Invariant mass spectrum for the selected $\Lambda ^0_ b \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} p \pi^-$ candidates.

Background-subtracted data and fit projections onto $ m_{p\pi} $. Fits are shown with models containing $N^*$ states only (EM) and with $N^*$ states (RM) plus exotic contributions.

Background-subtracted data and fit projections onto $ m_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} p} $ for (a) all events and (b) the $ m_{p\pi} >1.8$ $\mathrm{ Ge V}$ region. See the legend and caption of Fig. 2 for a description of the components.

Background-subtracted data and fit projections onto $ m_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \pi} $ for (a) all events and (b) the $ m_{p\pi} >1.8$ $\mathrm{ Ge V}$ region. See the legend and caption of Fig. 2 for a description of the components.

Background-subtracted data and fit projections of decay angles describing the $N^*$ decay chain, which are included in the amplitude fit. The helicity angle of particle $P$, $\theta_P$, is the polar angle in the rest frame of $P$ between a decay product of $P$ and the boost direction from the particle decaying to $P$. The azimuthal angle between decay planes of $\Lambda ^0_ b $ and $N^*$ (of $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} $) is denoted as $\phi_\pi$ ($\phi_\mu$). See Ref. [5] for more details.

Invariant mass squared of $p\pi ^- $ versus either (a) $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} p$ or (b) $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \pi$ for candidates within $\pm15\mathrm{ Me V} $ of the $\Lambda ^0_ b $ mass, which contain 17% background. The lines show the kinematic boundaries with the $\Lambda ^0_ b $ mass constrained to the known value.

(a) Relative signal efficiency and (b) background distribution on the Dalitz plane in arbitrary units.

Background-subtracted data and fit projections onto $ m_{p\pi} $. Fits are shown with models containing $N^*$ states only (EM) and with $N^*$ states (RM) plus exotic contributions. Individual fit components are shown only for the fit which includes all three exotic resonances.

Background-subtracted data and fit projections onto $ m_{p\pi} $. Fits are shown with models containing $N^*$ states only (EM) and with $N^*$ states (RM) plus exotic contributions. Individual fit components are shown only for the fit which includes all three exotic resonances.

Background-subtracted data and fit projections onto $ m_{p\pi} $. Fits are shown with models containing $N^*$ states only (EM) and with $N^*$ states (RM) plus the two $P_c^+$ resonances.

Background-subtracted data and fit projections onto $ m_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} p} $ for (a) all events and (b) the $ m_{p\pi} >1.8$ $\mathrm{ Ge V}$ region. See the legend and caption of Fig. 10 for a description of the components.

Background-subtracted data and fit projections onto $ m_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \pi} $ for (a) all events and (b) the $ m_{p\pi} >1.8$ $\mathrm{ Ge V}$ region. See the legend and caption of Fig. 10 for the description.

Background-subtracted data and fit projections onto $ m_{p\pi} $. Fits are shown with models containing $N^*$ states only (EM) and with $N^*$ states (RM) plus the $Z_c(4200)^-$ resonance.

Background-subtracted data and fit projections onto $ m_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} p} $ for (a) all events and (b) the $ m_{p\pi} >1.8$ $\mathrm{ Ge V}$ region. See the legend and caption of Fig. 13 for a description of the components.

Background-subtracted data and fit projections onto $ m_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \pi} $ for (a) all events and (b) the $ m_{p\pi} >1.8$ $\mathrm{ Ge V}$ region. See the legend and caption of Fig. 13 for a description of the components.

Coordinate axes for the spin quantization of particle $A$ (bottom part), chosen to be the helicity frame of $A$ ($\hat{z}_{0}||\vec{p}_{A}$ in the rest frame of its parent particle or in the laboratory frame), together with the polar (${\theta}_{{B}}^{ \F{ A }}$) and azimuthal (${\phi}_{{B}}^{ \F{ A }}$) angles of the momentum of its child $B$ in the $A$ rest frame (top part). Notice that the directions of these coordinate axes, denoted as ${\hat{x}}_{{0}}^{ \F{ A }}$, ${\hat{y}}_{{0}}^{ \F{ A }}$, and ${\hat{z}}_{{0}}^{ \F{ A }}$, do not change when boosting from the helicity frame of $A$ to its rest frame. After the Euler rotation ${\cal R}(\alpha={\phi}_{{B}}^{ \F{ A }},\beta={\theta}_{{B}}^{ \F{ A }},\gamma=0)$ (see the text), the rotated $z$ axis, ${\hat{z}}_{{2}}^{ \F{ A }}$, is aligned with the $B$ momentum; thus the rotated coordinates become the helicity frame of $B$. If $B$ has a sequential decay, then the same boost-rotation process is repeated to define the helicity frame for its decay products.

Definition of the decay angles in the $Z_c^-$ decay chain.

Animated gif made out of all figures.

The $N^*$ resonances used in the different fits. Parameters are taken from the PDG [16]. The number of $LS$ couplings is listed in the columns to the right for the two versions (RM and EM) of the $N^*$ model discussed in the text. To fix overall phase and magnitude conventions, the $N(1535)$ complex coupling of lowest $LS$ is set to (1,0).

Summary of absolute systematic uncertainties of the fit fractions in units of percent.

Fit fractions (%) from the RM and EM model fits with statistical uncertainties only.

Supplementary material full pdf

This ZIP file contains supplementary material for the publication LHCb-PAPER-2016-015. The files are: Supplementary.pdf: Details of the matrix element for the decay amplitude *.pdf, *png, *.eps : The figures in various formats