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.

https://doi.org/10.1007/JHEP07(2023)228

Symbolic expressions

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

Nominal amplitude model

JSON grids

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

Exported distributions

Inspect interactively

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

Interactive visualization

Compute polarization

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

Determination of polarization

Download this website as a single PDF file

_static/polarimetry.pdf

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 JHEP: J. High Energ. Phys. 2023, 228 (2023)

• 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

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

• Archived 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

Python package

Each of the pages contain code examples for how to reproduce the results with the Python package hosted at github.com/ComPWA/polarimetry. However, to quickly get import the model in another package, it is possible to install the package from PyPI:

pip install polarimetry-lc2pkpi

Each of the models can then simply be imported as

import polarimetry

model = polarimetry.published_model("Default amplitude model")
model.intensity.cleanup()

\[\displaystyle \sum_{\lambda_{0}=-1/2}^{1/2} \sum_{\lambda_{1}=-1/2}^{1/2}{\left|{\sum_{\lambda_0^{\prime}=-1/2}^{1/2} \sum_{\lambda_1^{\prime}=-1/2}^{1/2}{A^{1}_{\lambda_0^{\prime}, \lambda_1^{\prime}, 0, 0} d^{\frac{1}{2}}_{\lambda_1^{\prime},\lambda_{1}}\left(\zeta^1_{1(1)}\right) d^{\frac{1}{2}}_{\lambda_{0},\lambda_0^{\prime}}\left(\zeta^0_{1(1)}\right) + A^{2}_{\lambda_0^{\prime}, \lambda_1^{\prime}, 0, 0} d^{\frac{1}{2}}_{\lambda_1^{\prime},\lambda_{1}}\left(\zeta^1_{2(1)}\right) d^{\frac{1}{2}}_{\lambda_{0},\lambda_0^{\prime}}\left(\zeta^0_{2(1)}\right) + A^{3}_{\lambda_0^{\prime}, \lambda_1^{\prime}, 0, 0} d^{\frac{1}{2}}_{\lambda_1^{\prime},\lambda_{1}}\left(\zeta^1_{3(1)}\right) d^{\frac{1}{2}}_{\lambda_{0},\lambda_0^{\prime}}\left(\zeta^0_{3(1)}\right)}}\right|^{2}}\]

For more examples of how to use the codebase, see the following pages.

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. Polarimeter field serialization
  • 7.7. Model serialization
  • 7.8. Amplitude model with LS-couplings
  • 7.9. SU(2) → SO(3) homomorphism
  • 7.10. Determination of polarization
  • 7.11. Interactive visualization
• 8. Bibliography
• 9. API
  • formulate_polarimetry()
  • published_model()
  • expose_model_description()
  • 9.1. lhcb
  • 9.2. data
  • 9.3. function
  • 9.4. io
  • 9.5. plot

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	2024-06-21 18:36	cache	33.55	✅
appendix/alignment	2024-06-21 18:37	cache	85.4	✅
appendix/angles	2024-06-21 18:37	cache	2.7	✅
appendix/benchmark	2024-06-21 18:40	cache	181.11	✅
appendix/dynamics	2024-06-21 18:40	cache	2.56	✅
appendix/homomorphism	2024-06-21 18:41	cache	3.09	✅
appendix/ls-model	2024-06-21 18:46	cache	311.96	✅
appendix/model-serialization	2024-06-21 18:47	cache	49.67	✅
appendix/phase-space	2024-06-21 18:47	cache	19.44	✅
appendix/serialization	2024-06-21 18:48	cache	67.52	✅
appendix/widget	2024-06-21 18:58	cache	597.74	✅
cross-check	2024-06-21 19:00	cache	114.3	✅
index	2024-06-21 19:00	cache	2.28	✅
intensity	2024-06-21 19:04	cache	241.17	✅
polarimetry	2024-06-21 19:08	cache	232.48	✅
resonance-polarimetry	2024-06-21 19:58	cache	3011.43	✅
uncertainties	2024-06-21 20:24	cache	1558.61	✅
zz.polarization-fit	2024-06-21 20:28	cache	232.12	✅