The correlation matrix corresponding to the statistical uncertainties on the differential cross-section ($d\sigma/dp_T$) fit results for $W^-$. To combine with $W^+$ results (Fig8a), use the rows and columns ordered as $W^+$ and then $W^-$. Assume no correlation in the statistical uncertainties between $W^+$ and $W^-$ (zero entries in the off-diagonal blocks).

The correlation matrix corresponding to all of the systematic uncertainties on the differential cross-section ($d\sigma/dp_T$) fit results for $W^+$ and $W^-$ combined together, with rows and columns ordered as $W^+$ and then $W^-$.

Single Event Sensitivity (SES) for the $K^{+}\rightarrow\pi^{+}X$ search as a function of X mass.

Model-independent constraints on the branching ratio of the $K^{+}\rightarrow\pi^{+}X$ decay

Model-independent constraints on the branching ratio of the $K^{+}\rightarrow\pi^{+}X$ decay

Observed model-independent upper limits at 90 % CL of $\mathcal{B}(K^{+}\rightarrow\pi^{+}X)$ as function of $X$ mass, for several $X$ lifetime hypotheses, assuming $X$ decays to visible SM particles.

Observed model-independent upper limits at 90 % CL of $\mathcal{B}(K^{+}\rightarrow\pi^{+}X)$ as function of $X$ mass, for several $X$ lifetime hypotheses, assuming $X$ decays to visible SM particles.

Di-muon mass spectrum of selected $K^{+}\rightarrow\pi^{+}\mu^{+}\mu^{-}$ events from 2017–2018 data.

Di-muon mass spectrum of selected $K^{+}\rightarrow\pi^{+}\mu^{+}\mu^{-}$ events from 2017–2018 data.

Expected and observed model-independent upper limits at 90 % CL for $\mathcal{B}(K^{+}\rightarrow\pi^{+}X)\times\mathcal{B}(X\rightarrow\mu^{+}\mu^{-})$ as a function of $m_{X}$ for $\tau_{X}=0$.

Expected and observed model-independent upper limits at 90 % CL for $\mathcal{B}(K^{+}\rightarrow\pi^{+}X)\times\mathcal{B}(X\rightarrow\mu^{+}\mu^{-})$ as a function of $m_{X}$ for $\tau_{X}=0$.

Observed model-independent upper limits at 90 % CL for $\mathcal{B}(K^{+}\rightarrow\pi^{+}X)\times\mathcal{B}(X\rightarrow\mu^{+}\mu^{-})$ for several $\tau_{X}$ values.

Observed model-independent upper limits at 90 % CL for $\mathcal{B}(K^{+}\rightarrow\pi^{+}X)\times\mathcal{B}(X\rightarrow\mu^{+}\mu^{-})$ for several $\tau_{X}$ values.

Branching ratio of the $K^{+}\rightarrow\pi^{+}A^{\prime}$ decay divided by the kinetic mixing coupling squared, $\varepsilon^{2}$, as a function of $m_{A^{\prime}}$ for the BC2 model with dark photon $A^{\prime}$.

Branching ratio of the $K^{+}\rightarrow\pi^{+}A^{\prime}$ decay divided by the kinetic mixing coupling squared, $\varepsilon^{2}$, as a function of $m_{A^{\prime}}$ for the BC2 model with dark photon $A^{\prime}$.

Excluded region, at 90 % CL, of the parameter space $(m_{A^{\prime}},\varepsilon)$ for a dark photon $A^{\prime}$, decaying invisibly, in the BC2 model for the NA62 $K^{+}\rightarrow\pi^{+}X_{\rm inv}$ search.

Excluded region, at 90 % CL, of the parameter space $(m_{A^{\prime}},\varepsilon)$ for a dark photon $A^{\prime}$, decaying invisibly, in the BC2 model for the NA62 $K^{+}\rightarrow\pi^{+}X_{\rm inv}$ search.

Excluded region, at 90 % CL, of the parameter space $(m_{A^{\prime}},\varepsilon)$ for a dark photon $A^{\prime}$, decaying invisibly, in the BC2 model for the NA62 $\pi^{0}\rightarrow{\rm inv}$ search.

Excluded region, at 90 % CL, of the parameter space $(m_{A^{\prime}},\varepsilon)$ for a dark photon $A^{\prime}$, decaying invisibly, in the BC2 model for the NA62 $\pi^{0}\rightarrow{\rm inv}$ search.

Branching ratio of the $K^{+}\rightarrow\pi^{+}S$ decay divided by $\text{sin}^{2}\theta$, as a function of $m_{S}$.

Branching ratio of the $K^{+}\rightarrow\pi^{+}S$ decay divided by $\text{sin}^{2}\theta$, as a function of $m_{S}$.

