function of photon energy.

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V. DETERMINATION OF UPPER LIMIT ON D

\Lambda +

S WIDTH

It is straightforward to determine a limit on the intrinsic width of the D

\Lambda +s meson. The measured upper

limit on the intrinsic width of the D

\Lambda 0 is \Gamma ! 2:1 MeV [?]. If we perform a free fit to the mass-difference

signals observed in D

\Lambda 0 ! D0fl (Fig. 5) and D\Lambda +s ! Dsfl (Fig. 4), using the same signal shape but allowing

the width of the photon peak to vary, we obtain values of 4.50\Sigma 0.24 and 4.29\Sigma 0.40 MeV for the widths of the respective signals. Relating this to the intrinsic and experimental widths of the two resonances, we have:q

oe2D\Lambda 0 + oe2exptl = 4:50 \Sigma 0:24M eV; qoe2D\Lambda

s + oe

2 exptl = 4:29 \Sigma 0:40M eV: (1)

Assuming that the experimental resolutions oeexptl are identical for D

\Lambda 0 ! D0fl and D\Lambda +s ! Dsfl, we can

square and subtract these two expressions to obtain \Gamma D\Lambda s ! 4.9 MeV at 90% confidence level. This technique is, at present, limited by the statistical precision on the \Delta fl measurements.

VI. SUMMARY We have made a new measurement of the mass difference between the Ds and the D+ mesons, obtaining a value (99.5\Sigma 0.6\Sigma 0.3 MeV) in good agreement with the present world average, and with comparable errors. Calibrating our D

\Lambda +s -Ds mass-difference using the mass-difference observed in the D\Lambda 0 ! D0fl mode, we

determine ffiM=\Delta fls \Gamma \Delta flu=2.09\Sigma 0.47\Sigma 0.37 MeV. Combining this value with our previous measurement of the D

\Lambda 0 \Gamma D0 mass difference [?], we determine M(D\Lambda +s )-M(D+s )=144.22\Sigma 0.47\Sigma 0.37 MeV. This value is much

more precise than the previous world average of 142.4\Sigma 1.7 MeV [?].

It is of interest to compare the vector-pseudoscalar mass splitting for the c_s system with that of the c_d system. Two factors in the expression for the mass difference depend on the mass of the light quark: (i) the chromomagnetic effect is expected to be smaller for the c_s system due to the heavier strange quark, but (ii) the square of the wave function overlap at the origin is expected to be larger because of the larger reduced mass of the strange quark. Our measurements indicate a larger vector-pseudoscalar splitting in the c_s system than in the c_d system, indicating that wave function overlap is the dominant effect.

Finally, using the signal we observe in both the D

\Lambda 0 ! D0fl and D\Lambda +s ! Dsfl modes, we determine the

intrinsic full width of the D

\Lambda +s to be !4.91 MeV at 90% confidence level.

Table ?? summarizes the vector and pseudoscalar splittings obtained by this and previous measurements.

ACKNOWLEDGEMENTS We gratefully acknowledge the effort of the CESR staff in providing us with excellent luminosity and running conditions. This work was supported by the National Science Foundation and the U.S. Dept. of Energy.

[1] D. Bortoletto et al., Phys. Rev. Lett. 69, 2046 (1992). [2] H. Albrecht et al., Phys. Lett. B207, 349 (1988). [3] Y. Kubota et al., "The CLEO-II detector", Nucl. Instr. Methods. A320, 66 (1992). [4] The resolution for the crystal calorimeter is oeEE (%) = 0:35E0:75 + 1:9 \Gamma 0:1E, where E is the photon energy in GeV. [5] K. Hikasa et al., Phys. Rev. D 45, 1 (1992). [6] We use GEANT version 3.14, as documented in CERN DD/EE/84-1 (R. Brun et al.). [7] D. Bortoletto et al., Phys. Rev. D 37, 1719 (1988). [8] Y. Kubota et al., Phys. Rev. D 44, 593 (1991).

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3030194-005 FIG. 7. D

\Lambda 0 \Gamma D0 mass difference as a function of scaled D0 momentum (xp).

DOCA for all tracks in jr \Gamma OEj !5 mm

DOCA for all tracks in jr \Gamma zj !5 cm

jdE/dxj deposition for tracks ! 2oe=3oe from expected for K/ss Measured OE(! K+K

\Gamma ) mass \Sigma 2:5oe (10 MeV) of known mass

Measured D+s (! OEss+) mass \Sigma 2:5oe (21 MeV) of known mass Measured D0(! K

\Gamma ss+) mass \Sigma 2:5oe (26 MeV) of known mass

Charmed meson momentum xp ? 0:5 jcos`j for photon candidates !0.7 (barrel region)

Photon candidates unmatched to charged tracks Photon shower isolation ?50 mrad from other showers

Photon energy ? 50 MeV Photon lateral energy deposition 99% probability of coming from true photons

Photon ss0 veto inconsistent with coming from ss0 ! flfl

TABLE I. Summary of Cuts used in the Analysis. ("DOCA" denotes distance of closest approach to the interaction point.)

\Delta fls \Delta flu ffiM=\Delta fls \Gamma \Delta flu Raw \Delta M 144.70 142.61 2.09 Statistical Error \Sigma 0.42 \Sigma 0.21 \Sigma 0.47 Signal width systematic 0.1 0.03 0.1

Signal tail systematic 0.09 0.06 !0.05 Momentum cut systematic - - -

cos`fl cut systematic - - - Background fit systematic 0.3 0.2 0.36 Absolute Efl calibration systematic \Sigma 0.7 \Sigma 0.7 \Sigma 0.02

TABLE II. Summary of Mass-Difference Results. (All numbers are in MeV.)

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M(D+ \Gamma D0) 4.79\Sigma 0.10 MeV [?,?]

M(D+s -D+) 99.5\Sigma 0.67 MeV [?],[this measurement] M(D

\Lambda + \Gamma D\Lambda 0) 3.32\Sigma 0.08\Sigma 0.05 MeV [?]

M(D

\Lambda +s -D+s )-M(D\Lambda 0 \Gamma D0) 2.09\Sigma 0.47\Sigma 0.37 MeV [this measurement]

M(D

\Lambda +s -D+s ) 144.22\Sigma 0.47\Sigma 0.37 MeV [this measurement]

TABLE III. Summary of Charmed Meson Mass Splittings

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