CERN Accelerating science

(Color online) The schematic layout of the NA61/SHINE experiment at the CERN SPS during \textit{p+p} data taking (horizontal cut, not to scale). The beam and trigger detector configuration used for data taking in 2009 is shown in the inset (see Refs.~\cite{Abgrall:2014xwa, NA61SHINE:2013tiv, Aduszkiewicz:2015jna} for a detailed description). The chosen coordinate system is drawn on the lower left: its origin lies in the middle of the VTPC-2 on the beam axis.

Armenteros-Podolanski plots of $V^0$ candidates after all track and topology selection criteria for $p_{beam}=31, 40$ and $80$~\GeVc from left to right. The boundaries on the plots' left and right sides result from using the $cos\Theta^{*}$ cut, while the upper and lower boundaries are shaped by selecting a certain invariant mass range.

Armenteros-Podolanski plots of $V^0$ candidates after all track and topology selection criteria for $p_{beam}=31, 40$ and $80$~\GeVc from left to right. The boundaries on the plots' left and right sides result from using the $cos\Theta^{*}$ cut, while the upper and lower boundaries are shaped by selecting a certain invariant mass range.

Armenteros-Podolanski plots of $V^0$ candidates after all track and topology selection criteria for $p_{beam}=31, 40$ and $80$~\GeVc from left to right. The boundaries on the plots' left and right sides result from using the $cos\Theta^{*}$ cut, while the upper and lower boundaries are shaped by selecting a certain invariant mass range.

The invariant mass distribution of \Kshort candidates for experimental data (\textit{left}) and MC (\textit{right}) for the $p_{beam}=40$~\GeVc data set for $-0.25 \leq y < 0.25$ and $0.2 \leq p_{T} < 0.4$ after all selection criteria. The dashed-blue vertical lines indicate the regions where the \Kshort signal was integrated. The signal data points are black, the fitted background is orange, the fitted signal is blue, and the total fit results are red. Mass resolutions obtained from the fits are: $\sigma = (0.00925 \pm 0.00064)~\GeV$ for the experimental data and $\sigma = (0.00946 \pm 0.00017)~\GeV$ for the MC.

The invariant mass distribution of \Kshort candidates for experimental data (\textit{left}) and MC (\textit{right}) for the $p_{beam}=40$~\GeVc data set for $-0.25 \leq y < 0.25$ and $0.2 \leq p_{T} < 0.4$ after all selection criteria. The dashed-blue vertical lines indicate the regions where the \Kshort signal was integrated. The signal data points are black, the fitted background is orange, the fitted signal is blue, and the total fit results are red. Mass resolutions obtained from the fits are: $\sigma = (0.00925 \pm 0.00064)~\GeV$ for the experimental data and $\sigma = (0.00946 \pm 0.00017)~\GeV$ for the MC.

Uncorrected bin-by-bin multiplicities of \Kshort with their statistical uncertainties for $p_{beam}=31$~\GeVc (\textit{left}), $p_{beam}=40$~\GeVc (\textit{right}) and $p_{beam}=80$~\GeVc (\textit{bottom}).

Uncorrected bin-by-bin multiplicities of \Kshort with their statistical uncertainties for $p_{beam}=31$~\GeVc (\textit{left}), $p_{beam}=40$~\GeVc (\textit{right}) and $p_{beam}=80$~\GeVc (\textit{bottom}).

Uncorrected bin-by-bin multiplicities of \Kshort with their statistical uncertainties for $p_{beam}=31$~\GeVc (\textit{left}), $p_{beam}=40$~\GeVc (\textit{right}) and $p_{beam}=80$~\GeVc (\textit{bottom}).

Monte-Carlo correction factors (see Eq.~\ref{eq:cmc}) with their statistical uncertainties (see Eq.~\ref{eq:DMC}) in each ($y, p_T$) bin for $p_{beam}=31$~\GeVc (\textit{left}), $p_{beam}=40$~\GeVc (\textit{right}) and $p_{beam}=80$~\GeVc (\textit{bottom}).

Monte-Carlo correction factors (see Eq.~\ref{eq:cmc}) with their statistical uncertainties (see Eq.~\ref{eq:DMC}) in each ($y, p_T$) bin for $p_{beam}=31$~\GeVc (\textit{left}), $p_{beam}=40$~\GeVc (\textit{right}) and $p_{beam}=80$~\GeVc (\textit{bottom}).

