CERN Accelerating science

This figure illustrates the hypothetical track-length fitting method. In the bottom figure, the red solid line shows the mean energy loss $\left\langle\dedx\right\rangle$ as a function of distance from the stopping point (residual range) using Eq.~\ref{eq:Bethe-Blcoh} for a charged pion in LAr. An example of measured \dedx for an interacting charged pion is shown with a dashed line. The solid blue line shows the same measured \dedx curve with an additional offset on range with best match with the red solid line.

Three regions are defined using the $\kappa$ value. If $\kappa > 10$, the Gaussian PDF is used. If $\kappa < 0.01$, the Landau PDF is used. Otherwise, the Vavilov PDF is used. Plots are drawn for charged pions (left) and protons (right) in LAr using typical pitch (0.65 $\rm{cm}$) of the ProtoDUNE-SP.

Three regions are defined using the $\kappa$ value. If $\kappa > 10$, the Gaussian PDF is used. If $\kappa < 0.01$, the Landau PDF is used. Otherwise, the Vavilov PDF is used. Plots are drawn for charged pions (left) and protons (right) in LAr using typical pitch (0.65 $\rm{cm}$) of the ProtoDUNE-SP.

The \dedx PDFs for charged pions (left) and protons (right) in LAr. For charged pions, PDFs are shown with \KE of 10 \MeV (top), 200 \MeV (center), and 500 \MeV (bottom). For protons, PDFs are shown with \KE of 20 \MeV (top), 200 \MeV (center), and 500 \MeV (bottom). Green lines show mean \dedx values from Eq.~\ref{eq:Bethe-Blcoh} and blue lines show the most probable values (MPV) from the Landau-Vavilov-Bichsel formula. The $\kappa$ values and used functions for PDFs are noted on top-left corners of plots.

The \dedx PDFs for charged pions (left) and protons (right) in LAr. For charged pions, PDFs are shown with \KE of 10 \MeV (top), 200 \MeV (center), and 500 \MeV (bottom). For protons, PDFs are shown with \KE of 20 \MeV (top), 200 \MeV (center), and 500 \MeV (bottom). Green lines show mean \dedx values from Eq.~\ref{eq:Bethe-Blcoh} and blue lines show the most probable values (MPV) from the Landau-Vavilov-Bichsel formula. The $\kappa$ values and used functions for PDFs are noted on top-left corners of plots.

The \dedx PDFs for charged pions (left) and protons (right) in LAr. For charged pions, PDFs are shown with \KE of 10 \MeV (top), 200 \MeV (center), and 500 \MeV (bottom). For protons, PDFs are shown with \KE of 20 \MeV (top), 200 \MeV (center), and 500 \MeV (bottom). Green lines show mean \dedx values from Eq.~\ref{eq:Bethe-Blcoh} and blue lines show the most probable values (MPV) from the Landau-Vavilov-Bichsel formula. The $\kappa$ values and used functions for PDFs are noted on top-left corners of plots.

The \dedx PDFs for charged pions (left) and protons (right) in LAr. For charged pions, PDFs are shown with \KE of 10 \MeV (top), 200 \MeV (center), and 500 \MeV (bottom). For protons, PDFs are shown with \KE of 20 \MeV (top), 200 \MeV (center), and 500 \MeV (bottom). Green lines show mean \dedx values from Eq.~\ref{eq:Bethe-Blcoh} and blue lines show the most probable values (MPV) from the Landau-Vavilov-Bichsel formula. The $\kappa$ values and used functions for PDFs are noted on top-left corners of plots.

The \dedx PDFs for charged pions (left) and protons (right) in LAr. For charged pions, PDFs are shown with \KE of 10 \MeV (top), 200 \MeV (center), and 500 \MeV (bottom). For protons, PDFs are shown with \KE of 20 \MeV (top), 200 \MeV (center), and 500 \MeV (bottom). Green lines show mean \dedx values from Eq.~\ref{eq:Bethe-Blcoh} and blue lines show the most probable values (MPV) from the Landau-Vavilov-Bichsel formula. The $\kappa$ values and used functions for PDFs are noted on top-left corners of plots.

