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Properties of the underlying-event in $pp$ interactions are investigated primarily via the strange hadrons $K_{S}^{0}$, $\Lambda$ and $\bar\Lambda$, as reconstructed using the ATLAS detector at the LHC in minimum-bias $pp$ collision data at $\sqrt{s} = 13$ TeV. The hadrons are reconstructed via the identification of the displaced two-particle vertices corresponding to the decay modes $K_{S}^{0}\rightarrow\pi^+\pi^-$, $\Lambda\rightarrow\pi^-p$ and $\bar\Lambda\rightarrow\pi^+\bar{p}$. These are used in the construction of underlying-event observables in azimuthal regions computed relative to the leading charged-particle jet in the event. None of the hadronisation and underlying-event physics models considered can describe the data over the full kinematic range considered. Events with a leading charged-particle jet in the range of $10 < p_T \leq 40$ GeV are studied using the number of prompt charged particles in the transverse region. The ratio $N(\Lambda + \bar\Lambda)/N(K_{S}^{0})$ as a function of the number of such charged particles varies only slightly over this range. This disagrees with the expectations of some of the considered Monte Carlo models.
Mean multiplicity of $K^{0}_{S}$ per unit $(\eta, \phi)$ in the away region vs. leading-jet $p_{T}$
Statistical covariance between bins of Table 1
Mean multiplicity of $K^{0}_{S}$ per unit $(\eta, \phi)$ in the towards region vs. leading-jet $p_{T}$
Statistical covariance between bins of Table 2
Mean multiplicity of $K^{0}_{S}$ per unit $(\eta, \phi)$ in the transverse region vs. leading-jet $p_{T}$
Statistical covariance between bins of Table 3
Mean scalar sum-$p_{T}$ of $K^{0}_{S}$ per unit $(\eta, \phi)$ in the away region vs. leading-jet $p_{T}$
Statistical covariance between bins of Table 4
Mean scalar sum-$p_{T}$ of $K^{0}_{S}$ per unit $(\eta, \phi)$ in the towards region vs. leading-jet $p_{T}$
Statistical covariance between bins of Table 5
Mean scalar sum-$p_{T}$ of $K^{0}_{S}$ per unit $(\eta, \phi)$ in the transverse region vs. leading-jet $p_{T}$
Statistical covariance between bins of Table 6
Ratio of the multiplicity of $K^{0}_{S}$ to prompt charged particles in the away region vs. leading-jet $p_{T}$
Statistical covariance between bins of Table 7
Ratio of the multiplicity of $K^{0}_{S}$ to prompt charged particles in the towards region vs. leading-jet $p_{T}$
Statistical covariance between bins of Table 8
Ratio of the multiplicity of $K^{0}_{S}$ to prompt charged particles in the transverse region vs. leading-jet $p_{T}$
Statistical covariance between bins of Table 9
Ratio of the scalar sum-pt of $K^{0}_{S}$ to prompt charged particles in the away region vs. leading-jet $p_{T}$
Statistical covariance between bins of Table 10
Ratio of the scalar sum-pt of $K^{0}_{S}$ to prompt charged particles in the towards region vs. leading-jet $p_{T}$
Statistical covariance between bins of Table 11
Ratio of the scalar sum-pt of $K^{0}_{S}$ to prompt charged particles in the transverse region vs. leading-jet $p_{T}$
Statistical covariance between bins of Table 12
Mean-$p_{T}$ of $K^{0}_{S}$ in the away region vs. leading-jet $p_{T}$
Statistical covariance between bins of Table 13
