Charm Baryon Spectroscopy
Primary Authors: Felix Wick, Michal Kreps, Thomas Kuhr, Michael Feindt
The excited charm baryons &Lambda_{c}(2595), &Lambda_{c}(2625), &Sigma_{c}(2455) and &Sigma_{c}(2520) are examined in their strong decays to the &Lambda_{c} ground state, &Lambda_{c}^{*+} &rarr &Lambda_{c}^{+} &pi^{+} &pi^{} respective &Sigma_{c}^{0,++} &rarr &Lambda_{c}^{+} &pi^{,+}. Measurements of the mass differences of these resonances to the &Lambda_{c} mass and the corresponding decay widths are performed. It turns out that the &Lambda_{c}(2595) mass shape is affected by kinematical threshold effects in the resonant subdecays &Lambda_{c}(2595) &rarr &Sigma_{c}(2455) &pi . This leads to a &Lambda_{c}(2595) mass which is approximately 3 MeV/c^{2} lower than the previously measured values.
The results were blessed on July 1, 2010.
Because of its rich mass spectrum and the relatively narrow widths of the resonances the charmed baryon system makes a good testing ground for the heavy quark symmetry. With the excellent tracking and mass resolution of the CDF detector and the large amount of available data it is possible to improve previous mass difference and decay width measurements of the states &Lambda_{c}(2595)^{+}, &Lambda_{c}(2625)^{+}, &Sigma_{c}(2455)^{0,++} and &Sigma_{c}(2520)^{0,++}.
References to previous experimental results:
&Lambda_{c}(2595)^{+} 
&Lambda_{c}(2625)^{+} 
&Sigma_{c}(2455)^{0,++} 
&Sigma_{c}(2520)^{0,++} 
Phys. Lett. B402, 207 
Phys. Lett. B402, 207 
Phys. Rev. D65, 071101 
Phys. Rev. D71, 051101 
Phys. Lett. B365, 461 
Phys. Rev. Lett. 74, 3331 
Phys. Lett. B525, 205 
Phys. Rev. Lett. 78, 2304 
Phys. Rev. Lett. 74, 3331 
Phys. Rev. Lett. 72, 961 
Phys. Lett. B488, 218 

By means of a proper inclusion of kinematical threshold effects in the resonant decays &Lambda_{c}(2595)^{+} &rarr &Sigma_{c}(2455)^{0,++} &pi^{+,}, a direct experimental determination of the pion coupling constant h_{2} in the chiral Lagrangian is feasible (Phys. Rev. D67, 074033). The knowledge of h_{2} provides information about other excited charm and bottom baryons (Phys. Rev. D56, 5483; Phys. Rev. D56, 6738).
We take advantage of the hadronic trigger on displaced tracks for the selection of secondary vertex decays (Two Track Trigger). The &Lambda_{c}^{+} is reconstructed in its decay to p K^{} &pi^{+} and then combined with one respective two additional tracks with &pi^{+} mass hypothesis to build the &Sigma_{c} and &Lambda_{c}^{*} candidates. Our data sample corresponds to an integrated luminosity of 5.2 fb^{1}.
After some slight precuts, neural networks (NeuroBayes program package) are applied in two successive steps to distinguish between signal and background. First, a pure &Lambda_{c} network is employed which is then used as input for &Sigma_{c} and &Lambda_{c}^{*} networks. Thereby, the trainings are solely based upon real data by means of _{s}Plot weights, what has the advantage of being independent of simulated events.
A binned maximum likelihood method is employed in order to fit the distributions of the mass differences m(&Lambda_{c}^{+} &pi^{})m(&Lambda_{c}^{+}), m(&Lambda_{c}^{+} &pi^{+})m(&Lambda_{c}^{+}) and m(&Lambda_{c}^{+} &pi^{+} &pi^{})m(&Lambda_{c}^{+}) of the selected candidates. Thereby, the signals are convolutions of nonrelativistic BreitWigner functions with the corresponding detector resolutions which are determined from Monte Carlo simulations.
For the &Lambda_{c}(2595)^{+}, the consideration of kinematical threshold effects in the resonant decays to &Sigma_{c}(2455)^{0,++} &pi^{+,} is necessary. This is done by using a massdependent width in the BreitWigner function. Then, instead of &Gamma(&Lambda_{c}(2595)^{+}), the second parameter of the BreitWigner function is h_{2} which can therefore be determined directly.
The backgrounds consist of three different constituents:
 combinatorial background without real &Lambda_{c}^{+}
 real &Lambda_{c}^{+} with random tracks
 contaminations from &Lambda_{c}^{*} feeddown in &Sigma_{c} spectra and &Sigma_{c} with random track in &Lambda_{c}^{*} spectrum
Main sources of systematic uncertainties:
 detector resolutions (uncertainties on the Monte Carlo simulations)
 overall mass scale (magnetic field and energy loss uncertainties in momentum scale calibration)
 fit models
 external input for &Lambda_{c}(2595) signal shape (uncertainties on &Sigma_{c}(2455) PDG values)
In order to estimate the reliability of the detector resolutions determined from Monte Carlo simulations, the reference decays D^{*}(2010)^{+} &rarr D^{0} &pi^{+} and &psi(2S) &rarr J/&psi &pi^{+} &pi^{} are considered because of the similarities of their decay topologies to &Sigma_{c}^{0,++} &rarr &Lambda_{c}^{+} &pi^{,+} and &Lambda_{c}^{*+} &rarr &Lambda_{c}^{+} &pi^{+} &pi^{}, respectively. In particular, the dependencies of the detector resolutions in data and Monte Carlo on the transverse momenta of the slow pion(s) are examined.