The \dedx PDFs for charged pions (left) and protons (right) in LAr. For charged pions, PDFs are shown with \KE of 10 \MeV (top), 200 \MeV (center), and 500 \MeV (bottom). For protons, PDFs are shown with \KE of 20 \MeV (top), 200 \MeV (center), and 500 \MeV (bottom). Green lines show mean \dedx values from Eq.~\ref{eq:Bethe-Blcoh} and blue lines show the most probable values (MPV) from the Landau-Vavilov-Bichsel formula. The $\kappa$ values and used functions for PDFs are noted on top-left corners of plots.

A simple drawing of the ProtoDUNE-SP detector (left) and an illustration of the three wire planes on an APA (right) are shown. A black box in the left figure represents the active volume, divided into two parts by the cathode at the center. The six APAs are arranged into two anode planes, each consisting of three side-by-side APAs. The test beam enters through the beam plug, close to the right side of the cathode. The right-handed coordinate system is shown in addition to the dimensions of the active volume. For wire planes, only ten wires for each plane are shown for clarity.

A simple drawing of the ProtoDUNE-SP detector (left) and an illustration of the three wire planes on an APA (right) are shown. A black box in the left figure represents the active volume, divided into two parts by the cathode at the center. The six APAs are arranged into two anode planes, each consisting of three side-by-side APAs. The test beam enters through the beam plug, close to the right side of the cathode. The right-handed coordinate system is shown in addition to the dimensions of the active volume. For wire planes, only ten wires for each plane are shown for clarity.

The ${\chi}^{2}_{{\pi}^{\pm}}$ distributions of charged pions are shown. Left plot shows a two dimensional distribution as a function of truth \KE. Right plot shows one dimensional distribution of ${\chi}^{2}_{{\pi}^{\pm}}$. Reconstructed charged pions which are matched with truth-level charged pions are used in this plot.

The ${\chi}^{2}_{{\pi}^{\pm}}$ distributions of charged pions are shown. Left plot shows a two dimensional distribution as a function of truth \KE. Right plot shows one dimensional distribution of ${\chi}^{2}_{{\pi}^{\pm}}$. Reconstructed charged pions which are matched with truth-level charged pions are used in this plot.

Plots show the relationship between truth-level and range-based kinetic energies for charged pions before (left) and after (right) applying the ${\chi}^{2}_{{\pi}^{\pm}}$\!< 6 cut, respectively. The same charged pion selection used in figure~\ref{fig:Figure_005} is used.

Plots show the relationship between truth-level and range-based kinetic energies for charged pions before (left) and after (right) applying the ${\chi}^{2}_{{\pi}^{\pm}}$\!< 6 cut, respectively. The same charged pion selection used in figure~\ref{fig:Figure_005} is used.

Two-dimensional distributions of the fractional energy residual from the CSDA with incomplete tracks, using 15 to 30 (left) and 30 to 60 (right) hits.

Two-dimensional distributions of the fractional energy residual from the CSDA with incomplete tracks, using 15 to 30 (left) and 30 to 60 (right) hits.

Example two-dimensional distributions of the fractional energy residual from the Gaussian approximation method (top) and the maximum-likelihood method (bottom), using 15 to 30 (left) and 30 to 60 (right) hits.

Example two-dimensional distributions of the fractional energy residual from the Gaussian approximation method (top) and the maximum-likelihood method (bottom), using 15 to 30 (left) and 30 to 60 (right) hits.

Example two-dimensional distributions of the fractional energy residual from the Gaussian approximation method (top) and the maximum-likelihood method (bottom), using 15 to 30 (left) and 30 to 60 (right) hits.

Example two-dimensional distributions of the fractional energy residual from the Gaussian approximation method (top) and the maximum-likelihood method (bottom), using 15 to 30 (left) and 30 to 60 (right) hits.

Example plots of energy measurement resolutions based on truth-level \KE. Distributions and Gaussian fit results with truth-level \KE from 40 to 60 \MeV and 280 to 300 \MeV with number of hits from 15 to 30 and 60 to 90 are shown in the top and bottom panels, respectively.

Example plots of energy measurement resolutions based on truth-level \KE. Distributions and Gaussian fit results with truth-level \KE from 40 to 60 \MeV and 280 to 300 \MeV with number of hits from 15 to 30 and 60 to 90 are shown in the top and bottom panels, respectively.

Summarized plots of energy measurement performance of the hypothetical track-length fitting method based on maximum-likelihood method. Resolutions (left) and fractional biases (right) are shown as functions of charged pions' true \KE and number of hits.

Summarized plots of energy measurement performance of the hypothetical track-length fitting method based on maximum-likelihood method. Resolutions (left) and fractional biases (right) are shown as functions of charged pions' true \KE and number of hits.