Excluded regions, at 90 % CL, of the parameter space $(m_{S},\rm{sin}^{2}\theta)$ for a dark scalar $S$, in the BC4-inv model for the NA62 $K^{+}\rightarrow\pi^{+}X_{\rm inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{S},\rm{sin}^{2}\theta)$ for a dark scalar $S$, in the BC4-inv model for the NA62 $K^{+}\rightarrow\pi^{+}X_{\rm inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{S},\rm{sin}^{2}\theta)$ for a dark scalar $S$, in the BC4-inv model for the NA62 $\pi^{0}\rightarrow{\rm inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{S},\rm{sin}^{2}\theta)$ for a dark scalar $S$, in the BC4-inv model for the NA62 $\pi^{0}\rightarrow{\rm inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{S},\rm{sin}^{2}\theta$) for a dar scalar S, in the BC4 model, from the NA62 $K^{+}\rightarrow\pi^{+}X_{\rm inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{S},\rm{sin}^{2}\theta$) for a dar scalar S, in the BC4 model, from the NA62 $K^{+}\rightarrow\pi^{+}X_{\rm inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{S},\rm{sin}^{2}\theta$) for a dar scalar S, in the BC4 model, from the NA62 $K^{+}\rightarrow\pi^{+}\mu^{+}\mu^{-}$ study.

Excluded regions, at 90 % CL, of the parameter space $(m_{S},\rm{sin}^{2}\theta$) for a dar scalar S, in the BC4 model, from the NA62 $K^{+}\rightarrow\pi^{+}\mu^{+}\mu^{-}$ study.

Branching ratio of the $K^{+}\rightarrow\pi^{+}a$ decay divided by $(C_{ff}/\Lambda)^{2}$, as a function of $m_{a}$, assuming Λ = 1 TeV.

Branching ratio of the $K^{+}\rightarrow\pi^{+}a$ decay divided by $(C_{ff}/\Lambda)^{2}$, as a function of $m_{a}$, assuming Λ = 1 TeV.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{ff}/\Lambda)$ for an ALP $a$, in the BC10-inv model, evaluated assuming $\Lambda = 1$ TeV, for the NA62 $K^{+}\rightarrow\pi^{+}X_{\rm inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{ff}/\Lambda)$ for an ALP $a$, in the BC10-inv model, evaluated assuming $\Lambda = 1$ TeV, for the NA62 $K^{+}\rightarrow\pi^{+}X_{\rm inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{ff}/\Lambda)$ for an ALP $a$, in the BC10-inv model, evaluated assuming $\Lambda = 1$ TeV, for the NA62 $\pi^{0}\rightarrow\rm{inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{ff}/\Lambda)$ for an ALP $a$, in the BC10-inv model, evaluated assuming $\Lambda = 1$ TeV, for the NA62 $\pi^{0}\rightarrow\rm{inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{ff}/\lambda)$ for an ALP $a$, in the BC10 model, evaluated assuming $\Lambda = 1$ TeV for the NA62 $K^{+}\rightarrow\pi^{+}X_{\rm inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{ff}/\lambda)$ for an ALP $a$, in the BC10 model, evaluated assuming $\Lambda = 1$ TeV for the NA62 $K^{+}\rightarrow\pi^{+}X_{\rm inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{ff}/\lambda)$ for an ALP $a$, in the BC10 model, evaluated assuming $\Lambda = 1$ TeV for the NA62 $\pi^{0}\rightarrow\rm{inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{ff}/\lambda)$ for an ALP $a$, in the BC10 model, evaluated assuming $\Lambda = 1$ TeV for the NA62 $\pi^{0}\rightarrow\rm{inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{ff}/\lambda)$ for an ALP $a$, in the BC10 model, evaluated assuming $\Lambda = 1$ TeV for the NA62 $K^{+}\rightarrow\pi^{+}\mu^{+}\mu^{-}$ study.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{ff}/\lambda)$ for an ALP $a$, in the BC10 model, evaluated assuming $\Lambda = 1$ TeV for the NA62 $K^{+}\rightarrow\pi^{+}\mu^{+}\mu^{-}$ study.

Branching ratio of the $K^{+}\rightarrow\pi^{+}a$ decay divided by $(C_{GG}/\Lambda)^{2}$, as a function of $m_{a}$, assuming $\Lambda = 1$ TeV.

Branching ratio of the $K^{+}\rightarrow\pi^{+}a$ decay divided by $(C_{GG}/\Lambda)^{2}$, as a function of $m_{a}$, assuming $\Lambda = 1$ TeV.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{GG}/\Lambda)$ for an ALP $a$, of the BC11 model, evaluated assuming $\Lambda = 1$ TeV, from the NA62 search for $K^{+}\rightarrow\pi^{+}X_{\rm inv}$.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{GG}/\Lambda)$ for an ALP $a$, of the BC11 model, evaluated assuming $\Lambda = 1$ TeV, from the NA62 search for $K^{+}\rightarrow\pi^{+}X_{\rm inv}$.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{GG}/\Lambda)$ for an ALP $a$, of the BC11 model, evaluated assuming $\Lambda = 1$ TeV, from the NA62 search for $\pi^{0}\rightarrow\rm{inv}$.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{GG}/\Lambda)$ for an ALP $a$, of the BC11 model, evaluated assuming $\Lambda = 1$ TeV, from the NA62 search for $\pi^{0}\rightarrow\rm{inv}$.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{GG}/\Lambda)$ for an ALP $a$, of the BC11 model, evaluated assuming $\Lambda = 1$ TeV, from the NA62 $K^{+}\rightarrow\pi^{+}\gamma\gamma$ study.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{GG}/\Lambda)$ for an ALP $a$, of the BC11 model, evaluated assuming $\Lambda = 1$ TeV, from the NA62 $K^{+}\rightarrow\pi^{+}\gamma\gamma$ study.