m  m(&Lambda_{c}^{+}) [MeV/c^{2}] 
&Gamma [MeV/c^{2}] 
h_{2}^{2} 
&Sigma_{c}(2455)^{0} 
167.28 ± 0.03 (stat.) ± 0.12 (syst.) 
1.65 ± 0.11 (stat.) ± 0.49 (syst.) 

&Sigma_{c}(2455)^{++} 
167.44 ± 0.04 (stat.) ± 0.12 (syst.) 
2.34 ± 0.13 (stat.) ± 0.45 (syst.) 

&Sigma_{c}(2520)^{0} 
232.88 ± 0.43 (stat.) ± 0.16 (syst.) 
12.51 ± 1.82 (stat.) ± 1.37 (syst.) 

&Sigma_{c}(2520)^{++} 
230.73 ± 0.56 (stat.) ± 0.16 (syst.) 
15.03 ± 2.12 (stat.) ± 1.36 (syst.) 

&Lambda_{c}(2595)^{+} 
305.79 ± 0.14 (stat.) ± 0.20 (syst.) 
2.59 ± 0.30 (stat.) ± 0.47 (syst.) 
0.36 ± 0.04 (stat.) ± 0.07 (syst.) 
&Lambda_{c}(2625)^{+} 
341.65 ± 0.04 (stat.) ± 0.12 (syst.) 
< 0.97 (90% CL) 

Comparison of our measurements (statistical and systematic uncertainties added in quadrature) with PDG values (in parentheses):

