A full amplitude analysis of $\Lambda_b^0 \to J/\psi p \pi^$ decays is performed with a data sample acquired with the LHCb detector from 7 and 8 TeV $pp$ collisions, corresponding to an integrated luminosity of 3 fb$^{1}$. A significantly better description of the data is achieved when, in addition to the previously observed nucleon excitations $N\to p\pi^$, either the $P_c(4380)^+$ and $P_c(4450)^+\to J/\psi p$ states, previously observed in $\Lambda_b^0 \to J/\psi p K^$ decays, or the $Z_c(4200)^\to J/\psi \pi^$ state, previously reported in $B^0 \to J/\psi K^+ \pi^$ decays, or all three, are included in the amplitude models. The data support a model containing all three exotic states, with a significance of more than three standard deviations. Within uncertainties, the data are consistent with the $P_c(4380)^+$ and $P_c(4450)^+$ production rates expected from their previous observation taking account of Cabibbo suppression.
Invariant mass spectrum for the selected $\Lambda ^0_ b \rightarrow { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} p \pi^$ candidates. 
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Backgroundsubtracted 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. 
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Backgroundsubtracted 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. 
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Backgroundsubtracted 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. 
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mjpsik3.pdf [18 KiB] HiDef png [313 KiB] Thumbnail [253 KiB] *.C file 

Backgroundsubtracted 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. 
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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. 
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(a) Relative signal efficiency and (b) background distribution on the Dalitz plane in arbitrary units. 
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Backgroundsubtracted 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. 
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Backgroundsubtracted 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. 
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Backgroundsubtracted 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. 
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Backgroundsubtracted 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. 
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mjpsip[..].pdf [20 KiB] HiDef png [322 KiB] Thumbnail [256 KiB] *.C file 

Backgroundsubtracted 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. 
mjpsik[..].pdf [17 KiB] HiDef png [271 KiB] Thumbnail [228 KiB] *.C file 

mjpsik[..].pdf [17 KiB] HiDef png [301 KiB] Thumbnail [244 KiB] *.C file 

Backgroundsubtracted 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. 
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Backgroundsubtracted 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. 
mjpsip0zc.pdf [21 KiB] HiDef png [262 KiB] Thumbnail [215 KiB] *.C file 

mjpsip3zc.pdf [21 KiB] HiDef png [260 KiB] Thumbnail [214 KiB] *.C file 

Backgroundsubtracted 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. 
mjpsik0zc.pdf [17 KiB] HiDef png [253 KiB] Thumbnail [219 KiB] *.C file 

mjpsik3zc.pdf [17 KiB] HiDef png [242 KiB] Thumbnail [208 KiB] *.C file 

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 boostrotation process is repeated to define the helicity frame for its decay products. 
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Definition of the decay angles in the $Z_c^$ decay chain. 
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Animated gif made out of all figures. 
PAPER2016015.gif Thumbnail 
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). 
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Summary of absolute systematic uncertainties of the fit fractions in units of percent. 
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Fit fractions (%) from the RM and EM model fits with statistical uncertainties only. 
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Supplementary material full pdf 
supple[..].pdf [501 KiB] 

This ZIP file contains supplementary material for the publication LHCbPAPER2016015. The files are: Supplementary.pdf: Details of the matrix element for the decay amplitude *.pdf, *png, *.eps : The figures in various formats 
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Created on 19 February 2021.