Charm Baryon Spectroscopy

Primary Authors: Felix Wick, Michal Kreps, Thomas Kuhr, Michael Feindt

Contents

Analysis Overview

Motivation
Trigger and Selection
Fit Procedure
Systematic Uncertainties
Validation of Detector Resolutions

Final Results
List of main Tables
List of main Figures
List of supporting Tables
List of supporting Figures

Analysis Overview

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/c² lower than the previously measured values.

The results were blessed on July 1, 2010.

1. Motivation

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 h₂ in the chiral Lagrangian is feasible (Phys. Rev. D67, 074033). The knowledge of h₂ provides information about other excited charm and bottom baryons (Phys. Rev. D56, 5483; Phys. Rev. D56, 6738).

2. Trigger and Selection

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 _sPlot weights, what has the advantage of being independent of simulated events.

3. Fit Procedure

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 Breit-Wigner 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 mass-dependent width in the Breit-Wigner function. Then, instead of &Gamma(&Lambda_c(2595)⁺), the second parameter of the Breit-Wigner function is h₂ 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^* feed-down in &Sigma_c spectra and &Sigma_c with random track in &Lambda_c^* spectrum

4. Systematic Uncertainties

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)

5. Validation of Detector Resolutions

In order to estimate the reliability of the detector resolutions determined from Monte Carlo simulations, the reference decays D^*(2010)⁺ &rarr D⁰ &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.

Final Results

	m - m(&Lambda_c⁺) [MeV/c²]	&Gamma [MeV/c²]	h₂²
&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/c²]	&Gamma [MeV/c²]
&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.

List of main Tables

Table 1: Systematic Uncertainties on &Sigma_c⁰ (eps)
Table 2: Systematic Uncertainties on &Sigma_c⁺⁺ (eps)
Table 3: Systematic Uncertainties on &Lambda_c^* (eps)
Table 4: Final Results (eps)
Table 5: Results with combined Uncertainties (eps)

List of main Figures

Figure 1: &Sigma_c⁰ Spectrum (eps) (png)
Figure 2: &Sigma_c⁺⁺ Spectrum (eps) (png)
Figure 3: &Lambda_c^* Spectrum (eps) (png)
Figure 4: &Sigma_c⁰ Fit (eps) (png)
Figure 5: &Sigma_c⁺⁺ Fit (eps) (png)
Figure 6: &Lambda_c^* Fit (eps) (png)

List of supporting Tables

Table 6: &Lambda_c⁺ Precuts (eps)
Table 7: &Lambda_c⁺ Network Variables (eps)
Table 8: &Sigma_c Precuts (eps)
Table 9: &Sigma_c Network Variables (eps)
Table 10: &Lambda_c^* Precuts (eps)
Table 11: &Lambda_c^* Network Variables (eps)
Table 12: &Sigma_c Resolutions (eps)
Table 13: &Lambda_c^* Resolutions (eps)
Table 14: Resolutions with and without Monte Carlo Reweighting (eps)

