Polarimetry in Λ_c⁺ → p K⁻ π⁺

\(\Lambda^+_\mathrm{c}\) polarimetry using the dominant hadronic mode

The polarimeter vector field for multibody decays of a spin-half baryon is introduced as a generalisation of the baryon asymmetry parameters. Using a recent amplitude analysis of the \(\Lambda^+_\mathrm{c} \to p K^- \pi^+\) decay performed at the LHCb experiment, we compute the distribution of the kinematic-dependent polarimeter vector for this process in the space of Mandelstam variables to express the polarised decay rate in a model-agnostic form. The obtained representation can facilitate polarisation measurements of the \(\Lambda^+_\mathrm{c}\) baryon and eases inclusion of the \(\Lambda^+_\mathrm{c} \to p K^- \pi^+\) decay mode in hadronic amplitude analyses.

Symbolic expressions

Compute the amplitude model over large data samples with symbolic expressions.

JSON grids

Reuse the computed polarimeter field in any amplitude analysis involving \(\Lambda_\mathrm{c}^+\).

Inspect interactively

Investigate how parameters in the amplitude model affect the polarimeter field.

Compute polarization

Learn how to determine the polarization vector using the polarimeter field.

Download this website as a single PDF file

This website shows all analysis results that led to the publication of LHCb-PAPER-2022-044. More information on this publication can be found on the following pages:

• Publication on arXiv: arXiv:2301.07010

• Record on CDS: cds.cern.ch/record/2838694

• Record for the source code on Zenodo: 10.5281/zenodo.7544989

• Frozen documentation on GitLab Pages: lc2pkpi-polarimetry.docs.cern.ch

• Frozen repository on CERN GitLab: gitlab.cern.ch/polarimetry/Lc2pKpi

• Active repository on GitHub containing discussions: github.com/ComPWA/polarimetry

Behind SSO login (LHCb members only)

• LHCb TWiki page: twiki.cern.ch/twiki/bin/viewauth/LHCbPhysics/PolarimetryLc2pKpi

• Charm WG meeting: indico.cern.ch/event/1187317

• RC approval presentation: indico.cern.ch/event/1213570

• Silent approval to submit: indico.cern.ch/event/1242323

Table of contents

• 1. Nominal amplitude model
  • 1.1. Resonances and LS-scheme
  • 1.2. Amplitude
  • 1.3. Parameter definitions
• 2. Cross-check with LHCb data
  • 2.1. Lineshape comparison
  • 2.2. Amplitude comparison
• 3. Intensity distribution
  • 3.1. Definition of free parameters
  • 3.2. Distribution
  • 3.3. Decay rates
  • 3.4. Dominant decays
• 4. Polarimeter vector field
  • 4.1. Dominant contributions
  • 4.2. Total polarimetry vector field
  • 4.3. Aligned vector fields per chain
• 5. Uncertainties
  • 5.1. Model loading
  • 5.2. Statistical uncertainties
  • 5.3. Systematic uncertainties
  • 5.4. Uncertainty on polarimetry
  • 5.5. Decay rates
  • 5.6. Average polarimetry values
  • 5.7. Exported distributions
• 6. Average polarimeter per resonance
  • 6.1. Computations
  • 6.2. Result and comparison
  • 6.3. Distribution analysis
• 7. Appendix
  • 7.1. Dynamics lineshapes
  • 7.2. DPD angles
  • 7.3. Phase space sample
  • 7.4. Alignment consistency
  • 7.5. Benchmarking
  • 7.6. Serialization
  • 7.7. Amplitude model with LS-couplings
  • 7.8. SU(2) → SO(3) homomorphism
  • 7.9. Determination of polarization
  • 7.10. Interactive visualization
• 8. Bibliography
• 9. API
  • 9.1. amplitude
  • 9.2. lhcb
  • 9.3. data
  • 9.4. decay
  • 9.5. dynamics
  • 9.6. function
  • 9.7. io
  • 9.8. plot
  • 9.9. spin

Tip

Several cross-checks with Julia can be found here.

Tip

Figures for the paper can be downloaded here:

Figure 2

total-polarimetry-field-watermark.svg

Figure 3a

polarimetry-field-L1520-unaligned-watermark.svg

Figure 3b

polarimetry-field-L1520-aligned-watermark.svg

Figure 4

polarimetry-field-norm-uncertainties-watermark.png

All other exported figures can be found here.

Notebook execution times

Document	Modified	Method	Run Time (s)	Status
amplitude-model	2023-01-18 12:00	cache	21.62	✅
appendix/alignment	2023-01-18 12:02	cache	79.29	✅
appendix/angles	2023-01-04 14:29	cache	3.56	✅
appendix/benchmark	2023-01-18 12:04	cache	149.07	✅
appendix/dynamics	2023-01-18 12:04	cache	4.19	✅
appendix/homomorphism	2023-01-04 14:35	cache	4.66	✅
appendix/ls-model	2023-01-04 14:40	cache	273.6	✅
appendix/phase-space	2023-01-18 12:05	cache	48.6	✅
appendix/serialization	2023-01-18 15:58	cache	123.74	✅
appendix/widget	2023-01-04 15:02	cache	1188.16	✅
cross-check	2023-01-18 12:06	cache	45.81	✅
intensity	2023-01-18 12:14	cache	470.18	✅
polarimetry	2023-01-04 15:19	cache	426.89	✅
resonance-polarimetry	2023-01-18 13:11	cache	3450.05	✅
uncertainties	2023-01-11 17:15	cache	927.81	✅
zz.polarization-fit	2023-01-04 17:52	cache	396.85	✅