m  m(&Lambda_{c}^{+}) [MeV/c^{2}] 
&Gamma [MeV/c^{2}] 
&Sigma_{c}(2455)^{0} 
167.28 ± 0.12 (167.30 ± 0.11) 
1.65 ± 0.50 (2.2 ± 0.4) 
&Sigma_{c}(2455)^{++} 
167.44 ± 0.13 (167.56 ± 0.11) 
2.34 ± 0.47 (2.23 ± 0.30) 
&Sigma_{c}(2520)^{0} 
232.88 ± 0.46 (231.6 ± 0.5) 
12.51 ± 2.28 (16.1 ± 2.1) 
&Sigma_{c}(2520)^{++} 
230.73 ± 0.58 (231.9 ± 0.6) 
15.03 ± 2.52 (14.9 ± 1.9) 
&Lambda_{c}(2595)^{+} 
305.79 ± 0.24 (308.9 ± 0.6) 
2.59 ± 0.56 (3.6^{+2.0}_{1.3}) 
&Lambda_{c}(2625)^{+} 
341.65 ± 0.13 (341.7 ± 0.6) 
< 0.97 (90% CL) (1.9 (90% CL)) 
The analysis at hand is the one with the highest number of signal events for all the reviewed resonances, what leads to the most accurate values for the &Lambda_{c}^{*} properties. The significant difference in m(&Lambda_{c}(2595)^{+})m(&Lambda_{c}^{+}) is due to our proper treatment of the kinematical threshold effects. Furthermore, some of the previously measured values of the &Sigma_{c} properties show tensions between the different experiments, so that our measurements can have important impact.
 Table 1: Systematic Uncertainties on &Sigma_{c}^{0}
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 Table 2: Systematic Uncertainties on &Sigma_{c}^{++}
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 Table 3: Systematic Uncertainties on &Lambda_{c}^{*}
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 Table 4: Final Results
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 Table 5: Results with combined Uncertainties
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 Table 6: &Lambda_{c}^{+} Precuts
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 Table 7: &Lambda_{c}^{+} Network Variables
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 Table 8: &Sigma_{c} Precuts
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 Table 9: &Sigma_{c} Network Variables
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 Table 10: &Lambda_{c}^{*} Precuts
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 Table 11: &Lambda_{c}^{*} Network Variables
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 Table 12: &Sigma_{c} Resolutions
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 Table 13: &Lambda_{c}^{*} Resolutions
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 Table 14: Resolutions with and without Monte Carlo Reweighting
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 Figure 7: &Lambda_{c}^{+} Spectrum before Network Cut
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 Figure 8: &Lambda_{c}^{+} Dalitz Structure
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 Figure 9: &Lambda_{c}^{+} Network Variables (PID_{p})
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 Figure 10: &Lambda_{c}^{+} Network Variables (L_{xy} Error)
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 Figure 11: &Lambda_{c}^{+} Network Variables (PID_{K})
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 Figure 12: &Lambda_{c}^{+} Network Variables (Angle(p))
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 Figure 13: &Lambda_{c}^{+} Network Variables (&chi^{2})
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 Figure 14: &Lambda_{c}^{+} Network Variables (L_{xy})
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 Figure 15: &Lambda_{c}^{+} Network Variables (d_{0} Significance(&pi))
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 Figure 16: &Lambda_{c}^{+} Network Variables (p_{t}(p))
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 Figure 17: &Lambda_{c}^{+} Network Variables (Angle(K))
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 Figure 18: &Lambda_{c}^{+} Network Variables (p_{t}(&pi))
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 Figure 19: &Lambda_{c}^{+} Network Variables (d_{0} Significance(K))
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 Figure 20: &Lambda_{c}^{+} Network Variables (p_{t}(K))
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 Figure 21: &Lambda_{c}^{+} Network Variables (d_{0} Significance(p))
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 Figure 22: &Lambda_{c}^{+} Fit
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 Figure 23: &Sigma_{c}^{0} Spectrum before Network Cut
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 Figure 24: &Sigma_{c}^{++} Spectrum before Network Cut
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 Figure 25: &Sigma_{c}^{0} Network Variables (&Lambda_{c} NN Output)
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 Figure 26: &Sigma_{c}^{0} Network Variables (ct)
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 Figure 27: &Sigma_{c}^{0} Network Variables (&chi^{2})
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 Figure 28: &Sigma_{c}^{0} Network Variables (d_{0} Error)
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 Figure 29: &Sigma_{c}^{0} Network Variables (d_{0}(&pi))
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 Figure 30: &Sigma_{c}^{++} Network Variables (&Lambda_{c} NN Output)
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 Figure 31: &Sigma_{c}^{++} Network Variables (ct)
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 Figure 32: &Sigma_{c}^{++} Network Variables (&chi^{2})
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 Figure 33: &Sigma_{c}^{++} Network Variables (d_{0} Error)
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 Figure 34: &Sigma_{c}^{++} Network Variables (d_{0}(&pi))
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 Figure 35: &Sigma_{c}^{0} from &Lambda_{c}^{+} Sidebands
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 Figure 36: &Sigma_{c}^{++} from &Lambda_{c}^{+} Sidebands
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 Figure 37: &Sigma_{c}^{0} from &Lambda_{c}^{+} Sidebands (pt Cut)
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 Figure 38: &Sigma_{c}^{0} from &Lambda_{c}^{+} Sidebands (PIDK Cut)
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 Figure 39: &Lambda_{c}^{*} Spectrum before Network Cut
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 Figure 40: &Lambda_{c}^{*} Network Variables (&chi^{2})
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 Figure 41: &Lambda_{c}^{*} Network Variables (d_{0} Error)
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 Figure 42: &Lambda_{c}^{*} Network Variables (&Lambda_{c} NN Output)