List of supporting Figures

Figure 7: &Lambda_c⁺ Spectrum before Network Cut (eps) (png)
Figure 8: &Lambda_c⁺ Dalitz Structure (eps) (png)
Figure 9: &Lambda_c⁺ Network Variables (PID_p) (eps) (png)
Figure 10: &Lambda_c⁺ Network Variables (L_xy Error) (eps) (png)
Figure 11: &Lambda_c⁺ Network Variables (PID_K) (eps) (png)
Figure 12: &Lambda_c⁺ Network Variables (Angle(p)) (eps) (png)
Figure 13: &Lambda_c⁺ Network Variables (&chi²) (eps) (png)
Figure 14: &Lambda_c⁺ Network Variables (L_xy) (eps) (png)
Figure 15: &Lambda_c⁺ Network Variables (d₀ Significance(&pi)) (eps) (png)
Figure 16: &Lambda_c⁺ Network Variables (p_t(p)) (eps) (png)
Figure 17: &Lambda_c⁺ Network Variables (Angle(K)) (eps) (png)
Figure 18: &Lambda_c⁺ Network Variables (p_t(&pi)) (eps) (png)
Figure 19: &Lambda_c⁺ Network Variables (d₀ Significance(K)) (eps) (png)
Figure 20: &Lambda_c⁺ Network Variables (p_t(K)) (eps) (png)
Figure 21: &Lambda_c⁺ Network Variables (d₀ Significance(p)) (eps) (png)
Figure 22: &Lambda_c⁺ Fit (eps) (png)
Figure 23: &Sigma_c⁰ Spectrum before Network Cut (eps) (png)
Figure 24: &Sigma_c⁺⁺ Spectrum before Network Cut (eps) (png)
Figure 25: &Sigma_c⁰ Network Variables (&Lambda_c NN Output) (eps) (png)
Figure 26: &Sigma_c⁰ Network Variables (ct) (eps) (png)
Figure 27: &Sigma_c⁰ Network Variables (&chi²) (eps) (png)
Figure 28: &Sigma_c⁰ Network Variables (d₀ Error) (eps) (png)
Figure 29: &Sigma_c⁰ Network Variables (d₀(&pi)) (eps) (png)
Figure 30: &Sigma_c⁺⁺ Network Variables (&Lambda_c NN Output) (eps) (png)
Figure 31: &Sigma_c⁺⁺ Network Variables (ct) (eps) (png)
Figure 32: &Sigma_c⁺⁺ Network Variables (&chi²) (eps) (png)
Figure 33: &Sigma_c⁺⁺ Network Variables (d₀ Error) (eps) (png)
Figure 34: &Sigma_c⁺⁺ Network Variables (d₀(&pi)) (eps) (png)
Figure 35: &Sigma_c⁰ from &Lambda_c⁺ Sidebands (eps) (png)
Figure 36: &Sigma_c⁺⁺ from &Lambda_c⁺ Sidebands (eps) (png)
Figure 37: &Sigma_c⁰ from &Lambda_c⁺ Sidebands (pt Cut) (eps) (png)
Figure 38: &Sigma_c⁰ from &Lambda_c⁺ Sidebands (PIDK Cut) (eps) (png)
Figure 39: &Lambda_c^* Spectrum before Network Cut (eps) (png)
Figure 40: &Lambda_c^* Network Variables (&chi²) (eps) (png)
Figure 41: &Lambda_c^* Network Variables (d₀ Error) (eps) (png)
Figure 42: &Lambda_c^* Network Variables (&Lambda_c NN Output) (eps) (png)
Figure 43: &Lambda_c^* Network Variables (ct) (eps) (png)
Figure 44: &Lambda_c^* from &Lambda_c⁺ Sidebands (eps) (png)
Figure 45: &Lambda_c^* Wrong Sign Combinations (eps) (png)
Figure 46: &Lambda_c^* Right and Wrong Sign Combinations (eps) (png)
Figure 47: p_t Distributions of &Sigma_c(2455)⁰ Decay Products before reweighting (&pi(&Sigma_c)) (eps) (png)
Figure 48: p_t Distributions of &Sigma_c(2455)⁰ Decay Products before reweighting (p(&Lambda_c)) (eps) (png)
Figure 49: p_t Distributions of &Sigma_c(2455)⁰ Decay Products before reweighting (K(&Lambda_c)) (eps) (png)
Figure 50: p_t Distributions of &Sigma_c(2455)⁰ Decay Products before reweighting (&pi(&Lambda_c)) (eps) (png)
Figure 51: p_t Distributions of &Sigma_c(2455)⁰ Decay Products after reweighting (&pi(&Sigma_c)) (eps) (png)
Figure 52: p_t Distributions of &Sigma_c(2455)⁰ Decay Products after reweighting (p(&Lambda_c)) (eps) (png)
