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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.

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PsiPHMass.pdf

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.

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mppi.pdf

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$ $\mathrm{\,GeV}$ region. See the legend and caption of Fig. 2 for a description of the components.

mjpsip0.pdf [22 KiB]
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mjpsip0.pdf
mjpsip3.pdf [23 KiB]
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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$ $\mathrm{\,GeV}$ region. See the legend and caption of Fig. 2 for a description of the components.

mjpsik0.pdf [19 KiB]
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mjpsik0.pdf
mjpsik3.pdf [18 KiB]
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mjpsik3.pdf

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]
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angle.pdf

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{\,MeV} $ 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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dlz-point.pdf
dlzk-point.pdf [123 KiB]
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dlzk-point.pdf

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

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dlzeff.pdf
dlzbkg.pdf [43 KiB]
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dlzbkg.pdf

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]
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mppi-all.pdf

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]
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mppi-linear.pdf

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]
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mppi-2pc.pdf

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$ $\mathrm{\,GeV}$ region. See the legend and caption of Fig. 10 for a description of the components.

mjpsip[..].pdf [18 KiB]
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mjpsip0-2pc.pdf
mjpsip[..].pdf [20 KiB]
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mjpsip3-2pc.pdf

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$ $\mathrm{\,GeV}$ region. See the legend and caption of Fig. 10 for the description.

mjpsik[..].pdf [17 KiB]
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mjpsik0-2pc.pdf
mjpsik[..].pdf [17 KiB]
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mjpsik3-2pc.pdf

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]
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mppi-zc.pdf

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$ $\mathrm{\,GeV}$ region. See the legend and caption of Fig. 13 for a description of the components.

mjpsip0-zc.pdf [21 KiB]
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mjpsip0-zc.pdf
mjpsip3-zc.pdf [21 KiB]
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mjpsip3-zc.pdf

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$ $\mathrm{\,GeV}$ region. See the legend and caption of Fig. 13 for a description of the components.

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mjpsik0-zc.pdf
mjpsik3-zc.pdf [17 KiB]
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mjpsik3-zc.pdf

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 (${\theta}_{{B}}^{\,\,\{\}{\!A\!}}$) and azimuthal (${\phi}_{{B}}^{\,\,\{\}{\!A\!}}$) 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 ${\hat{x}}_{{0}}^{\,\,\{\}{\!A\!}}$, ${\hat{y}}_{{0}}^{\,\,\{\}{\!A\!}}$, and ${\hat{z}}_{{0}}^{\,\,\{\}{\!A\!}}$, do not change when boosting from the helicity frame of $A$ to its rest frame. After the Euler rotation ${\cal R}(\alpha={\phi}_{{B}}^{\,\,\{\}{\!A\!}},\beta={\theta}_{{B}}^{\,\,\{\}{\!A\!}},\gamma=0)$ (see the text), the rotated $z$ axis, ${\hat{z}}_{{2}}^{\,\,\{\}{\!A\!}}$, 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]
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HelicityFrames.pdf

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

Matrix[..].pdf [165 KiB]
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MatrixElement-Zc.pdf

Animated gif made out of all figures.

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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).

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Table_1.pdf

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

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Table_2.pdf

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

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Table_3.pdf

Supplementary Material [file]

Supplementary material full pdf

supple[..].pdf [501 KiB]
supplementary.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

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Created on 09 December 2018.Citation count from INSPIRE on 18 December 2018.