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 Figure 43: &Lambda_{c}^{*} Network Variables (ct)
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 Figure 44: &Lambda_{c}^{*} from &Lambda_{c}^{+} Sidebands
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 Figure 45: &Lambda_{c}^{*} Wrong Sign Combinations
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 Figure 46: &Lambda_{c}^{*} Right and Wrong Sign Combinations
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 Figure 47: p_{t} Distributions of &Sigma_{c}(2455)^{0} Decay Products before reweighting (&pi(&Sigma_{c}))
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 Figure 48: p_{t} Distributions of &Sigma_{c}(2455)^{0} Decay Products before reweighting (p(&Lambda_{c}))
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 Figure 49: p_{t} Distributions of &Sigma_{c}(2455)^{0} Decay Products before reweighting (K(&Lambda_{c}))
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 Figure 50: p_{t} Distributions of &Sigma_{c}(2455)^{0} Decay Products before reweighting (&pi(&Lambda_{c}))
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 Figure 51: p_{t} Distributions of &Sigma_{c}(2455)^{0} Decay Products after reweighting (&pi(&Sigma_{c}))
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 Figure 52: p_{t} Distributions of &Sigma_{c}(2455)^{0} Decay Products after reweighting (p(&Lambda_{c}))
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 Figure 53: p_{t} Distributions of &Sigma_{c}(2455)^{0} Decay Products after reweighting (K(&Lambda_{c}))
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 Figure 54: p_{t} Distributions of &Sigma_{c}(2455)^{0} Decay Products after reweighting (&pi(&Lambda_{c}))
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 Figure 55: p_{t} Distributions of &Sigma_{c}(2455)^{++} Decay Products before reweighting (&pi(&Sigma_{c}))
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 Figure 56: p_{t} Distributions of &Sigma_{c}(2455)^{++} Decay Products before reweighting (p(&Lambda_{c}))
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 Figure 57: p_{t} Distributions of &Sigma_{c}(2455)^{++} Decay Products before reweighting (K(&Lambda_{c}))
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 Figure 58: p_{t} Distributions of &Sigma_{c}(2455)^{++} Decay Products before reweighting (&pi(&Lambda_{c}))
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 Figure 59: p_{t} Distributions of &Sigma_{c}(2455)^{++} Decay Products after reweighting (&pi(&Sigma_{c}))
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 Figure 60: p_{t} Distributions of &Sigma_{c}(2455)^{++} Decay Products after reweighting (p(&Lambda_{c}))
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 Figure 61: p_{t} Distributions of &Sigma_{c}(2455)^{++} Decay Products after reweighting (K(&Lambda_{c}))
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 Figure 62: p_{t} Distributions of &Sigma_{c}(2455)^{++} Decay Products after reweighting (&pi(&Lambda_{c}))
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 Figure 63: p_{t} Distributions of &Lambda_{c}(2625)^{+} Decay Products before reweighting (&pi_{1}(&Lambda_{c}^{*}))
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 Figure 64: p_{t} Distributions of &Lambda_{c}(2625)^{+} Decay Products before reweighting (&pi_{2}(&Lambda_{c}^{*}))
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 Figure 65: p_{t} Distributions of &Lambda_{c}(2625)^{+} Decay Products before reweighting (p(&Lambda_{c}))
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 Figure 66: p_{t} Distributions of &Lambda_{c}(2625)^{+} Decay Products before reweighting (K(&Lambda_{c}))
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 Figure 67: p_{t} Distributions of &Lambda_{c}(2625)^{+} Decay Products before reweighting (&pi(&Lambda_{c}))
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 Figure 68: p_{t} Distributions of &Lambda_{c}(2625)^{+} Decay Products after reweighting (&pi_{1}(&Lambda_{c}^{*}))
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 Figure 69: p_{t} Distributions of &Lambda_{c}(2625)^{+} Decay Products after reweighting (&pi_{2}(&Lambda_{c}^{*}))
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 Figure 70: p_{t} Distributions of &Lambda_{c}(2625)^{+} Decay Products after reweighting (p(&Lambda_{c}))
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 Figure 71: p_{t} Distributions of &Lambda_{c}(2625)^{+} Decay Products after reweighting (K(&Lambda_{c}))
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 Figure 72: p_{t} Distributions of &Lambda_{c}(2625)^{+} Decay Products after reweighting (&pi(&Lambda_{c}))
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 Figure 73: &Sigma_{c}(2455)^{0} Resolution
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 Figure 74: &Sigma_{c}(2455)^{++} Resolution
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 Figure 75: &Sigma_{c}(2520)^{0} Resolution
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 Figure 76: &Sigma_{c}(2520)^{++} Resolution
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 Figure 77: &Lambda_{c}(2595)^{+} Resolution
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 Figure 78: &Lambda_{c}(2625)^{+} Resolution
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 Figure 79: &Sigma_{c}^{0} from &Lambda_{c}^{+} Sidebands Fit
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 Figure 80: &Sigma_{c}^{++} from &Lambda_{c}^{+} Sidebands Fit
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 Figure 81: &Lambda_{c}^{*} TwoBody Spectra
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 Figure 82:&Lambda_{c}(2595)^{+} TwoBody Fits (&Sigma_{c}(2455)^{0})
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 Figure 83: &Lambda_{c}(2595)^{+} TwoBody Fits (&Sigma_{c}(2455)^{++})
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 Figure 84: &Lambda_{c}(2595)^{+} Widths
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 Figure 85: &Lambda_{c}^{*} from &Lambda_{c}^{+} Sidebands Fit
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 Figure 86: &Sigma_{c} Yields in &Lambda_{c}^{*} Spectrum (&Sigma_{c}^{0})
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 Figure 87: &Sigma_{c} Yields in &Lambda_{c}^{*} Spectrum (&Sigma_{c}^{0})
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 Figure 88: &Gamma(&Lambda_{c}(2625)^{+}) Upper Limit
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