cern.ch

$\Lambda_c^+$ polarimetry using the dominant hadronic mode

[to restricted-access page]

Information

Tools

Abstract

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.

Figures and captions

Definition of the decay-plane orientation angles $\phi$, $\theta$, and $\chi$ related to polarisation of the particle $A$, produced in the process $P+Q \rightarrow A+X$, and observed in the decay, $A\rightarrow B+C+D$. The left yellow plane contains the momenta of the production process, while the right green plane contains the momenta of the decay reaction. The central blue plane is defined by the momenta $\vec{p}_X$ and $\vec{p}_D$ in the rest frame of the decay particle $A$. The white arrows show the orientation of the two different quantisation axes of the particle $A$ spin in its rest frame.

 Fig1.pdf [35 KiB]
HiDef png [357 KiB]
Thumbnail [258 KiB]
*.C file
Fig1.pdf

Aligned polarimeter vector field in Dalitz-plot coordinates. The $z$ and $x$ components of the $\alpha$ vector are shown by the horizontal and vertical projections of the arrow, respectively. The colour indicates the length of the polarimeter vector. The sketch in the top right corner shows the decay-plane orientation. The momentum arrows for the pion and the kaon are shown in gray, since their orientation depends on the kinematic variables, $m^2( K ^- \pi ^+ )$ and $m^2(p K ^- )$.

 Fig2.pdf [58 KiB]
HiDef png [459 KiB]
Thumbnail [270 KiB]
*.C file
Fig2.pdf

The aligned polarimeter vector field in Dalitz-plot coordinates for the $\Lambda ^+_ c \rightarrow \Lambda (1520)(\rightarrow p K^-) \pi^+$ decay chain only. The decay plane in the rest frame of the $\Lambda ^+_ c $ baryon is aligned to the $K^{**0}$ decay chains and $\Lambda ^{**}$ decay chain for the left and right panel, respectively. See Fig. ??? for notations.

 Fig3a.pdf [34 KiB]
HiDef png [184 KiB]
Thumbnail [155 KiB]
*.C file
Fig3a.pdf
Fig3b.pdf [38 KiB]
HiDef png [216 KiB]
Thumbnail [195 KiB]
*.C file
Fig3b.pdf

Uncertainties on the length of the aligned polarimeter vector for each phase-space point. The left panel shows combined statistical and systematic uncertainties, and the right panel shows the model uncertainties.

 Fig4.png [162 KiB]
HiDef png [188 KiB]
Thumbnail [79 KiB]
*.C file
Fig4.png

Animated gif made out of all figures.

 PAPER-2022-044.gif
Thumbnail
thumbnail_PAPER-2022-044.gif

Tables and captions

Averaged values of the polarimetry fields in Cartesian and spherical coordinates. The central value and the model uncertainties are shown in the second and fourth columns, respectively. The second column presents the standard deviation of the distribution in the parameter sampling that includes both statistical and systematic uncertainties.

 Table_1.pdf [45 KiB]
HiDef png [74 KiB]
Thumbnail [34 KiB]
tex code 		Table_1.pdf

Created on 27 April 2024.