FIT USING INCOHERENT SUM OF BREIT-WIGNER RESONANCES AND BACKGROUND TERM.

EVENTS SELECTED BY CUTS 1.16 < M(P PI+) < 1.26 GEV AND COS(THETA) > 0. BACKGROUND IS LESS THAN 10 PCT.

TRANSVERSITY FRAME MULTIPOLE PARAMETERS.

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$\Delta \chi^2$ map of phase-I+II data calculated by a raster-scan method. To be used in combination with the $\Delta \chi^2_{\text{crit},x}$ values to generate exclusion contours at $x$% C.L. for phase-I+II data. Additional explanations are given there.

Data from Figure 34 – STEREO exclusion and exclusion sensitivity contours at 95% C.L. for 179 days reactor-on (phase-I+II) using the raster-scan method. A graphical presentation can be downloaded at "Resources" for reference.

Data from Figure 34 – STEREO exclusion and exclusion sensitivity contours at 95% C.L. for 179 days reactor-on (phase-I+II) using the raster-scan method. A graphical presentation can be downloaded at "Resources" for reference.

Data from Figure 34 – STEREO exclusion and exclusion sensitivity contours at 95% C.L. for 179 days reactor-on (phase-I+II) using the CLs method. A graphical presentation can be downloaded at "Resources" for reference.

Data from Figure 34 – STEREO exclusion and exclusion sensitivity contours at 95% C.L. for 179 days reactor-on (phase-I+II) using the CLs method. A graphical presentation can be downloaded at "Resources" for reference.

The $\Delta \chi^2_{\text{crit},x}$ map accounts for the fact that the $\Delta \chi^2$ values of the oscillation fit do not follow a $\chi^2$ distribution with 2 degrees of freedom. Therefore, the $\Delta \chi^2_{\text{crit},x}$ value for x% C.L. of each point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ in the parameter space, $\Delta \chi^2_{\text{crit},x}(\sin^2(2\theta_{ee}), \Delta m^2_{41})$, is determined from the $\Delta \chi^2$ obtained in pseudo-experiments at that point, such that $\Delta \chi^2 \leq \Delta \chi^2_{\text{crit},x}$, for $x$% of the pseudo-experiments. Applying these $\Delta \chi^2_{\text{crit},x}$ values to the $\Delta \chi^2$ map obtained with the data, $x$% C.L. exclusion contours are obtained. The point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ is excluded by the data at $x$% C.L. if $\Delta \chi^2(\sin^2(2\theta_{ee}), \Delta m^2_{41}) > \Delta \chi^2_{\text{crit},x}(\sin^2(2\theta_{ee}), \Delta m^2_{41})$. In order to obtain the $\Delta \chi^2_{\text{crit},x}$ map, $10^4$ pseudo-experiments were generated for each point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ in the parameter space, taking into account all statistical and systematic uncertainties. The $\Delta \chi^2$ value of a pseudo-experiment is calculated by subtracting the $\chi^2$ value of the best-fit in the parameter space from the $\chi^2$ value of the fit at the $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ used in the generation of the pseudo-dataset, where all nuisance parameters are free within their pull terms. When combining the exclusion contours with other experimental data, special care should be exercised. The assumption of a standard $\chi^2$ law instead of the provided $\Delta \chi^2_{\text{crit},x}$ values derived from non-standard $\chi^2$ distributions leads to slightly modified contours. In addition, the contours were derived using a raster-scan in several fixed values of $\Delta m_{41}^2$. While this method is particularly suited to derive exclusion contours, it cannot be used to calculate allowed confidence regions for $\Delta m_{41}^2$ and consequently two-dimensional allowed confidence regions. This is because $\Delta \chi^2$ values are not reflecting the likelihood of individual $\Delta m_{41}^2$ values. Thus, a direct comparison of $\Delta \chi^2$ values across different $\Delta m_{41}^2$ values is not possible in a statistically meaningful way. When generating the exclusion contours with the aforementioned procedure, spurious exclusion regions at low values of $\sin^2(2\theta_{ee})$ can be encountered for some values of $\Delta m^2_{41}$. These should be ignored and are owed to the raster-scan procedure used to generate the maps.