Monte-Carlo correction factors (see Eq.~\ref{eq:cmc}) with their statistical uncertainties (see Eq.~\ref{eq:DMC}) in each ($y, p_T$) bin for $p_{beam}=31$~\GeVc (\textit{left}), $p_{beam}=40$~\GeVc (\textit{right}) and $p_{beam}=80$~\GeVc (\textit{bottom}).

(Color online) Corrected lifetime distributions for \Kshort mesons produced in inelastic \textit{p+p} interactions at beam energies of $p_{beam}=31$~\GeVc (\textit{top left}), $p_{beam}=40$~\GeVc (\textit{top right}), and $p_{beam}=80$~\GeVc (\textit{bottom}). The straight lines show the results of exponential fits used to obtain the mean lifetimes (normalized to the PDG value) in rapidity bins. Statistical uncertainties are smaller than the marker size and are not visible on the plots.

(Color online) Corrected lifetime distributions for \Kshort mesons produced in inelastic \textit{p+p} interactions at beam energies of $p_{beam}=31$~\GeVc (\textit{top left}), $p_{beam}=40$~\GeVc (\textit{top right}), and $p_{beam}=80$~\GeVc (\textit{bottom}). The straight lines show the results of exponential fits used to obtain the mean lifetimes (normalized to the PDG value) in rapidity bins. Statistical uncertainties are smaller than the marker size and are not visible on the plots.

(Color online) Corrected lifetime distributions for \Kshort mesons produced in inelastic \textit{p+p} interactions at beam energies of $p_{beam}=31$~\GeVc (\textit{top left}), $p_{beam}=40$~\GeVc (\textit{top right}), and $p_{beam}=80$~\GeVc (\textit{bottom}). The straight lines show the results of exponential fits used to obtain the mean lifetimes (normalized to the PDG value) in rapidity bins. Statistical uncertainties are smaller than the marker size and are not visible on the plots.

(Color online) Mean \Kshort lifetimes (normalized to the PDG value) obtained from fits to the lifetime distributions of Fig.~\ref{fig:dndtau} for the $p_{beam}=40$~\GeVc (\textit{left}) and $p_{beam}=80$~\GeVc (\textit{right}) data sets versus the rapidity $y$. The error bars indicate the statistical uncertainties.

(Color online) Mean \Kshort lifetimes (normalized to the PDG value) obtained from fits to the lifetime distributions of Fig.~\ref{fig:dndtau} for the $p_{beam}=40$~\GeVc (\textit{left}) and $p_{beam}=80$~\GeVc (\textit{right}) data sets versus the rapidity $y$. The error bars indicate the statistical uncertainties.

(Color online) Double-differential \Kshort spectra in inelastic \textit{p+p} interaction at 31~\GeVc (\textit{left}), 40~\GeVc (\textit{middle}) and 80~\GeVc (\textit{right}) at mid-rapidity ($y \approx 0$) calculated according to Eq.~\ref{eq:dndydpt}. Measured points are shown as blue full triangles up (for $p_{beam}=31$~\GeVc), green full triangles down (for $p_{beam}=40$~\GeVc) and orange full squares (for $p_{beam}=80$~\GeVc). The solid curves are fitted to the data points using the exponential function (Eq.~\ref{eq:fit_to_dndydpt}). Vertical bars indicate statistical uncertainties (for some points smaller than the symbol size). Shaded boxes show systematic uncertainties. Only statistical uncertainties are taken into account in the fit, because the systematic uncertainties do not depend on \pt. The numerical values of the data points are listed in Table~\ref{tab:dndydpt}.

(Color online) Double-differential \Kshort spectra in inelastic \textit{p+p} interaction at 31~\GeVc (\textit{left}), 40~\GeVc (\textit{middle}) and 80~\GeVc (\textit{right}) at mid-rapidity ($y \approx 0$) calculated according to Eq.~\ref{eq:dndydpt}. Measured points are shown as blue full triangles up (for $p_{beam}=31$~\GeVc), green full triangles down (for $p_{beam}=40$~\GeVc) and orange full squares (for $p_{beam}=80$~\GeVc). The solid curves are fitted to the data points using the exponential function (Eq.~\ref{eq:fit_to_dndydpt}). Vertical bars indicate statistical uncertainties (for some points smaller than the symbol size). Shaded boxes show systematic uncertainties. Only statistical uncertainties are taken into account in the fit, because the systematic uncertainties do not depend on \pt. The numerical values of the data points are listed in Table~\ref{tab:dndydpt}.

