The data sample of $\Lambda_b^0\to J/\psi p K^$ decays acquired with the LHCb detector from 7 and 8 TeV $pp$ collisions, corresponding to an integrated luminosity of 3 fb$^{1}$, is inspected for the presence of $J/\psi p$ or $J/\psi K^$ contributions with minimal assumptions about $K^ p$ contributions. It is demonstrated at more than 9 standard deviations that $\Lambda_b^0\to J/\psi p K^$ decays cannot be described with $K^ p$ contributions alone, and that $J/\psi p$ contributions play a dominant role in this incompatibility. These modelindependent results support the previously obtained modeldependent evidence for $P_c^+\to J/\psi p$ charmoniumpentaquark states in the same data sample.
Excitations of the $\Lambda $ baryon. States predicted in Ref. [7] are shown as short horizontal bars (black) and experimentally wellestablished $\Lambda ^*$ states are shown as green boxes covering the mass ranges from $M_0\Gamma_0$ to $M_0+\Gamma_0$. The $m_{Kp}$ mass range probed in $\Lambda ^0_ b \rightarrow { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} p K ^ $ decays is shown by long horizontal lines (blue). The $l_{\rm max}(m_{Kp})$ filter is shown as a stepped line (red). All contributions from $\Lambda ^*$ states with $J^P$ values to the left of the red line are accepted by the filter. The filter works well also for the excitations of the $\Sigma $ baryon [11,7] (not shown). 
lmax_new.pdf [14 KiB] HiDef png [140 KiB] Thumbnail [125 KiB] *.C file 

Efficiencycorrected and backgroundsubtracted $m_{Kp}$ distribution of the data (black points with error bars), with $\cal F(m_{Kp}H_0)$ superimposed (solid blue line). $\cal F(m_{Kp}H_0)$ fits the data by construction. 
Data_mkp.pdf [25 KiB] HiDef png [127 KiB] Thumbnail [100 KiB] *.C file 

Legendre moments of $\cos\theta_{\Lambda ^*}$ as a function of $m_{Kp}$ in the data. Regions excluded by the $l\lel_{\rm max}(m_{Kp})$ filter are shaded. 
UMom_A[..].pdf [40 KiB] HiDef png [459 KiB] Thumbnail [359 KiB] *.C file 

Efficiencycorrected and backgroundsubtracted $m_{ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} p}$ distribution of the data (black points with error bars), with $\cal F(m_{ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} p}H_0)$ (solid blue line) and $\cal F(m_{ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} p}H_1)$ (dashed black line) superimposed. 
Data_m[..].pdf [31 KiB] HiDef png [153 KiB] Thumbnail [106 KiB] *.C file 

Distributions of $\Delta( 2\ln L )$ in the modelindependent pseudoexperiments corresponding to $H_0$ (red falling hatched) compared to the distributions for pseudoexperiments generated from various amplitude models and, in the inset, to the bifurcated Gaussian fit function (solid line) and the value obtained for the data (vertical bar). 
dll.pdf [24 KiB] HiDef png [557 KiB] Thumbnail [337 KiB] *.C file 

Efficiencycorrected and backgroundsubtracted $m_{ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} K}$ distribution of the data (black points with error bars), with $\cal F(m_{ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} K}H_0)$ (solid blue line) and $\cal F(m_{ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} K}H_1)$ (dashed black line) superimposed. 
Data_m[..].pdf [73 KiB] HiDef png [151 KiB] Thumbnail [105 KiB] *.C file 

Distribution of $m_{ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} p K}$ in the data with the fit of signal and background components superimposed [3]. The fit is used to determine the background fraction $\beta$ in the $\pm2\sigma$ signal region around the $\Lambda ^0_ b $ peak (shown by the vertical red bars). The sidebands used in the background subtraction are also shown. 
mjpsipk.pdf [28 KiB] HiDef png [179 KiB] Thumbnail [137 KiB] *.C file 

Backgroundsubtracted and efficiencycorrected distribution of the cosine of the $\Lambda ^*$ helicity angle versus $m_{Kp}$ for the data. 
Data_K[..].pdf [46 KiB] HiDef png [904 KiB] Thumbnail [679 KiB] *.C file 

Distribution in a pseudoexperiment of the cosine of the $\Lambda ^*$ helicity angle versus $m_{Kp}$ for the amplitude model with $\Lambda ^*$ resonances only. 
Lz_KpR[..].pdf [52 KiB] HiDef png [714 KiB] Thumbnail [555 KiB] *.C file 

Distribution in a pseudoexperiment of the cosine of the $\Lambda ^*$ helicity angle versus $m_{Kp}$ for the amplitude model with the $P_c(4380)^+$ and $P_c(4450)^+$ resonances only. 
TwoPc_[..].pdf [51 KiB] HiDef png [675 KiB] Thumbnail [541 KiB] *.C file 

Legendre moments of $\cos\theta_{\Lambda ^*}$ as a function of $m_{Kp}$ for the simulated data from the amplitude models with only $\Lambda ^*$ (solid blue lines) and with only $P_c(4380)^+$, $P_c(4450)^+$ contributions (dashed red lines), scaled by $0.5$. The regions excluded by the $l\lel_{\rm max}(m_{Kp})$ filter are shaded. 
UMom_C[..].pdf [96 KiB] HiDef png [570 KiB] Thumbnail [402 KiB] *.C file 

Legendre moments of $\cos\theta_{\Lambda ^*}$ as a function of $m_{Kp}$ for the simulated data from amplitude models with only $P_c(4380)^+$ (solid blue lines) and only $P_c(4450)^+$ contributions (dashed red line). 
UMom_IndPc.pdf [59 KiB] HiDef png [673 KiB] Thumbnail [469 KiB] *.C file 

Animated gif made out of all figures. 
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Created on 19 February 2021.