Example two-dimensional distributions of the fractional energy residual using \KEfull as reference. Results are coming from reconstructed charged pions with 15 to 30 hits. Top plots show results for MC true pions (left) and true protons (right). Bottom plots show results using all reconstructed charged pions for data (left) and MC sample (right).

Example two-dimensional distributions of the fractional energy residual using \KEfull as reference. Results are coming from reconstructed charged pions with 15 to 30 hits. Top plots show results for MC true pions (left) and true protons (right). Bottom plots show results using all reconstructed charged pions for data (left) and MC sample (right).

Example two-dimensional distributions of the fractional energy residual using \KEfull as reference. Results are coming from reconstructed charged pions with 15 to 30 hits. Top plots show results for MC true pions (left) and true protons (right). Bottom plots show results using all reconstructed charged pions for data (left) and MC sample (right).

Example two-dimensional distributions of the fractional energy residual using \KEfull as reference. Results are coming from reconstructed charged pions with 15 to 30 hits. Top plots show results for MC true pions (left) and true protons (right). Bottom plots show results using all reconstructed charged pions for data (left) and MC sample (right).

Example distributions of the fractional energy residual using range-based \KE as reference. Results are coming from reconstructed charged pions with 15 to 30 hits. Top plots show results for MC true pions (a) and true protons (b). Bottom plots show results using all reconstructed charged pions for data (c) and MC sample (d), where green and blue Gaussian functions represent charged pion and proton contributions, respectively.

Example distributions of the fractional energy residual using range-based \KE as reference. Results are coming from reconstructed charged pions with 15 to 30 hits. Top plots show results for MC true pions (a) and true protons (b). Bottom plots show results using all reconstructed charged pions for data (c) and MC sample (d), where green and blue Gaussian functions represent charged pion and proton contributions, respectively.

Example distributions of the fractional energy residual using range-based \KE as reference. Results are coming from reconstructed charged pions with 15 to 30 hits. Top plots show results for MC true pions (a) and true protons (b). Bottom plots show results using all reconstructed charged pions for data (c) and MC sample (d), where green and blue Gaussian functions represent charged pion and proton contributions, respectively.

Example distributions of the fractional energy residual using range-based \KE as reference. Results are coming from reconstructed charged pions with 15 to 30 hits. Top plots show results for MC true pions (a) and true protons (b). Bottom plots show results using all reconstructed charged pions for data (c) and MC sample (d), where green and blue Gaussian functions represent charged pion and proton contributions, respectively.

Example distributions of the fractional energy residual using range-based \KE as reference. Results come from reconstructed charged pions with 15 to 30 hits. Top plots show results for MC true pions (a) and true protons (b). Bottom plots show results using all reconstructed charged pions for data (c) and the MC sample (d), where green and blue Gaussian functions represent charged pion and proton contributions, respectively.

Example distributions of the fractional energy residual using range-based \KE as reference. Results come from reconstructed charged pions with 15 to 30 hits. Top plots show results for MC true pions (a) and true protons (b). Bottom plots show results using all reconstructed charged pions for data (c) and the MC sample (d), where green and blue Gaussian functions represent charged pion and proton contributions, respectively.

Example distributions of the fractional energy residual using range-based \KE as reference. Results come from reconstructed charged pions with 15 to 30 hits. Top plots show results for MC true pions (a) and true protons (b). Bottom plots show results using all reconstructed charged pions for data (c) and the MC sample (d), where green and blue Gaussian functions represent charged pion and proton contributions, respectively.

Example distributions of the fractional energy residual using range-based \KE as reference. Results come from reconstructed charged pions with 15 to 30 hits. Top plots show results for MC true pions (a) and true protons (b). Bottom plots show results using all reconstructed charged pions for data (c) and the MC sample (d), where green and blue Gaussian functions represent charged pion and proton contributions, respectively.

Summarized plots of energy measurement performance of the hypothetical track-length fitting method based on the maximum-likelihood method. Resolutions (left) and fractional biases (right) are shown as functions of charged pions' range-based \KE and number of hits. Pure secondary charged pions are selected from the MC sample.

Summarized plots of energy measurement performance of the hypothetical track-length fitting method based on the maximum-likelihood method. Resolutions (left) and fractional biases (right) are shown as functions of charged pions' range-based \KE and number of hits. Pure secondary charged pions are selected from the MC sample.