Mean-$p_{T}$ of $K^{0}_{S}$ in the towards region vs. leading-jet $p_{T}$
Statistical covariance between bins of Table 14
Mean-$p_{T}$ of $K^{0}_{S}$ in the transverse region vs. leading-jet $p_{T}$
Statistical covariance between bins of Table 15
Mean multiplicity of $\Lambda$ and $\bar{\Lambda}$ per unit $(\eta, \phi)$ in the away region vs. leading-jet $p_{T}$
Statistical covariance between bins of Table 16
Mean multiplicity of $\Lambda$ and $\bar{\Lambda}$ per unit $(\eta, \phi)$ in the towards region vs. leading-jet $p_{T}$
Statistical covariance between bins of Table 17
Mean multiplicity of $\Lambda$ and $\bar{\Lambda}$ per unit $(\eta, \phi)$ in the transverse region vs. leading-jet $p_{T}$
Statistical covariance between bins of Table 18
Mean scalar sum-$p_{T}$ of $\Lambda$ and $\bar{\Lambda}$ per unit $(\eta, \phi)$ in the away region vs. leading-jet $p_{T}$
Statistical covariance between bins of Table 19
Mean scalar sum-$p_{T}$ of $\Lambda$ and $\bar{\Lambda}$ per unit $(\eta, \phi)$ in the towards region vs. leading-jet $p_{T}$
Statistical covariance between bins of Table 20
Mean scalar sum-$p_{T}$ of $\Lambda$ and $\bar{\Lambda}$ per unit $(\eta, \phi)$ in the transverse region vs. leading-jet $p_{T}$
Statistical covariance between bins of Table 21
Ratio of the multiplicity of $\Lambda$ and $\bar{\Lambda}$ to prompt charged particles in the away region vs. leading-jet $p_{T}$
Statistical covariance between bins of Table 22
Ratio of the multiplicity of $\Lambda$ and $\bar{\Lambda}$ to prompt charged particles in the towards region vs. leading-jet $p_{T}$
Statistical covariance between bins of Table 23
Ratio of the multiplicity of $\Lambda$ and $\bar{\Lambda}$ to prompt charged particles in the transverse region vs. leading-jet $p_{T}$
Statistical covariance between bins of Table 24
Ratio of the scalar sum-pt of $\Lambda$ and $\bar{\Lambda}$ to prompt charged particles in the away region vs. leading-jet $p_{T}$
Statistical covariance between bins of Table 25
Ratio of the scalar sum-pt of $\Lambda$ and $\bar{\Lambda}$ to prompt charged particles in the towards region vs. leading-jet $p_{T}$
Statistical covariance between bins of Table 26
Ratio of the scalar sum-pt of $\Lambda$ and $\bar{\Lambda}$ to prompt charged particles in the transverse region vs. leading-jet $p_{T}$
Statistical covariance between bins of Table 27
Ratio of the multiplicity of $\Lambda$ and $\bar{\Lambda}$ to $K^{0}_{S}$ in the away region vs. leading-jet $p_{T}$
Statistical covariance between bins of Table 28
Ratio of the multiplicity of $\Lambda$ and $\bar{\Lambda}$ to $K^{0}_{S}$ in the towards region vs. leading-jet $p_{T}$
Statistical covariance between bins of Table 29
Ratio of the multiplicity of $\Lambda$ and $\bar{\Lambda}$ to $K^{0}_{S}$ in the transverse region vs. leading-jet $p_{T}$
Statistical covariance between bins of Table 30
Ratio of the scalar sum-pt of $\Lambda$ and $\bar{\Lambda}$ to $K^{0}_{S}$ in the away region vs. leading-jet $p_{T}$
Statistical covariance between bins of Table 31
Ratio of the scalar sum-pt of $\Lambda$ and $\bar{\Lambda}$ to $K^{0}_{S}$ in the towards region vs. leading-jet $p_{T}$
Statistical covariance between bins of Table 32