(Color online) Double-differential \Kshort spectra in inelastic \textit{p+p} interaction at 31~\GeVc (\textit{left}), 40~\GeVc (\textit{middle}) and 80~\GeVc (\textit{right}) at mid-rapidity ($y \approx 0$) calculated according to Eq.~\ref{eq:dndydpt}. Measured points are shown as blue full triangles up (for $p_{beam}=31$~\GeVc), green full triangles down (for $p_{beam}=40$~\GeVc) and orange full squares (for $p_{beam}=80$~\GeVc). The solid curves are fitted to the data points using the exponential function (Eq.~\ref{eq:fit_to_dndydpt}). Vertical bars indicate statistical uncertainties (for some points smaller than the symbol size). Shaded boxes show systematic uncertainties. Only statistical uncertainties are taken into account in the fit, because the systematic uncertainties do not depend on \pt. The numerical values of the data points are listed in Table~\ref{tab:dndydpt}.

(Color online) Rapidity distribution $dn/dy$ obtained by \pt-integration of data and extrapolation. Statistical uncertainties are shown by vertical bars (often smaller than the marker size), while shaded boxes indicate systematic uncertainties. The curves indicate the result of the Gaussian fit to the measured points. Points for \textit{p+p} at $\sqrt{s_{NN}}=17.3$ \GeV are taken from \cite{NA61SHINE:2021iay}.

(Color online) $dn/dy$ as a function of scaled rapidity $y/y_{beam}$ of \Kshort mesons in inelastic \textit{p+p} interactions at 31, 40 and 80~\GeVc. Measured points are shown as blue full triangles up (for $p_{beam}=31$~\GeVc), green full triangles down (for $p_{beam}=40$~\GeVc) and orange full squares (for $p_{beam}=80$~\GeVc). Results from other experiments are shown as azure-colored diamonds (for Blobel $et$ $al.$ at 24~\GeVc) and yellow-colored diamonds (for Ammosov $et$ $al.$ at 69~\GeVc). Vertical bars indicate statistical uncertainties (for some points smaller than the symbol size).

(Color online) Rapidity distribution $dn/dy$ of \Kshort mesons in inelastic \textit{p+p} interactions at 31, 40, 80 and 158~\GeVc. Measured points are shown as blue full triangles up for $p_{beam}=31$~\GeVc (\textit{top left}), green full triangles down for $p_{beam}=40$~\GeVc (\textit{top right}), orange full squares for $p_{beam}=80$~\GeVc (\textit{bottom left}) and red full circles for $p_{beam}=158$~\GeVc (\textit{bottom right}). Results for charged kaons obtained by formula $\frac{1}{4}(N_{K^+}+3 \cdot N_{K^-})$ are shown by open colored symbols for all data sets, while the results obtained by formula $\frac{1}{2}(N_{K^+} + N_{K^-})$ are shown by grey opened symbols. Vertical bars indicate statistical uncertainties (for some points smaller than the symbol size).

(Color online) Rapidity distribution $dn/dy$ of \Kshort mesons in inelastic \textit{p+p} interactions at 31, 40, 80 and 158~\GeVc. Measured points are shown as blue full triangles up for $p_{beam}=31$~\GeVc (\textit{top left}), green full triangles down for $p_{beam}=40$~\GeVc (\textit{top right}), orange full squares for $p_{beam}=80$~\GeVc (\textit{bottom left}) and red full circles for $p_{beam}=158$~\GeVc (\textit{bottom right}). Results for charged kaons obtained by formula $\frac{1}{4}(N_{K^+}+3 \cdot N_{K^-})$ are shown by open colored symbols for all data sets, while the results obtained by formula $\frac{1}{2}(N_{K^+} + N_{K^-})$ are shown by grey opened symbols. Vertical bars indicate statistical uncertainties (for some points smaller than the symbol size).