Summarized plots of energy measurement performance of the hypothetical track-length fitting method based on maximum-likelihood method. Resolutions (left) and fractional biases (right) are shown as functions of charged pions' range-based \KE and number of hits. All reconstructed secondary charged pions passing the stopping charged pion cut are used. Monte Carlo points are shown with dashed horizontal bars and the data points are shown with solid horizontal bars.

Summarized plots of energy measurement performance of the hypothetical track-length fitting method based on maximum-likelihood method. Resolutions (left) and fractional biases (right) are shown as functions of charged pions' range-based \KE and number of hits. All reconstructed secondary charged pions passing the stopping charged pion cut are used. Monte Carlo points are shown with dashed horizontal bars and the data points are shown with solid horizontal bars.

The \dedx of beam muons is shown as a function of residual range for both data (blue) and MC (red). The results of fits to a Landau function convoluted with a Gaussian are also shown in the legends. The $\mathrm{\sigma_{Landau}}$ is intrinsic width of the Landau function, MPV is fitted most probable value, $\mathrm{{Par}_{2}}$ is normalization factor, and $\mathrm{\sigma_{Gaus}}$ is the width of the Gaussian.

The \dedx of beam muons is shown as a function of residual range for both data (blue) and MC (red). The results of fits to a Landau function convoluted with a Gaussian are also shown in the legends. The $\mathrm{\sigma_{Landau}}$ is intrinsic width of the Landau function, MPV is fitted most probable value, $\mathrm{{Par}_{2}}$ is normalization factor, and $\mathrm{\sigma_{Gaus}}$ is the width of the Gaussian.

The \dedx of beam muons is shown as a function of residual range for both data (blue) and MC (red). The results of fits to a Landau function convoluted with a Gaussian are also shown in the legends. The $\mathrm{\sigma_{Landau}}$ is intrinsic width of the Landau function, MPV is fitted most probable value, $\mathrm{{Par}_{2}}$ is normalization factor, and $\mathrm{\sigma_{Gaus}}$ is the width of the Gaussian.

The \dedx of beam muons is shown as a function of residual range for both data (blue) and MC (red). The results of fits to a Landau function convoluted with a Gaussian are also shown in the legends. The $\mathrm{\sigma_{Landau}}$ is intrinsic width of the Landau function, MPV is fitted most probable value, $\mathrm{{Par}_{2}}$ is normalization factor, and $\mathrm{\sigma_{Gaus}}$ is the width of the Gaussian.

Ratio of fitted MPV values between MC and data as a function of MC MPV. Each MPV value is fitted using beam muon's hits with a 1 $\mathrm{cm}$ interval in residual range from 2 to 100 $\mathrm{cm}$. Ratio is calculated for each residual range interval. Vertical error bars show statistical uncertainties only. Left figure shows the ratio distribution with respect to the unity. Right figure shows how the \dedx correction for the Bragg peak region is derived using a linear fit.

Ratio of fitted MPV values between MC and data as a function of MC MPV. Each MPV value is fitted using beam muon's hits with a 1 $\mathrm{cm}$ interval in residual range from 2 to 100 $\mathrm{cm}$. Ratio is calculated for each residual range interval. Vertical error bars show statistical uncertainties only. Left figure shows the ratio distribution with respect to the unity. Right figure shows how the \dedx correction for the Bragg peak region is derived using a linear fit.

The measured \dedx values for hits along beam muon tracks are shown as a function of residual range for both data (blue) and MC (red). Fitting results with the convoluted functions of the Gaussian and the Landau functions are also shown in the legends. The parameter $\mathrm{\sigma_{Landau}}$ is the intrinsic width of the Landau function, MPV is the fitted most probable value, $\mathrm{{Par}_{2}}$ is the normalization factor, and $\mathrm{\sigma_{Gaus}}$ is the width of the Gaussian part. The scale correction shown in figure~\ref{fig:Figure_017} for \dedx values is applied for MC sample.

The measured \dedx values for hits along beam muon tracks are shown as a function of residual range for both data (blue) and MC (red). Fitting results with the convoluted functions of the Gaussian and the Landau functions are also shown in the legends. The parameter $\mathrm{\sigma_{Landau}}$ is the intrinsic width of the Landau function, MPV is the fitted most probable value, $\mathrm{{Par}_{2}}$ is the normalization factor, and $\mathrm{\sigma_{Gaus}}$ is the width of the Gaussian part. The scale correction shown in figure~\ref{fig:Figure_017} for \dedx values is applied for MC sample.