Ratio of the scalar sum-pt of $\Lambda$ and $\bar{\Lambda}$ to $K^{0}_{S}$ in the transverse region vs. leading-jet $p_{T}$
Statistical covariance between bins of Table 33
Mean-$p_{T}$ of $\Lambda$ and $\bar{\Lambda}$ in the away region vs. leading-jet $p_{T}$
Statistical covariance between bins of Table 34
Mean-$p_{T}$ of $\Lambda$ and $\bar{\Lambda}$ in the towards region vs. leading-jet $p_{T}$
Statistical covariance between bins of Table 35
Mean-$p_{T}$ of $\Lambda$ and $\bar{\Lambda}$ in the transverse region vs. leading-jet $p_{T}$
Statistical covariance between bins of Table 36
Mean multiplicity of $K^{0}_{S}$ per unit $(\eta, \phi)$ in the away region vs. $N_\textrm{ch,trans}$
Statistical covariance between bins of Table 37
Mean multiplicity of $K^{0}_{S}$ per unit $(\eta, \phi)$ in the towards region vs. $N_\textrm{ch,trans}$
Statistical covariance between bins of Table 38
Mean multiplicity of $K^{0}_{S}$ per unit $(\eta, \phi)$ in the transverse region vs. $N_\textrm{ch,trans}$
Statistical covariance between bins of Table 39
Mean scalar sum-$p_{T}$ of $K^{0}_{S}$ per unit $(\eta, \phi)$ in the away region vs. $N_\textrm{ch,trans}$
Statistical covariance between bins of Table 40
Mean scalar sum-$p_{T}$ of $K^{0}_{S}$ per unit $(\eta, \phi)$ in the towards region vs. $N_\textrm{ch,trans}$
Statistical covariance between bins of Table 41
Mean scalar sum-$p_{T}$ of $K^{0}_{S}$ per unit $(\eta, \phi)$ in the transverse region vs. $N_\textrm{ch,trans}$
Statistical covariance between bins of Table 42
Ratio of the multiplicity of $K^{0}_{S}$ to prompt charged particles in the away region vs. $N_\textrm{ch,trans}$
Statistical covariance between bins of Table 43
Ratio of the multiplicity of $K^{0}_{S}$ to prompt charged particles in the towards region vs. $N_\textrm{ch,trans}$
Statistical covariance between bins of Table 44
Ratio of the multiplicity of $K^{0}_{S}$ to prompt charged particles in the transverse region vs. $N_\textrm{ch,trans}$
Statistical covariance between bins of Table 45
Ratio of the scalar sum-pt of $K^{0}_{S}$ to prompt charged particles in the away region vs. $N_\textrm{ch,trans}$
Statistical covariance between bins of Table 46
Ratio of the scalar sum-pt of $K^{0}_{S}$ to prompt charged particles in the towards region vs. $N_\textrm{ch,trans}$
Statistical covariance between bins of Table 47
Ratio of the scalar sum-pt of $K^{0}_{S}$ to prompt charged particles in the transverse region vs. $N_\textrm{ch,trans}$
Statistical covariance between bins of Table 48
Mean-$p_{T}$ of $K^{0}_{S}$ in the away region vs. $N_\textrm{ch,trans}$
Statistical covariance between bins of Table 49
Mean-$p_{T}$ of $K^{0}_{S}$ in the towards region vs. $N_\textrm{ch,trans}$
Statistical covariance between bins of Table 50
Mean-$p_{T}$ of $K^{0}_{S}$ in the transverse region vs. $N_\textrm{ch,trans}$
Statistical covariance between bins of Table 51
Mean multiplicity of $\Lambda$ and $\bar{\Lambda}$ per unit $(\eta, \phi)$ in the away region vs. $N_\textrm{ch,trans}$
Statistical covariance between bins of Table 52
Mean multiplicity of $\Lambda$ and $\bar{\Lambda}$ per unit $(\eta, \phi)$ in the towards region vs. $N_\textrm{ch,trans}$
Statistical covariance between bins of Table 53