Groomed $B^\pm$-tagged jet invariant mass $m_{\textrm{jet,gr}}/p_{\textrm{T,jet}}$ for $R=0.5$ jets reconstructed in pp data, without any WTA flavour requirement. Normalization is set to unity. $20 < p_{\textrm{T,jet}} < 30$ GeV, soft drop $z_{\textrm{cut}}=0.1, \beta=0$.

Groomed $B^\pm$-tagged jet invariant mass $m_{\textrm{jet,gr}}/p_{\textrm{T,jet}}$ for $R=0.5$ jets reconstructed in pp data, without any WTA flavour requirement. Normalization is set to unity. $30 < p_{\textrm{T,jet}} < 50$ GeV, soft drop $z_{\textrm{cut}}=0.1, \beta=0$.

Groomed $B^\pm$-tagged jet invariant mass $m_{\textrm{jet,gr}}/p_{\textrm{T,jet}}$ for $R=0.5$ jets reconstructed in pp data, without any WTA flavour requirement. Normalization is set to unity. $50 < p_{\textrm{T,jet}} < 100$ GeV, soft drop $z_{\textrm{cut}}=0.1, \beta=0$.

Groomed $B^\pm$-tagged jet invariant mass $m_{\textrm{jet,gr}}/p_{\textrm{T,jet}}$ for $R=0.5$ jets reconstructed in pp data, without any WTA flavour requirement. Normalization is set to the soft drop tagging fraction, given by the number of groomed jets (without any WTA flavour requirement) to number of ungroomed jets (without any WTA flavour requirement). $10 < p_{\textrm{T,jet}} < 12$ GeV, soft drop $z_{\textrm{cut}}=0.1, \beta=0$.

Groomed $B^\pm$-tagged jet invariant mass $m_{\textrm{jet,gr}}/p_{\textrm{T,jet}}$ for $R=0.5$ jets reconstructed in pp data, without any WTA flavour requirement. Normalization is set to the soft drop tagging fraction, given by the number of groomed jets (without any WTA flavour requirement) to number of ungroomed jets (without any WTA flavour requirement). $12 < p_{\textrm{T,jet}} < 15$ GeV, soft drop $z_{\textrm{cut}}=0.1, \beta=0$.

Groomed $B^\pm$-tagged jet invariant mass $m_{\textrm{jet,gr}}/p_{\textrm{T,jet}}$ for $R=0.5$ jets reconstructed in pp data, without any WTA flavour requirement. Normalization is set to the soft drop tagging fraction, given by the number of groomed jets (without any WTA flavour requirement) to number of ungroomed jets (without any WTA flavour requirement). $15 < p_{\textrm{T,jet}} < 20$ GeV, soft drop $z_{\textrm{cut}}=0.1, \beta=0$.

Groomed $B^\pm$-tagged jet invariant mass $m_{\textrm{jet,gr}}/p_{\textrm{T,jet}}$ for $R=0.5$ jets reconstructed in pp data, without any WTA flavour requirement. Normalization is set to the soft drop tagging fraction, given by the number of groomed jets (without any WTA flavour requirement) to number of ungroomed jets (without any WTA flavour requirement). $20 < p_{\textrm{T,jet}} < 30$ GeV, soft drop $z_{\textrm{cut}}=0.1, \beta=0$.

Groomed $B^\pm$-tagged jet invariant mass $m_{\textrm{jet,gr}}/p_{\textrm{T,jet}}$ for $R=0.5$ jets reconstructed in pp data, without any WTA flavour requirement. Normalization is set to the soft drop tagging fraction, given by the number of groomed jets (without any WTA flavour requirement) to number of ungroomed jets (without any WTA flavour requirement). $30 < p_{\textrm{T,jet}} < 50$ GeV, soft drop $z_{\textrm{cut}}=0.1, \beta=0$.

Groomed $B^\pm$-tagged jet invariant mass $m_{\textrm{jet,gr}}/p_{\textrm{T,jet}}$ for $R=0.5$ jets reconstructed in pp data, without any WTA flavour requirement. Normalization is set to the soft drop tagging fraction, given by the number of groomed jets (without any WTA flavour requirement) to number of ungroomed jets (without any WTA flavour requirement). $50 < p_{\textrm{T,jet}} < 100$ GeV, soft drop $z_{\textrm{cut}}=0.1, \beta=0$.

Ungroomed $B^\pm$-tagged jet invariant mass $m_{\textrm{jet}}/p_{\textrm{T,jet}}$ for $R=0.5$ jets reconstructed in pp data, without any WTA flavour requirement. Normalization is set to unity. $10 < p_{\textrm{T,jet}} < 12$ GeV.

Ungroomed $B^\pm$-tagged jet invariant mass $m_{\textrm{jet}}/p_{\textrm{T,jet}}$ for $R=0.5$ jets reconstructed in pp data, without any WTA flavour requirement. Normalization is set to unity. $12 < p_{\textrm{T,jet}} < 15$ GeV.

Ungroomed $B^\pm$-tagged jet invariant mass $m_{\textrm{jet}}/p_{\textrm{T,jet}}$ for $R=0.5$ jets reconstructed in pp data, without any WTA flavour requirement. Normalization is set to unity. $15 < p_{\textrm{T,jet}} < 20$ GeV.