The measured \dedx values for hits along beam muon tracks are shown as a function of residual range for both data (blue) and MC (red). Fitting results with the convoluted functions of the Gaussian and the Landau functions are also shown in the legends. The parameter $\mathrm{\sigma_{Landau}}$ is the intrinsic width of the Landau function, MPV is the fitted most probable value, $\mathrm{{Par}_{2}}$ is the normalization factor, and $\mathrm{\sigma_{Gaus}}$ is the width of the Gaussian part. The scale correction shown in figure~\ref{fig:Figure_017} for \dedx values is applied for MC sample.

The measured \dedx values for hits along beam muon tracks are shown as a function of residual range for both data (blue) and MC (red). Fitting results with the convoluted functions of the Gaussian and the Landau functions are also shown in the legends. The parameter $\mathrm{\sigma_{Landau}}$ is the intrinsic width of the Landau function, MPV is the fitted most probable value, $\mathrm{{Par}_{2}}$ is the normalization factor, and $\mathrm{\sigma_{Gaus}}$ is the width of the Gaussian part. The scale correction shown in figure~\ref{fig:Figure_017} for \dedx values is applied for MC sample.

The measured \dedx values of hits along beam muon tracks are shown for residual ranges between 3 and 4~cm for data (blue) and MC (red). Fitting results with the convoluted functions of the Gaussian and the Landau functions are also shown in the legends. The parameter $\mathrm{\sigma_{Landau}}$ is the intrinsic width of the Landau function, MPV is the fitted most probable value, $\mathrm{{Par}_{2}}$ is the normalization factor, and $\mathrm{\sigma_{Gaus}}$ is the width of the Gaussian component. Modified box model parameters are each shifted by one standard deviation~\cite{ArgoNeuT:2013kpa} for data. Distributions of MC are the same in each of the four plots.

The measured \dedx values of hits along beam muon tracks are shown for residual ranges between 3 and 4~cm for data (blue) and MC (red). Fitting results with the convoluted functions of the Gaussian and the Landau functions are also shown in the legends. The parameter $\mathrm{\sigma_{Landau}}$ is the intrinsic width of the Landau function, MPV is the fitted most probable value, $\mathrm{{Par}_{2}}$ is the normalization factor, and $\mathrm{\sigma_{Gaus}}$ is the width of the Gaussian component. Modified box model parameters are each shifted by one standard deviation~\cite{ArgoNeuT:2013kpa} for data. Distributions of MC are the same in each of the four plots.

The measured \dedx values of hits along beam muon tracks are shown for residual ranges between 3 and 4~cm for data (blue) and MC (red). Fitting results with the convoluted functions of the Gaussian and the Landau functions are also shown in the legends. The parameter $\mathrm{\sigma_{Landau}}$ is the intrinsic width of the Landau function, MPV is the fitted most probable value, $\mathrm{{Par}_{2}}$ is the normalization factor, and $\mathrm{\sigma_{Gaus}}$ is the width of the Gaussian component. Modified box model parameters are each shifted by one standard deviation~\cite{ArgoNeuT:2013kpa} for data. Distributions of MC are the same in each of the four plots.

The measured \dedx values of hits along beam muon tracks are shown for residual ranges between 3 and 4~cm for data (blue) and MC (red). Fitting results with the convoluted functions of the Gaussian and the Landau functions are also shown in the legends. The parameter $\mathrm{\sigma_{Landau}}$ is the intrinsic width of the Landau function, MPV is the fitted most probable value, $\mathrm{{Par}_{2}}$ is the normalization factor, and $\mathrm{\sigma_{Gaus}}$ is the width of the Gaussian component. Modified box model parameters are each shifted by one standard deviation~\cite{ArgoNeuT:2013kpa} for data. Distributions of MC are the same in each of the four plots.

Summary of studies considering the impact of \dedx modeling. Resolutions (left) and fractional biases (right) are shown as functions of charged pions' \KEfull and number of hits. Black points show data results with gray error bars that are measured with biggest differences between data and 8 sets of shifted modified box model parameters. Green points show central MC results. Red points show results with linear scale correction on MC that is shown as a red solid line in figure~\ref{fig:Figure_017}. Orange and blue points show results with constant \dedx scale corrections on MC with 0.985 and 0.975, respectively.