$\Delta \chi^2$ map of phase-I+II data calculated by the two-dimensional method. To be used in combination with the $\Delta \chi^2_{\text{crit},x}$ values of the two-dimensional method to generate exclusion contours at $x$% C.L. for phase-I+II data. Additional explanations are given there.

$\Delta \chi^2$ map of phase-I+II data calculated by the two-dimensional method. To be used in combination with the $\Delta \chi^2_{\text{crit},x}$ values of the two-dimensional method to generate exclusion contours at $x$% C.L. for phase-I+II data. Additional explanations are given there.

The $\Delta \chi^2_{\text{crit},x}$ map accounts for the fact that the $\Delta \chi^2$ values of the oscillation fit do not follow a $\chi^2$ distribution with 2 degrees of freedom. Therefore, the $\Delta \chi^2_{\text{crit},x}$ value for x% C.L. of each point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ in the parameter space, $\Delta \chi^2_{\text{crit},x}(\sin^2(2\theta_{ee}), \Delta m^2_{41})$, is determined from the $\Delta \chi^2$ obtained in pseudo-experiments at that point, such that $\Delta \chi^2 \leq \Delta \chi^2_{\text{crit},x}$, for $x$% of the pseudo-experiments. Applying these $\Delta \chi^2_{\text{crit},x}$ values to the $\Delta \chi^2$ map obtained with the data, $x$% C.L. exclusion contours are obtained. The point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ is excluded by the data at $x$% C.L. if $\Delta \chi^2(\sin^2(2\theta_{ee}), \Delta m^2_{41}) > \Delta \chi^2_{\text{crit},x}(\sin^2(2\theta_{ee}), \Delta m^2_{41})$. In order to obtain the $\Delta \chi^2_{\text{crit},x}$ map, $10^4$ pseudo-experiments were generated for each point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ in the parameter space, taking into account all statistical and systematic uncertainties. The $\Delta \chi^2$ value of a pseudo-experiment is calculated by subtracting the $\chi^2$ value of the best-fit in the parameter space from the $\chi^2$ value of the fit at the $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ used in the generation of the pseudo-dataset, where all nuisance parameters are free within their pull terms. When combining the exclusion contours with other experimental data, special care should be exercised. The assumption of a standard $\chi^2$ law instead of the provided $\Delta \chi^2_{\text{crit},x}$ values derived from non-standard $\chi^2$ distributions leads to modified contours. In addition, for the interpretation of derived allowed confidence regions, one should always consider additional available information, in particular rate information. This is especially advisable considering the expected distribution of best-fit points in a prediction-free shape-only analysis, as discussed in the main publication.

The $\Delta \chi^2_{\text{crit},x}$ map accounts for the fact that the $\Delta \chi^2$ values of the oscillation fit do not follow a $\chi^2$ distribution with 2 degrees of freedom. Therefore, the $\Delta \chi^2_{\text{crit},x}$ value for x% C.L. of each point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ in the parameter space, $\Delta \chi^2_{\text{crit},x}(\sin^2(2\theta_{ee}), \Delta m^2_{41})$, is determined from the $\Delta \chi^2$ obtained in pseudo-experiments at that point, such that $\Delta \chi^2 \leq \Delta \chi^2_{\text{crit},x}$, for $x$% of the pseudo-experiments. Applying these $\Delta \chi^2_{\text{crit},x}$ values to the $\Delta \chi^2$ map obtained with the data, $x$% C.L. exclusion contours are obtained. The point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ is excluded by the data at $x$% C.L. if $\Delta \chi^2(\sin^2(2\theta_{ee}), \Delta m^2_{41}) > \Delta \chi^2_{\text{crit},x}(\sin^2(2\theta_{ee}), \Delta m^2_{41})$. In order to obtain the $\Delta \chi^2_{\text{crit},x}$ map, $10^4$ pseudo-experiments were generated for each point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ in the parameter space, taking into account all statistical and systematic uncertainties. The $\Delta \chi^2$ value of a pseudo-experiment is calculated by subtracting the $\chi^2$ value of the best-fit in the parameter space from the $\chi^2$ value of the fit at the $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ used in the generation of the pseudo-dataset, where all nuisance parameters are free within their pull terms. When combining the exclusion contours with other experimental data, special care should be exercised. The assumption of a standard $\chi^2$ law instead of the provided $\Delta \chi^2_{\text{crit},x}$ values derived from non-standard $\chi^2$ distributions leads to modified contours. In addition, for the interpretation of derived allowed confidence regions, one should always consider additional available information, in particular rate information. This is especially advisable considering the expected distribution of best-fit points in a prediction-free shape-only analysis, as discussed in the main publication.