Ungroomed $B^\pm$-tagged jet invariant mass $m_{\textrm{jet}}/p_{\textrm{T,jet}}$ for $R=0.5$ jets reconstructed in pp data, without any WTA flavour requirement. Normalization is set to unity. $20 < p_{\textrm{T,jet}} < 30$ GeV.

Ungroomed $B^\pm$-tagged jet invariant mass $m_{\textrm{jet}}/p_{\textrm{T,jet}}$ for $R=0.5$ jets reconstructed in pp data, without any WTA flavour requirement. Normalization is set to unity. $30 < p_{\textrm{T,jet}} < 50$ GeV.

Ungroomed $B^\pm$-tagged jet invariant mass $m_{\textrm{jet}}/p_{\textrm{T,jet}}$ for $R=0.5$ jets reconstructed in pp data, without any WTA flavour requirement. Normalization is set to unity. $50 < p_{\textrm{T,jet}} < 100$ GeV.

Groomed $B^\pm$-tagged jet invariant mass $m_{\textrm{jet,gr}}/p_{\textrm{T,jet}}$ for $R=0.5$ jets reconstructed in pp data tagged with WTA flavour. Normalization is set to the WTA tagging fraction, given by the number of (groomed) jets tagged with WTA flavour to number of (groomed) jets without WTA flavour tagging. $10 < p_{\textrm{T,jet}} < 12$ GeV, soft drop $z_{\textrm{cut}}=0.1, \beta=0$.

Groomed $B^\pm$-tagged jet invariant mass $m_{\textrm{jet,gr}}/p_{\textrm{T,jet}}$ for $R=0.5$ jets reconstructed in pp data tagged with WTA flavour. Normalization is set to the WTA tagging fraction, given by the number of (groomed) jets tagged with WTA flavour to number of (groomed) jets without WTA flavour tagging. $12 < p_{\textrm{T,jet}} < 15$ GeV, soft drop $z_{\textrm{cut}}=0.1, \beta=0$.

Groomed $B^\pm$-tagged jet invariant mass $m_{\textrm{jet,gr}}/p_{\textrm{T,jet}}$ for $R=0.5$ jets reconstructed in pp data tagged with WTA flavour. Normalization is set to the WTA tagging fraction, given by the number of (groomed) jets tagged with WTA flavour to number of (groomed) jets without WTA flavour tagging. $15 < p_{\textrm{T,jet}} < 20$ GeV, soft drop $z_{\textrm{cut}}=0.1, \beta=0$.

Groomed $B^\pm$-tagged jet invariant mass $m_{\textrm{jet,gr}}/p_{\textrm{T,jet}}$ for $R=0.5$ jets reconstructed in pp data tagged with WTA flavour. Normalization is set to the WTA tagging fraction, given by the number of (groomed) jets tagged with WTA flavour to number of (groomed) jets without WTA flavour tagging. $20 < p_{\textrm{T,jet}} < 30$ GeV, soft drop $z_{\textrm{cut}}=0.1, \beta=0$.

Groomed $B^\pm$-tagged jet invariant mass $m_{\textrm{jet,gr}}/p_{\textrm{T,jet}}$ for $R=0.5$ jets reconstructed in pp data tagged with WTA flavour. Normalization is set to the WTA tagging fraction, given by the number of (groomed) jets tagged with WTA flavour to number of (groomed) jets without WTA flavour tagging. $30 < p_{\textrm{T,jet}} < 50$ GeV, soft drop $z_{\textrm{cut}}=0.1, \beta=0$.

Groomed $B^\pm$-tagged jet invariant mass $m_{\textrm{jet,gr}}/p_{\textrm{T,jet}}$ for $R=0.5$ jets reconstructed in pp data tagged with WTA flavour. Normalization is set to the WTA tagging fraction, given by the number of (groomed) jets tagged with WTA flavour to number of (groomed) jets without WTA flavour tagging. $50 < p_{\textrm{T,jet}} < 100$ GeV, soft drop $z_{\textrm{cut}}=0.1, \beta=0$.

Groomed $B^\pm$-tagged jet invariant mass $m_{\textrm{jet,gr}}/p_{\textrm{T,jet}}$ for $R=0.5$ jets reconstructed in pp data tagged with WTA flavour. Normalization is set to the soft drop tagging fraction, given by the number of groomed jets (tagged with WTA flavour) to number of ungroomed jets (tagged with WTA flavour). $10 < p_{\textrm{T,jet}} < 12$ GeV, soft drop $z_{\textrm{cut}}=0.1, \beta=0$.

Groomed $B^\pm$-tagged jet invariant mass $m_{\textrm{jet,gr}}/p_{\textrm{T,jet}}$ for $R=0.5$ jets reconstructed in pp data tagged with WTA flavour. Normalization is set to the soft drop tagging fraction, given by the number of groomed jets (tagged with WTA flavour) to number of ungroomed jets (tagged with WTA flavour). $12 < p_{\textrm{T,jet}} < 15$ GeV, soft drop $z_{\textrm{cut}}=0.1, \beta=0$.

Groomed $B^\pm$-tagged jet invariant mass $m_{\textrm{jet,gr}}/p_{\textrm{T,jet}}$ for $R=0.5$ jets reconstructed in pp data tagged with WTA flavour. Normalization is set to the soft drop tagging fraction, given by the number of groomed jets (tagged with WTA flavour) to number of ungroomed jets (tagged with WTA flavour). $15 < p_{\textrm{T,jet}} < 20$ GeV, soft drop $z_{\textrm{cut}}=0.1, \beta=0$.