Summary of studies considering the impact of \dedx modeling. Resolutions (left) and fractional biases (right) are shown as functions of charged pions' \KEfull and number of hits. Black points show data results with gray error bars that are measured with biggest differences between data and 8 sets of shifted modified box model parameters. Green points show central MC results. Red points show results with linear scale correction on MC that is shown as a red solid line in figure~\ref{fig:Figure_017}. Orange and blue points show results with constant \dedx scale corrections on MC with 0.985 and 0.975, respectively.

Summary of studies considering the impact of \dedx modeling. Resolutions (left) and fractional biases (right) are shown as functions of charged pions' \KEfull and number of hits. Black points show data results with gray error bars that are measured with biggest differences between data and 8 sets of shifted modified box model parameters. Green points show central MC results. Red points show results with linear scale correction on MC that is shown as a red solid line in figure~\ref{fig:Figure_017}. Orange and blue points show results with constant \dedx scale corrections on MC with 0.985 and 0.975, respectively.

Summary of studies considering the impact of \dedx modeling. Resolutions (left) and fractional biases (right) are shown as functions of charged pions' \KEfull and number of hits. Black points show data results with gray error bars that are measured with biggest differences between data and 8 sets of shifted modified box model parameters. Green points show central MC results. Red points show results with linear scale correction on MC that is shown as a red solid line in figure~\ref{fig:Figure_017}. Orange and blue points show results with constant \dedx scale corrections on MC with 0.985 and 0.975, respectively.

Summary of studies considering the impact of \dedx modeling. Resolutions (left) and fractional biases (right) are shown as functions of charged pions' \KEfull and number of hits. Black points show data results with gray error bars that are measured with biggest differences between data and 8 sets of shifted modified box model parameters. Green points show central MC results. Red points show results with linear scale correction on MC that is shown as a red solid line in figure~\ref{fig:Figure_017}. Orange and blue points show results with constant \dedx scale corrections on MC with 0.985 and 0.975, respectively.

Summary of studies considering the impact of \dedx modeling. Resolutions (left) and fractional biases (right) are shown as functions of charged pions' \KEfull and number of hits. Black points show data results with gray error bars that are measured with biggest differences between data and 8 sets of shifted modified box model parameters. Green points show central MC results. Red points show results with linear scale correction on MC that is shown as a red solid line in figure~\ref{fig:Figure_017}. Orange and blue points show results with constant \dedx scale corrections on MC with 0.985 and 0.975, respectively.

Summary of studies considering the impact of \dedx modeling. Resolutions (left) and fractional biases (right) are shown as functions of charged pions' \KEfull and number of hits. Black points show data results with gray error bars that are measured with biggest differences between data and 8 sets of shifted modified box model parameters. Green points show central MC results. Red points show results with linear scale correction on MC that is shown as a red solid line in figure~\ref{fig:Figure_017}. Orange and blue points show results with constant \dedx scale corrections on MC with 0.985 and 0.975, respectively.

Summary of studies considering the impact of \dedx modeling. Resolutions (left) and fractional biases (right) are shown as functions of charged pions' \KEfull and number of hits. Black points show data results with gray error bars that are measured with biggest differences between data and 8 sets of shifted modified box model parameters. Green points show central MC results. Red points show results with linear scale correction on MC that is shown as a red solid line in figure~\ref{fig:Figure_017}. Orange and blue points show results with constant \dedx scale corrections on MC with 0.985 and 0.975, respectively.

Summary of studies considering the impact of \dedx modeling. Resolutions (left) and fractional biases (right) are shown as functions of charged pions' \KEfull and number of hits. Black points show data results with gray error bars that are measured with biggest differences between data and 8 sets of shifted modified box model parameters. Green points show central MC results. Red points show results with linear scale correction on MC that is shown as a red solid line in figure~\ref{fig:Figure_017}. Orange and blue points show results with constant \dedx scale corrections on MC with 0.985 and 0.975, respectively.

Summary of studies considering the impact of \dedx modeling. Resolutions (left) and fractional biases (right) are shown as functions of charged pions' \KEfull and number of hits. Black points show data results with gray error bars that are measured with biggest differences between data and 8 sets of shifted modified box model parameters. Green points show central MC results. Red points show results with linear scale correction on MC that is shown as a red solid line in figure~\ref{fig:Figure_017}. Orange and blue points show results with constant \dedx scale corrections on MC with 0.985 and 0.975, respectively.