$\Delta \chi^2$ map of phase-I+II data calculated by the raster-scan method. To be used in combination with the $\Delta \chi^2_{\text{crit},x}$ values of the raster-scan method to generate exclusion contours at $x$% C.L. for phase-I+II data. Additional explanations are given there.

$\Delta \chi^2$ map of phase-I+II data calculated by the raster-scan method. To be used in combination with the $\Delta \chi^2_{\text{crit},x}$ values of the raster-scan method to generate exclusion contours at $x$% C.L. for phase-I+II data. Additional explanations are given there.

The $\Delta \chi^2_{\text{crit},x}$ and $\Delta \chi^2$ values in the raster-scan method serve the same purpose as in the two-dimensional method. The explanations given there also apply here, with the following changes: Instead of the two free oscillation parameters $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$, the raster-scan method fits only $\sin^2(2\theta_{ee})$ as free oscillation parameter while repeating the fit for several fixed values of $\Delta m_{41}^2$. While this method is particularly suited to derive exclusion contours, it cannot be used to calculate allowed confidence regions for $\Delta m_{41}^2$ and consequently two-dimensional allowed confidence regions. This is because $\Delta \chi^2$ values are not reflecting the likelihood of individual $\Delta m_{41}^2$ values. Thus, a direct comparison of $\Delta \chi^2$ values across different $\Delta m_{41}^2$ values is not possible in a statistically meaningful way. Moreover, when generating the exclusion contours with the aforementioned procedure, spurious exclusion regions at low values of $\sin^2(2\theta_{ee})$ can be encountered for some values of $\Delta m^2_{41}$. These should be ignored and are owed to the raster-scan procedure used to generate the maps.

The $\Delta \chi^2_{\text{crit},x}$ and $\Delta \chi^2$ values in the raster-scan method serve the same purpose as in the two-dimensional method. The explanations given there also apply here, with the following changes: Instead of the two free oscillation parameters $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$, the raster-scan method fits only $\sin^2(2\theta_{ee})$ as free oscillation parameter while repeating the fit for several fixed values of $\Delta m_{41}^2$. While this method is particularly suited to derive exclusion contours, it cannot be used to calculate allowed confidence regions for $\Delta m_{41}^2$ and consequently two-dimensional allowed confidence regions. This is because $\Delta \chi^2$ values are not reflecting the likelihood of individual $\Delta m_{41}^2$ values. Thus, a direct comparison of $\Delta \chi^2$ values across different $\Delta m_{41}^2$ values is not possible in a statistically meaningful way. Moreover, when generating the exclusion contours with the aforementioned procedure, spurious exclusion regions at low values of $\sin^2(2\theta_{ee})$ can be encountered for some values of $\Delta m^2_{41}$. These should be ignored and are owed to the raster-scan procedure used to generate the maps.

$\Delta T$ map of phase-I+II data calculated by the CLs method. To be used in combination with the $\Delta T_{\text{crit},x}$ values of the CLs method to generate exclusion contours at $x$% C.L. for phase-I+II data. Additional explanations are given there.

$\Delta T$ map of phase-I+II data calculated by the CLs method. To be used in combination with the $\Delta T_{\text{crit},x}$ values of the CLs method to generate exclusion contours at $x$% C.L. for phase-I+II data. Additional explanations are given there.