Mean multiplicity of $\Lambda$ and $\bar{\Lambda}$ per unit $(\eta, \phi)$ in the transverse region vs. $N_\textrm{ch,trans}$
Statistical covariance between bins of Table 54
Mean scalar sum-$p_{T}$ of $\Lambda$ and $\bar{\Lambda}$ per unit $(\eta, \phi)$ in the away region vs. $N_\textrm{ch,trans}$
Statistical covariance between bins of Table 55
Mean scalar sum-$p_{T}$ of $\Lambda$ and $\bar{\Lambda}$ per unit $(\eta, \phi)$ in the towards region vs. $N_\textrm{ch,trans}$
Statistical covariance between bins of Table 56
Mean scalar sum-$p_{T}$ of $\Lambda$ and $\bar{\Lambda}$ per unit $(\eta, \phi)$ in the transverse region vs. $N_\textrm{ch,trans}$
Statistical covariance between bins of Table 57
Ratio of the multiplicity of $\Lambda$ and $\bar{\Lambda}$ to prompt charged particles in the away region vs. $N_\textrm{ch,trans}$
Statistical covariance between bins of Table 58
Ratio of the multiplicity of $\Lambda$ and $\bar{\Lambda}$ to prompt charged particles in the towards region vs. $N_\textrm{ch,trans}$
Statistical covariance between bins of Table 59
Ratio of the multiplicity of $\Lambda$ and $\bar{\Lambda}$ to prompt charged particles in the transverse region vs. $N_\textrm{ch,trans}$
Statistical covariance between bins of Table 60
Ratio of the scalar sum-pt of $\Lambda$ and $\bar{\Lambda}$ to prompt charged particles in the away region vs. $N_\textrm{ch,trans}$
Statistical covariance between bins of Table 61
Ratio of the scalar sum-pt of $\Lambda$ and $\bar{\Lambda}$ to prompt charged particles in the towards region vs. $N_\textrm{ch,trans}$
Statistical covariance between bins of Table 62
Ratio of the scalar sum-pt of $\Lambda$ and $\bar{\Lambda}$ to prompt charged particles in the transverse region vs. $N_\textrm{ch,trans}$
Statistical covariance between bins of Table 63
Ratio of the multiplicity of $\Lambda$ and $\bar{\Lambda}$ to $K^{0}_{S}$ in the away region vs. $N_\textrm{ch,trans}$
Statistical covariance between bins of Table 64
Ratio of the multiplicity of $\Lambda$ and $\bar{\Lambda}$ to $K^{0}_{S}$ in the towards region vs. $N_\textrm{ch,trans}$
Statistical covariance between bins of Table 65
Ratio of the multiplicity of $\Lambda$ and $\bar{\Lambda}$ to $K^{0}_{S}$ in the transverse region vs. $N_\textrm{ch,trans}$
Statistical covariance between bins of Table 66
Ratio of the scalar sum-pt of $\Lambda$ and $\bar{\Lambda}$ to $K^{0}_{S}$ in the away region vs. $N_\textrm{ch,trans}$
Statistical covariance between bins of Table 67
Ratio of the scalar sum-pt of $\Lambda$ and $\bar{\Lambda}$ to $K^{0}_{S}$ in the towards region vs. $N_\textrm{ch,trans}$
Statistical covariance between bins of Table 68
Ratio of the scalar sum-pt of $\Lambda$ and $\bar{\Lambda}$ to $K^{0}_{S}$ in the transverse region vs. $N_\textrm{ch,trans}$
Statistical covariance between bins of Table 69
Mean-$p_{T}$ of $\Lambda$ and $\bar{\Lambda}$ in the away region vs. $N_\textrm{ch,trans}$
Statistical covariance between bins of Table 70
Mean-$p_{T}$ of $\Lambda$ and $\bar{\Lambda}$ in the towards region vs. $N_\textrm{ch,trans}$
Statistical covariance between bins of Table 71
Mean-$p_{T}$ of $\Lambda$ and $\bar{\Lambda}$ in the transverse region vs. $N_\textrm{ch,trans}$
Statistical covariance between bins of Table 72
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