Groomed $B^\pm$-tagged jet invariant mass $m_{\textrm{jet,gr}}/p_{\textrm{T,jet}}$ for $R=0.5$ jets reconstructed in pp data tagged with WTA flavour. Normalization is set to the soft drop tagging fraction, given by the number of groomed jets (tagged with WTA flavour) to number of ungroomed jets (tagged with WTA flavour). $20 < p_{\textrm{T,jet}} < 30$ GeV, soft drop $z_{\textrm{cut}}=0.1, \beta=0$.

Groomed $B^\pm$-tagged jet invariant mass $m_{\textrm{jet,gr}}/p_{\textrm{T,jet}}$ for $R=0.5$ jets reconstructed in pp data tagged with WTA flavour. Normalization is set to the soft drop tagging fraction, given by the number of groomed jets (tagged with WTA flavour) to number of ungroomed jets (tagged with WTA flavour). $30 < p_{\textrm{T,jet}} < 50$ GeV, soft drop $z_{\textrm{cut}}=0.1, \beta=0$.

Groomed $B^\pm$-tagged jet invariant mass $m_{\textrm{jet,gr}}/p_{\textrm{T,jet}}$ for $R=0.5$ jets reconstructed in pp data tagged with WTA flavour. Normalization is set to the soft drop tagging fraction, given by the number of groomed jets (tagged with WTA flavour) to number of ungroomed jets (tagged with WTA flavour). $50 < p_{\textrm{T,jet}} < 100$ GeV, soft drop $z_{\textrm{cut}}=0.1, \beta=0$.

Ungroomed $B^\pm$-tagged jet invariant mass $m_{\textrm{jet}}/p_{\textrm{T,jet}}$ for $R=0.5$ jets reconstructed in pp data tagged with WTA flavour. Normalization is set to the WTA tagging fraction, given by the number of (ungroomed) jets tagged with WTA flavour to number of (ungroomed) jets without WTA flavour tagging. $10 < p_{\textrm{T,jet}} < 12$ GeV.

Ungroomed $B^\pm$-tagged jet invariant mass $m_{\textrm{jet}}/p_{\textrm{T,jet}}$ for $R=0.5$ jets reconstructed in pp data tagged with WTA flavour. Normalization is set to the WTA tagging fraction, given by the number of (ungroomed) jets tagged with WTA flavour to number of (ungroomed) jets without WTA flavour tagging. $12 < p_{\textrm{T,jet}} < 15$ GeV.

Ungroomed $B^\pm$-tagged jet invariant mass $m_{\textrm{jet}}/p_{\textrm{T,jet}}$ for $R=0.5$ jets reconstructed in pp data tagged with WTA flavour. Normalization is set to the WTA tagging fraction, given by the number of (ungroomed) jets tagged with WTA flavour to number of (ungroomed) jets without WTA flavour tagging. $15 < p_{\textrm{T,jet}} < 20$ GeV.

Ungroomed $B^\pm$-tagged jet invariant mass $m_{\textrm{jet}}/p_{\textrm{T,jet}}$ for $R=0.5$ jets reconstructed in pp data tagged with WTA flavour. Normalization is set to the WTA tagging fraction, given by the number of (ungroomed) jets tagged with WTA flavour to number of (ungroomed) jets without WTA flavour tagging. $20 < p_{\textrm{T,jet}} < 30$ GeV.

Ungroomed $B^\pm$-tagged jet invariant mass $m_{\textrm{jet}}/p_{\textrm{T,jet}}$ for $R=0.5$ jets reconstructed in pp data tagged with WTA flavour. Normalization is set to the WTA tagging fraction, given by the number of (ungroomed) jets tagged with WTA flavour to number of (ungroomed) jets without WTA flavour tagging. $30 < p_{\textrm{T,jet}} < 50$ GeV.

Ungroomed $B^\pm$-tagged jet invariant mass $m_{\textrm{jet}}/p_{\textrm{T,jet}}$ for $R=0.5$ jets reconstructed in pp data tagged with WTA flavour. Normalization is set to the WTA tagging fraction, given by the number of (ungroomed) jets tagged with WTA flavour to number of (ungroomed) jets without WTA flavour tagging. $50 < p_{\textrm{T,jet}} < 100$ GeV.

Ungroomed $B^\pm$-tagged jet invariant mass $m_{\textrm{jet}}/p_{\textrm{T,jet}}$ for $R=0.5$ jets reconstructed in pp data tagged with WTA flavour. Normalization is set to unity. $10 < p_{\textrm{T,jet}} < 12$ GeV.

Ungroomed $B^\pm$-tagged jet invariant mass $m_{\textrm{jet}}/p_{\textrm{T,jet}}$ for $R=0.5$ jets reconstructed in pp data tagged with WTA flavour. Normalization is set to unity. $12 < p_{\textrm{T,jet}} < 15$ GeV.

Ungroomed $B^\pm$-tagged jet invariant mass $m_{\textrm{jet}}/p_{\textrm{T,jet}}$ for $R=0.5$ jets reconstructed in pp data tagged with WTA flavour. Normalization is set to unity. $15 < p_{\textrm{T,jet}} < 20$ GeV.

