# Evidence for exotic hadron contributions to $\Lambda_b^0 \to J/\psi p \pi^-$ decays

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## Abstract

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.

## Figures and captions

 Invariant mass spectrum for the selected $\Lambda ^0_ b \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} p \pi^-$ candidates. PsiPHMass.pdf [23 KiB] HiDef png [311 KiB] Thumbnail [241 KiB] *.C file 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. mppi.pdf [34 KiB] HiDef png [421 KiB] Thumbnail [300 KiB] *.C file 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. mjpsip0.pdf [22 KiB] HiDef png [300 KiB] Thumbnail [233 KiB] *.C file mjpsip3.pdf [23 KiB] HiDef png [351 KiB] Thumbnail [269 KiB] *.C file 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. mjpsik0.pdf [19 KiB] HiDef png [295 KiB] Thumbnail [239 KiB] *.C file mjpsik3.pdf [18 KiB] HiDef png [327 KiB] Thumbnail [255 KiB] *.C file 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. angle.pdf [40 KiB] HiDef png [459 KiB] Thumbnail [364 KiB] *.C file 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. dlz-point.pdf [220 KiB] HiDef png [272 KiB] Thumbnail [266 KiB] *.C file dlzk-point.pdf [123 KiB] HiDef png [275 KiB] Thumbnail [272 KiB] *.C file (a) Relative signal efficiency and (b) background distribution on the Dalitz plane in arbitrary units. dlzeff.pdf [44 KiB] HiDef png [375 KiB] Thumbnail [311 KiB] *.C file dlzbkg.pdf [43 KiB] HiDef png [320 KiB] Thumbnail [266 KiB] *.C file 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. mppi-all.pdf [54 KiB] HiDef png [690 KiB] Thumbnail [425 KiB] *.C file 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. mppi-l[..].pdf [53 KiB] HiDef png [509 KiB] Thumbnail [376 KiB] *.C file 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. mppi-2pc.pdf [32 KiB] HiDef png [396 KiB] Thumbnail [280 KiB] *.C file 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. mjpsip[..].pdf [18 KiB] HiDef png [283 KiB] Thumbnail [224 KiB] *.C file mjpsip[..].pdf [20 KiB] HiDef png [333 KiB] Thumbnail [258 KiB] *.C file 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. mjpsik[..].pdf [17 KiB] HiDef png [281 KiB] Thumbnail [230 KiB] *.C file mjpsik[..].pdf [17 KiB] HiDef png [313 KiB] Thumbnail [246 KiB] *.C file 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. mppi-zc.pdf [32 KiB] HiDef png [317 KiB] Thumbnail [225 KiB] *.C file 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. mjpsip0-zc.pdf [21 KiB] HiDef png [272 KiB] Thumbnail [217 KiB] *.C file mjpsip3-zc.pdf [21 KiB] HiDef png [269 KiB] Thumbnail [217 KiB] *.C file 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. mjpsik0-zc.pdf [17 KiB] HiDef png [262 KiB] Thumbnail [222 KiB] *.C file mjpsik3-zc.pdf [17 KiB] HiDef png [252 KiB] Thumbnail [210 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 boost-rotation process is repeated to define the helicity frame for its decay products. Helici[..].pdf [922 KiB] HiDef png [270 KiB] Thumbnail [161 KiB] *.C file Definition of the decay angles in the $Z_c^-$ decay chain. Matrix[..].pdf [165 KiB] HiDef png [258 KiB] Thumbnail [140 KiB] *.C file Animated gif made out of all figures. PAPER-2016-015.gif Thumbnail

## Tables and captions

 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). Table_1.pdf [45 KiB] HiDef png [160 KiB] Thumbnail [81 KiB] tex code Summary of absolute systematic uncertainties of the fit fractions in units of percent. Table_2.pdf [82 KiB] HiDef png [161 KiB] Thumbnail [81 KiB] tex code Fit fractions (%) from the RM and EM model fits with statistical uncertainties only. Table_3.pdf [52 KiB] HiDef png [352 KiB] Thumbnail [160 KiB] tex code

## Supplementary Material [file]

 Supplementary material full pdf supple[..].pdf [501 KiB] 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 Fig15.pdf [922 KiB] HiDef png [270 KiB] Thumbnail [161 KiB] *C file Fig16.pdf [165 KiB] HiDef png [258 KiB] Thumbnail [140 KiB] *C file

Created on 18 October 2019.