(Color online) Rapidity distribution $dn/dy$ of \Kshort mesons in inelastic \textit{p+p} interactions at 31, 40, 80 and 158~\GeVc. Measured points are shown as blue full triangles up for $p_{beam}=31$~\GeVc (\textit{top left}), green full triangles down for $p_{beam}=40$~\GeVc (\textit{top right}), orange full squares for $p_{beam}=80$~\GeVc (\textit{bottom left}) and red full circles for $p_{beam}=158$~\GeVc (\textit{bottom right}). Results for charged kaons obtained by formula $\frac{1}{4}(N_{K^+}+3 \cdot N_{K^-})$ are shown by open colored symbols for all data sets, while the results obtained by formula $\frac{1}{2}(N_{K^+} + N_{K^-})$ are shown by grey opened symbols. Vertical bars indicate statistical uncertainties (for some points smaller than the symbol size).

(Color online) Rapidity distribution $dn/dy$ of \Kshort mesons in inelastic \textit{p+p} interactions at 31, 40, 80 and 158~\GeVc. Measured points are shown as blue full triangles up for $p_{beam}=31$~\GeVc (\textit{top left}), green full triangles down for $p_{beam}=40$~\GeVc (\textit{top right}), orange full squares for $p_{beam}=80$~\GeVc (\textit{bottom left}) and red full circles for $p_{beam}=158$~\GeVc (\textit{bottom right}). Results for charged kaons obtained by formula $\frac{1}{4}(N_{K^+}+3 \cdot N_{K^-})$ are shown by open colored symbols for all data sets, while the results obtained by formula $\frac{1}{2}(N_{K^+} + N_{K^-})$ are shown by grey opened symbols. Vertical bars indicate statistical uncertainties (for some points smaller than the symbol size).

(Color online) Comparison of the experimental \Kshort rapidity distributions with model calculations. Colored symbols show the new measurements of \NASixtyOne as follows: $p_{beam}=31$~\GeVc (\textit{top}), $p_{beam}=40$~\GeVc (\textit{middle}) and $p_{beam}=80$~\GeVc (\textit{bottom}). The black curves show the result of the model calculations: \EposLong (solid), PHSD (dotted) and SMASH~2.0 (dashed).

(Color online) Comparison of the experimental \Kshort rapidity distributions with model calculations. Colored symbols show the new measurements of \NASixtyOne as follows: $p_{beam}=31$~\GeVc (\textit{top}), $p_{beam}=40$~\GeVc (\textit{middle}) and $p_{beam}=80$~\GeVc (\textit{bottom}). The black curves show the result of the model calculations: \EposLong (solid), PHSD (dotted) and SMASH~2.0 (dashed).

(Color online) Comparison of the experimental \Kshort rapidity distributions with model calculations. Colored symbols show the new measurements of \NASixtyOne as follows: $p_{beam}=31$~\GeVc (\textit{top}), $p_{beam}=40$~\GeVc (\textit{middle}) and $p_{beam}=80$~\GeVc (\textit{bottom}). The black curves show the result of the model calculations: \EposLong (solid), PHSD (dotted) and SMASH~2.0 (dashed).

(Color online) Collision energy dependence of mean multiplicity of \Kshort mesons produced in \textit{p+p} interactions. The measurements from \NASixtyOne are shown with colored symbols as follows: blue full triangle up for $p_{beam}=31$~\GeVc, green full triangle down for $p_{beam}=40$~\GeVc, orange full square for $p_{beam}=80$~\GeVc and red full circle for $p_{beam}=158$~\GeVc~\cite{NA61SHINE:2021iay}. The results published by other experiments are shown by the grey open circles~\cite{PhysRev.123.1465, Alexander:1967zz, Firebaugh:1968rq, Blobel:1973jc, Fesefeldt:1979, Bogolyubsky:1988ei, Ammosov:1975bt, AstonGarnjost:1975im, Chapman:1973fn, Brick:1980vj, Jaeger1974pk, Sheng1976, Lopinto:1980ct, EHS-RCBC:1984bxo, Kass:1979nf, Kichimi:1979te}. Statistical uncertainties are smaller than the marker size, while shaded boxes indicate systematic uncertainties.