Ungroomed $B^\pm$-tagged jet invariant mass $m_{\textrm{jet}}/p_{\textrm{T,jet}}$ for $R=0.5$ jets reconstructed in pp data tagged with WTA flavour. Normalization is set to unity. $20 < p_{\textrm{T,jet}} < 30$ GeV.

Ungroomed $B^\pm$-tagged jet invariant mass $m_{\textrm{jet}}/p_{\textrm{T,jet}}$ for $R=0.5$ jets reconstructed in pp data tagged with WTA flavour. Normalization is set to unity. $30 < p_{\textrm{T,jet}} < 50$ GeV.

Ungroomed $B^\pm$-tagged jet invariant mass $m_{\textrm{jet}}/p_{\textrm{T,jet}}$ for $R=0.5$ jets reconstructed in pp data tagged with WTA flavour. Normalization is set to unity. $50 < p_{\textrm{T,jet}} < 100$ GeV.

90% CL upper limit in axion-like particle coupling to SM fermions at UV scale Lambda=1TeV vs mass parameter space for di-lepton final states.

90% CL upper limit in axion-like particle coupling to SM gluons at UV scale Lambda=1TeV vs mass parameter space for hadronic final states.

Number of expected $a \to K^+K^-\pi^0$ events for BR = 1 in the plane (mass, width) after full selection, for production in B meson decays assuming production coupling $C_{bs}/\Lambda=1\,\mathrm{GeV}^{-1}$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $a \to \pi^+\pi^-\eta$ events for BR = 1 in the plane (mass, width) after full selection, for production in B meson decays assuming production coupling $C_{bs}/\Lambda=1\,\mathrm{GeV}^{-1}$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $a \to \pi^+\pi^-\gamma$ events for BR = 1 in the plane (mass, width) after full selection, for production in B meson decays assuming production coupling $C_{bs}/\Lambda=1\,\mathrm{GeV}^{-1}$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $a \to \pi^+\pi^-\pi^0$ events for BR = 1 in the plane (mass, width) after full selection, for production in B meson decays assuming production coupling $C_{bs}/\Lambda=1\,\mathrm{GeV}^{-1}$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $a \to \pi^+\pi^-\pi^0\pi^0$ events for BR = 1 in the plane (mass, width) after full selection, for production in B meson decays assuming production coupling $C_{bs}/\Lambda=1\,\mathrm{GeV}^{-1}$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $a \to e^+e^-$ events for BR = 1 in the plane (mass, width) after full selection, for production in mixing with $\pi^0$ assuming production coupling $\theta_{\pi^0} = 1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $a \to \mu^+\mu^-$ events for BR = 1 in the plane (mass, width) after full selection, for production in mixing with $\pi^0$ assuming production coupling $\theta_{\pi^0} = 1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $a \to K^+K^-\pi^0$ events for BR = 1 in the plane (mass, width) after full selection, for production in mixing with $\pi^0$ assuming production coupling $\theta_{\pi^0} = 1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $a \to \pi^+\pi^-\eta$ events for BR = 1 in the plane (mass, width) after full selection, for production in mixing with $\pi^0$ assuming production coupling $\theta_{\pi^0} = 1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $a \to \pi^+\pi^-\gamma$ events for BR = 1 in the plane (mass, width) after full selection, for production in mixing with $\pi^0$ assuming production coupling $\theta_{\pi^0} = 1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $a \to \pi^+\pi^-\pi^0$ events for BR = 1 in the plane (mass, width) after full selection, for production in mixing with $\pi^0$ assuming production coupling $\theta_{\pi^0} = 1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $a \to \pi^+\pi^-\pi^0\pi^0$ events for BR = 1 in the plane (mass, width) after full selection, for production in mixing with $\pi^0$ assuming production coupling $\theta_{\pi^0} = 1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $a \to e^+e^-$ events for BR = 1 in the plane (mass, width) after full selection, for production in mixing with $\eta$ assuming production coupling $\theta_{\eta} = 1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $a \to \mu^+\mu^-$ events for BR = 1 in the plane (mass, width) after full selection, for production in mixing with $\eta$ assuming production coupling $\theta_{\eta} = 1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $a \to K^+K^-\pi^0$ events for BR = 1 in the plane (mass, width) after full selection, for production in mixing with $\eta$ assuming production coupling $\theta_{\eta} = 1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $a \to \pi^+\pi^-\eta$ events for BR = 1 in the plane (mass, width) after full selection, for production in mixing with $\eta$ assuming production coupling $\theta_{\eta} = 1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $a \to \pi^+\pi^-\gamma$ events for BR = 1 in the plane (mass, width) after full selection, for production in mixing with $\eta$ assuming production coupling $\theta_{\eta} = 1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $a \to \pi^+\pi^-\pi^0$ events for BR = 1 in the plane (mass, width) after full selection, for production in mixing with $\eta$ assuming production coupling $\theta_{\eta} = 1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $a \to \pi^+\pi^-\pi^0\pi^0$ events for BR = 1 in the plane (mass, width) after full selection, for production in mixing with $\eta$ assuming production coupling $\theta_{\eta} = 1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $a \to e^+e^-$ events for BR = 1 in the plane (mass, width) after full selection, for production in mixing with $\eta^\prime$ assuming production coupling $\theta_{\eta^\prime} = 1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $a \to \mu^+\mu^-$ events for BR = 1 in the plane (mass, width) after full selection, for production in mixing with $\eta^\prime$ assuming production coupling $\theta_{\eta^\prime} = 1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $a \to K^+K^-\pi^0$ events for BR = 1 in the plane (mass, width) after full selection, for production in mixing with $\eta^\prime$ assuming production coupling $\theta_{\eta^\prime} = 1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $a \to \pi^+\pi^-\eta$ events for BR = 1 in the plane (mass, width) after full selection, for production in mixing with $\eta^\prime$ assuming production coupling $\theta_{\eta^\prime} = 1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $a \to \pi^+\pi^-\gamma$ events for BR = 1 in the plane (mass, width) after full selection, for production in mixing with $\eta^\prime$ assuming production coupling $\theta_{\eta^\prime} = 1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $a \to \pi^+\pi^-\pi^0$ events for BR = 1 in the plane (mass, width) after full selection, for production in mixing with $\eta^\prime$ assuming production coupling $\theta_{\eta^\prime} = 1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $a \to \pi^+\pi^-\pi^0\pi^0$ events for BR = 1 in the plane (mass, width) after full selection, for production in mixing with $\eta^\prime$ assuming production coupling $\theta_{\eta^\prime} = 1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $a \to e^+e^-$ events for BR = 1 in the plane (mass, width) after full selection, for Primakoff production assuming production coupling $C_{\gamma\gamma}/\Lambda=1\,\mathrm{GeV}^{-1}$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $a \to \mu^+\mu^-$ events for BR = 1 in the plane (mass, width) after