The $\Delta T_{\text{crit},x}$ and $\Delta T$ values in the CLs method fulfil a similar purpose as the $\Delta \chi^2_{\text{crit},x}$ and $\Delta \chi^2$ values in the two-dimensional method. The explanations given there also apply here, with the following changes: The CLs method differs from the two-dimensional method as it normalises the confidence level of the oscillation-hypothesis to the confidence level of the null-hypothesis (i.e. no-oscillation-hypothesis), instead of the best-fit. The $\Delta T$ value of a dataset at the parameter space-point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ is computed by subtracting the $\chi^2$ value of the fit under the no-oscillation hypothesis from the $\chi^2$ value of the fit with the oscillation parameters fixed to $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$. With this definition, $\Delta T$ values can be positive or negative as opposed to $\Delta \chi^2$ values. Note that the values used to compare with are $-\Delta T$ and not $\Delta T$ directly. The CLs value of a parameter space-point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ is defined as $\text{CL}_\text{s}(\sin^2(2\theta_{ee}), \Delta m^2_{41}):=(1-p_1)/(1-p_0)$ where $(1-p_0)$ and $(1-p_1)$ are the confidence levels of the dataset, determined from the distributions of $-\Delta T$ created in pseudo-experiments assuming the oscillation parameters $[0,0]$ and $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$, respectively. The point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ is excluded by the data at $x$% C.L. if $\Delta T(\sin^2(2\theta_{ee}), \Delta m^2_{41}) < \Delta T_{\text{crit},x}(\sin^2(2\theta_{ee}), \Delta m^2_{41})$. Note the flipped sign with respect to the two-dimensional method and the raster-scan method. More information on the CLs method can be found at "Resources".

The $\Delta T_{\text{crit},x}$ and $\Delta T$ values in the CLs method fulfil a similar purpose as the $\Delta \chi^2_{\text{crit},x}$ and $\Delta \chi^2$ values in the two-dimensional method. The explanations given there also apply here, with the following changes: The CLs method differs from the two-dimensional method as it normalises the confidence level of the oscillation-hypothesis to the confidence level of the null-hypothesis (i.e. no-oscillation-hypothesis), instead of the best-fit. The $\Delta T$ value of a dataset at the parameter space-point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ is computed by subtracting the $\chi^2$ value of the fit under the no-oscillation hypothesis from the $\chi^2$ value of the fit with the oscillation parameters fixed to $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$. With this definition, $\Delta T$ values can be positive or negative as opposed to $\Delta \chi^2$ values. Note that the values used to compare with are $-\Delta T$ and not $\Delta T$ directly. The CLs value of a parameter space-point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ is defined as $\text{CL}_\text{s}(\sin^2(2\theta_{ee}), \Delta m^2_{41}):=(1-p_1)/(1-p_0)$ where $(1-p_0)$ and $(1-p_1)$ are the confidence levels of the dataset, determined from the distributions of $-\Delta T$ created in pseudo-experiments assuming the oscillation parameters $[0,0]$ and $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$, respectively. The point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ is excluded by the data at $x$% C.L. if $\Delta T(\sin^2(2\theta_{ee}), \Delta m^2_{41}) < \Delta T_{\text{crit},x}(\sin^2(2\theta_{ee}), \Delta m^2_{41})$. Note the flipped sign with respect to the two-dimensional method and the raster-scan method. More information on the CLs method can be found at "Resources".

Map of mean $\Delta \chi^2$ values derived from simulations of phase-I+II and calculated by the two-dimensional method. To be used analogously to the $\Delta \chi^2$ map of phase-I+II data in combination with the $\Delta \chi^2_{\text{crit},x}$ values of the two-dimensional method to generate sensitivity contours at $x$% C.L. for phase-I+II. Additional explanations are given there.

Differential cross section as a function of the excitation energy of the K+ K- pair.

Differential cross section as a function of the excitation energy of the K+ K- pair.

Differential cross section as a function of the excitation energy in the K-HE3 system.

Differential cross section as a function of the excitation energy in the K-HE3 system.

Differential cross section as a function of the excitation energy in the K-HE3 system.

Differential cross section as a function of the opening angle between the K+ and K-.

Differential cross section as a function of the opening angle between the K+ and K-.

Differential cross section as a function of the opening angle between the K+ and K-.

Differential cross section as a function of the angle between the outgoing kaon and the incident proton in the overall cm system.

Differential cross section as a function of the angle between the outgoing kaon and the incident proton in the overall cm system.

Differential cross section as a function of the angle between the outgoing kaon and the incident proton in the overall cm system.

Angular distribution of the kaons as a function of the Helicity angle.

Angular distribution of the kaons as a function of the Jackson angle for two different ranges of excitation energy of the K+ K- pair.

Angular distribution of the kaons as a function of the Jackson angle for two different ranges of excitation energy of the K+ K- pair.

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