Figure 53: p_t Distributions of &Sigma_c(2455)⁰ Decay Products after reweighting (K(&Lambda_c)) (eps) (png)
Figure 54: p_t Distributions of &Sigma_c(2455)⁰ Decay Products after reweighting (&pi(&Lambda_c)) (eps) (png)
Figure 55: p_t Distributions of &Sigma_c(2455)⁺⁺ Decay Products before reweighting (&pi(&Sigma_c)) (eps) (png)
Figure 56: p_t Distributions of &Sigma_c(2455)⁺⁺ Decay Products before reweighting (p(&Lambda_c)) (eps) (png)
Figure 57: p_t Distributions of &Sigma_c(2455)⁺⁺ Decay Products before reweighting (K(&Lambda_c)) (eps) (png)
Figure 58: p_t Distributions of &Sigma_c(2455)⁺⁺ Decay Products before reweighting (&pi(&Lambda_c)) (eps) (png)
Figure 59: p_t Distributions of &Sigma_c(2455)⁺⁺ Decay Products after reweighting (&pi(&Sigma_c)) (eps) (png)
Figure 60: p_t Distributions of &Sigma_c(2455)⁺⁺ Decay Products after reweighting (p(&Lambda_c)) (eps) (png)
Figure 61: p_t Distributions of &Sigma_c(2455)⁺⁺ Decay Products after reweighting (K(&Lambda_c)) (eps) (png)
Figure 62: p_t Distributions of &Sigma_c(2455)⁺⁺ Decay Products after reweighting (&pi(&Lambda_c)) (eps) (png)
Figure 63: p_t Distributions of &Lambda_c(2625)⁺ Decay Products before reweighting (&pi₁(&Lambda_c^*)) (eps) (png)
Figure 64: p_t Distributions of &Lambda_c(2625)⁺ Decay Products before reweighting (&pi₂(&Lambda_c^*)) (eps) (png)
Figure 65: p_t Distributions of &Lambda_c(2625)⁺ Decay Products before reweighting (p(&Lambda_c)) (eps) (png)
Figure 66: p_t Distributions of &Lambda_c(2625)⁺ Decay Products before reweighting (K(&Lambda_c)) (eps) (png)
Figure 67: p_t Distributions of &Lambda_c(2625)⁺ Decay Products before reweighting (&pi(&Lambda_c)) (eps) (png)
Figure 68: p_t Distributions of &Lambda_c(2625)⁺ Decay Products after reweighting (&pi₁(&Lambda_c^*)) (eps) (png)
Figure 69: p_t Distributions of &Lambda_c(2625)⁺ Decay Products after reweighting (&pi₂(&Lambda_c^*)) (eps) (png)
Figure 70: p_t Distributions of &Lambda_c(2625)⁺ Decay Products after reweighting (p(&Lambda_c)) (eps) (png)
Figure 71: p_t Distributions of &Lambda_c(2625)⁺ Decay Products after reweighting (K(&Lambda_c)) (eps) (png)
Figure 72: p_t Distributions of &Lambda_c(2625)⁺ Decay Products after reweighting (&pi(&Lambda_c)) (eps) (png)
Figure 73: &Sigma_c(2455)⁰ Resolution (eps) (png)
Figure 74: &Sigma_c(2455)⁺⁺ Resolution (eps) (png)
Figure 75: &Sigma_c(2520)⁰ Resolution (eps) (png)
Figure 76: &Sigma_c(2520)⁺⁺ Resolution (eps) (png)
Figure 77: &Lambda_c(2595)⁺ Resolution (eps) (png)
Figure 78: &Lambda_c(2625)⁺ Resolution (eps) (png)
Figure 79: &Sigma_c⁰ from &Lambda_c⁺ Sidebands Fit (eps) (png)
Figure 80: &Sigma_c⁺⁺ from &Lambda_c⁺ Sidebands Fit (eps) (png)
Figure 81: &Lambda_c^* Two-Body Spectra (eps) (png)
Figure 82:&Lambda_c(2595)⁺ Two-Body Fits (&Sigma_c(2455)⁰) (eps) (png)
Figure 83: &Lambda_c(2595)⁺ Two-Body Fits (&Sigma_c(2455)⁺⁺) (eps) (png)
Figure 84: &Lambda_c(2595)⁺ Widths (eps) (png)
Figure 85: &Lambda_c^* from &Lambda_c⁺ Sidebands Fit (eps) (png)
Figure 86: &Sigma_c Yields in &Lambda_c^* Spectrum (&Sigma_c⁰) (eps) (png)
Figure 87: &Sigma_c Yields in &Lambda_c^* Spectrum (&Sigma_c⁰) (eps) (png)
Figure 88: &Gamma(&Lambda_c(2625)⁺) Upper Limit (eps) (png)