Production of charged pions, kaons, and protons in $e^{\mathbf{+}}{e}^{\mathbf{-}}$ annihilations into hadrons at $\sqrt{s}\mathbf{=}10.54\mathrm{GeV}$

Inclusive production cross sections of ${\pi }^{\pm }$, $K^{\pm }$ and $p/\overline{p}$ per hadronic $e^{+}{e}^{-}$ annihilation event are measured at a center-of-mass energy of 10.54 GeV, using a relatively small sample of very high quality data from the BABAR experiment at the PEP-II $B$-factory at the SLAC National Accelerator Laboratory. The drift chamber and Cherenkov detector provide clean samples of identified ${\pi }^{\pm }$, $K^{\pm }$, and $p/\overline{p}$ over a wide range of momenta. Since the center-of-mass energy is below the threshold to produce a $B\overline{B}$ pair, with $B$ a bottom-quark meson, these data represent a pure $e^{+}{e}^{-}\to q\overline{q}$ sample with four quark flavors, and are used to test QCD predictions and hadronization models. Combined with measurements at other energies, in particular at the $Z^0$ resonance, they also provide precise constraints on the scaling properties of the hadronization process over a wide energy range.

Figure 1

Distributions of the total visible energy per event, after all other selection criteria have been applied, in the on-resonance data and simulation. The sum of the hadronic and $\tau$-pair simulations is normalized to the data in the region above 5 GeV, and the $\gamma \gamma$ simulation is normalized arbitrarily.

Figure 2

Simulated distribution of the $K\mathrm{\text{−}}\pi$ log-likelihood difference $l_{K\pi }$ from the DCH vs that from the DIRC for ${\pi }^{\pm }$ and $K^{\pm }$ in hadronic events generated with $0.6<p_{\mathrm{lab}}<0.625\mathrm{GeV}/c$ and $\cos {\theta }_{\mathrm{lab}}>0.05$. The ${\pi }^{\pm }$ and $K^{\pm }$ are concentrated in the lower left and upper right regions, respectively. The edge bins include overflows. The solid (dashed) line represents an upper (lower) bound on identified ${\pi }^{\pm }$ ($K^{\pm }$).

Figure 3

The simulated (dashed lines) and corrected (gray/green bands) efficiency matrix for the most forward polar angle region, $\theta 6$, where $0.77<\cos {\theta }_{\mathrm{lab}}<0.88$. The widths of the bands indicate the uncertainties derived from the control samples discussed in the text. The off-diagonal elements have been scaled up by a factor of 10 for clarity.

Figure 4

Raw ${\pi }^{\pm }$ (circles), $K^{\pm }$ (squares) and $p/\overline{p}$ (diamonds) fractions measured in $\theta 6$, the most forward $\cos {\theta }_{\mathrm{lab}}$ region. The solid (open) symbols represent the results with (without) the constraint that they sum to unity in each $p_{\mathrm{lab}}$ bin. They are indistinguishable in most cases. The sums of unconstrained fractions are shown as the triangles, and in an expanded view in the upper plot. The error bars include statistics and the systematic uncertainties arising from the calibration of the particle identification efficiencies.

Figure 5

Fractional contributions to the selected track sample from $\tau$-pair (up triangles), $\gamma \gamma \to 2{\pi }^{+}2{\pi }^{-}$ (down triangles) and radiative Bhabha (line) events in $\theta 6$, as functions of the measured $p_{\mathrm{lab}}$. The $\gamma \gamma \to 2{\pi }^{+}2{\pi }^{-}$ cross section is scaled as discussed in the text, and represents an upper bound.

Figure 6

Simulated fractional contributions to the overall selected track sample (left) and the selected tracks of the same type (right) from pions (circles), kaons (squares) and protons (diamonds) produced through interactions in the detector material. Results for tracks in the on-resonance sample in $\theta 6$ are shown, and the point-to-point variations have been smoothed.

Figure 7

Efficiencies for charged pions (left), kaons (center) and protons (right) to produce a selected track in the most forward $\cos {\theta }_{\mathrm{lab}}$ region in the on-resonance sample. The solid (dashed) lines represent the simulated fractions of such particles that are in selected events (of those particles that produce a selected track), and the gray/green bands are the products of the corrections discussed in the text, with their half-widths representing the uncertainties. The points are the products of the three lines/bands.

Figure 8

Ratios of fully corrected cross sections from each $\cos {\theta }_{\mathrm{lab}}$ region to their average value. The error bars are statistical only, and some bins have been combined for clarity. The solid and dashed lines indicate the variations expected at one and two standard deviations, respectively.

Figure 9

Simulated electron (down triangles), muon (up triangles) and total lepton (circles) cross sections divided by the $(e\mu \pi )$ cross section in $e^{+}{e}^{-}\to q\overline{q}$ events as functions of $p^{*}$.

Figure 10

Differential production cross sections for prompt (filled symbols) and conventional (open symbols) ${\pi }^{\pm }$ (circles), $K^{\pm }$ (squares) and $p/\overline{p}$ (diamonds) per $e^{+}{e}^{-}\to q\overline{q}$ event as functions of $p^{*}$. The insets show the high momentum regions with expanded vertical scales. The prompt and conventional $K^{\pm }$ cross sections are indistinguishable.

Figure 11

Relative uncertainties in percent on the differential production cross sections for prompt (gray/green) and conventional (black) ${\pi }^{\pm }$ (top), $K^{\pm }$ (middle) and $p/\overline{p}$ (bottom) as functions of $p^{*}$. The totals are shown along with several important components. Some uncertainties become large at high $p^{*}$, and are not shown.

Figure 12

Comparison of our differential cross sections for prompt ${\pi }^{\pm }$ (top), $K^{\pm }$ (middle) and $p/\overline{p}$ (bottom) with previous results from ARGUS at $\sqrt{s}=9.98\mathrm{GeV}$. The error bars represent combined statistical and systematic uncertainties.

Figure 13

Comparison of the prompt ${\pi }^{\pm }$ (circles), $K^{\pm }$ (squares) and $p/\overline{p}$ (diamonds) cross sections in $e^{+}{e}^{-}\to q\overline{q}$ events with the predictions of the ucla (solid line), jetset (dashed) and herwig (dotted) hadronization models.

Figure 14

Conventional ${\pi }^{\pm }$ (top), $K^{\pm }$ (middle) and $p/\overline{p}$ (bottom) cross sections measured at three different CM energies, compared with the predictions of the simulations described in the text.

Figure 15

Differential cross sections in $\xi$ for prompt ${\pi }^{\pm }$ (top), $K^{\pm }$ (middle), and $p/\overline{p}$ (bottom). The error bars are statistical only, and the gray bands represent the systematic uncertainties, which are strongly correlated from point to point. Also shown are the results of the Gaussian (solid lines) and distorted Gaussian (dashed lines) fits described in the text over their maximum ranges (see Table 4); they are continued as dotted and dot-dashed lines, respectively, outside those ranges.

Figure 16

Peak positions ${\xi }^{*}$ vs CM energy for pions (circles), kaons (squares) and protons (diamonds) on a logarithmic horizontal scale. The lines join our points with those from the averages of the $Z^0$ experiments.

Figure 17

Prompt (top) and conventional (bottom) ${\pi }^{\pm }$, $K^{\pm }$, and $p/\overline{p}$ fractions. The error bars are statistical only, and the gray bands represent the systematic uncertainties, which are strongly correlated from point to point. Also shown are the predictions of the three hadronization models.