full selection, for Primakoff production assuming production coupling $C_{\gamma\gamma}/\Lambda=1\,\mathrm{GeV}^{-1}$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $a \to K^+K^-\pi^0$ events for BR = 1 in the plane (mass, width) after full selection, for Primakoff production assuming production coupling $C_{\gamma\gamma}/\Lambda=1\,\mathrm{GeV}^{-1}$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $a \to \pi^+\pi^-\eta$ events for BR = 1 in the plane (mass, width) after full selection, for Primakoff production assuming production coupling $C_{\gamma\gamma}/\Lambda=1\,\mathrm{GeV}^{-1}$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $a \to \pi^+\pi^-\gamma$ events for BR = 1 in the plane (mass, width) after full selection, for Primakoff production assuming production coupling $C_{\gamma\gamma}/\Lambda=1\,\mathrm{GeV}^{-1}$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $a \to \pi^+\pi^-\pi^0$ events for BR = 1 in the plane (mass, width) after full selection, for Primakoff production assuming production coupling $C_{\gamma\gamma}/\Lambda=1\,\mathrm{GeV}^{-1}$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $a \to \pi^+\pi^-\pi^0\pi^0$ events for BR = 1 in the plane (mass, width) after full selection, for Primakoff production assuming production coupling $C_{\gamma\gamma}/\Lambda=1\,\mathrm{GeV}^{-1}$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $A^\prime \to e^+e^-$ events for BR = 1 in the plane (mass, width) after full selection, for Bremsstrahlung production assuming production coupling $\varepsilon=1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $A^\prime \to \mu^+\mu^-$ events for BR = 1 in the plane (mass, width) after full selection, for Bremsstrahlung production assuming production coupling $\varepsilon=1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $A^\prime \to K^+K^-$ events for BR = 1 in the plane (mass, width) after full selection, for Bremsstrahlung production assuming production coupling $\varepsilon=1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $A^\prime \to K^+K^-\pi^0$ events for BR = 1 in the plane (mass, width) after full selection, for Bremsstrahlung production assuming production coupling $\varepsilon=1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $A^\prime \to \pi^+\pi^-$ events for BR = 1 in the plane (mass, width) after full selection, for Bremsstrahlung production assuming production coupling $\varepsilon=1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $A^\prime \to \pi^+\pi^-\pi^0$ events for BR = 1 in the plane (mass, width) after full selection, for Bremsstrahlung production assuming production coupling $\varepsilon=1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $A^\prime \to \pi^+\pi^-\pi^0\pi^0$ events for BR = 1 in the plane (mass, width) after full selection, for Bremsstrahlung production assuming production coupling $\varepsilon=1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $A^\prime \to e^+e^-$ events for BR = 1 in the plane (mass, width) after full selection, for mixing production assuming production coupling $\varepsilon=1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $A^\prime \to \mu^+\mu^-$ events for BR = 1 in the plane (mass, width) after full selection, for mixing production assuming production coupling $\varepsilon=1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $A^\prime \to K^+K^-$ events for BR = 1 in the plane (mass, width) after full selection, for mixing production assuming production coupling $\varepsilon=1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $A^\prime \to K^+K^-\pi^0$ events for BR = 1 in the plane (mass, width) after full selection, for mixing production assuming production coupling $\varepsilon=1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $A^\prime \to \pi^+\pi^-$ events for BR = 1 in the plane (mass, width) after full selection, for mixing production assuming production coupling $\varepsilon=1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $A^\prime \to \pi^+\pi^-\pi^0$ events for BR = 1 in the plane (mass, width) after full selection, for mixing production assuming production coupling $\varepsilon=1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $A^\prime \to \pi^+\pi^-\pi^0\pi^0$ events for BR = 1 in the plane (mass, width) after full selection, for mixing production assuming production coupling $\varepsilon=1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $A^\prime \to e^+e^-$ events for BR = 1 in the plane (mass, width) after full selection, for production in light meson decays assuming production coupling $\varepsilon=1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $A^\prime \to \mu^+\mu^-$ events for BR = 1 in the plane (mass, width) after full selection, for production in light meson decays assuming production coupling $\varepsilon=1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $A^\prime \to \pi^+\pi^-$ events for BR = 1 in the plane (mass, width) after full selection, for production in light meson decays assuming production coupling $\varepsilon=1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $A^\prime \to \pi^+\pi^-\pi^0$ events for BR = 1 in the plane (mass, width) after full selection, for production in light meson decays assuming production coupling $\varepsilon=1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $A^\prime \to \pi^+\pi^-\pi^0\pi^0$ events for BR = 1 in the plane (mass, width) after full selection, for production in light meson decays assuming production coupling $\varepsilon=1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $S \to e^+e^-$ events for BR = 1 in the plane (mass, width) after full selection, for Bremsstrahlung production assuming production coupling $\mathrm{sin}^2\theta=1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $S \to \mu^+\mu^-$ events for BR = 1 in the plane (mass, width) after full selection, for Bremsstrahlung production assuming production coupling $\mathrm{sin}^2\theta=1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $S \to K^+K^-$ events for BR = 1 in the plane (mass, width) after full selection, for Bremsstrahlung production assuming production coupling $\mathrm{sin}^2\theta=1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $S \to \pi^+\pi^-$ events for BR = 1 in the plane (mass, width) after full selection, for Bremsstrahlung production assuming production coupling $\mathrm{sin}^2\theta=1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $S \to \pi^+\pi^-\pi^0\pi^0$ events for BR = 1 in the plane (mass, width) after full selection, for Bremsstrahlung production assuming production coupling $\mathrm{sin}^2\theta=1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $S \to e^+e^-$ events for BR = 1 in the plane (mass, width) after full selection, for production in B meson decays assuming production coupling $\mathrm{sin}^2\theta=1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $S \to \mu^+\mu^-$ events for BR = 1 in the plane (mass, width) after full selection, for production in B meson decays assuming production coupling $\mathrm{sin}^2\theta=1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $S \to K^+K^-$ events for BR = 1 in the plane (mass, width) after full selection, for production in B meson decays assuming production coupling $\mathrm{sin}^2\theta=1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

Number of expected $S \to \pi^+\pi^-$ events for BR = 1 in the plane (mass, width) after full selection, for production in B meson decays assuming production coupling $\mathrm{sin}^2\theta=1$. Acceptance for particles that reach the FV and decay therein and mass resolution.

$\chi_{c0}(4500) \to J/\psi(\to \mu^+ \mu^-)\phi(\to K^+ K^-)$ diffractive production cross-section, multiplied by $\mathcal{B}(J/\psi \to \mu^+ \mu^-)$ and $\mathcal{B}(\phi \to K^+ K^-)$ branching ratios.

$\chi_{c1}(4685) \ \mathrm{or} \ \chi_{c0}(4700) \to J/\psi(\to \mu^+ \mu^-)\phi(\to K^+ K^-)$ diffractive production cross-section, multiplied by $\mathcal{B}(J/\psi \to \mu^+ \mu^-)$ and $\mathcal{B}(\phi \to K^+ K^-)$ branching ratios.

Nonresonant $J/\psi(\to \mu^+ \mu^-)\phi(\to K^+ K^-)$ diffractive production cross-section, multiplied by $\mathcal{B}(J/\psi \to \mu^+ \mu^-)$ and $\mathcal{B}(\phi \to K^+ K^-)$ branching ratios.

90% CL upper limit in dark photon coupling vs mass parameter space for the $A^\prime \rightarrow l^+l^-$ analysis.

90% CL upper limit in $BR(B \rightarrow K a, a \rightarrow e^+e^-)$ vs lifetime $\tau$ parameter space.

90% CL upper limit in $BR(B \rightarrow K a, a \rightarrow e^+e^-)$ vs lifetime $\tau$ parameter space.

Upper limits at 90% CL of $B(K^+\to\pi^+a)\times B(a\to\gamma\gamma)$ in the prompt ALP decay assumption.

See caption of Figure 9.

See caption of Figure 9.

See caption of Figure 9.

See caption of Figure 9.

See caption of Figure 9.

See caption of Figure 9.

Measured single differential cross-sections in bins of $y^{Z}$. The first uncertainty is statistical, the second systematic, and the third is from the uncertainty on the integrated luminosity.

Measured single differential cross-sections in bins of $p_{T}^{Z}$. The first uncertainty is statistical, the second systematic, and the third is due to the luminosity.

Measured single differential cross-sections in bins of $\phi_{\eta}^{*}$. The first uncertainty is statistical, the second systematic, and the third is due to the luminosity.

Statistical correlation matrix for the one-dimensional $y^{Z}$ measurement.

Statistical correlation matrix for the one-dimensional $p_{T}^{Z}$ measurement.

Statistical correlation matrix for the one-dimensional $\phi_{\eta}^{*}$ measurement.

Correlation matrix for the efficiency uncertainty of the one-dimensional $y^{Z}$ measurement.

Correlation matrix for the efficiency uncertainty of the one-dimensional $p_{T}^{Z}$ measurement.

Correlation matrix for the efficiency uncertainty of the one-dimensional $\phi_{\eta}^{*}$ measurement.