EUROPEAN LABORATORY FOR PARTICLE PHYSICS (CERN)
欧洲粒子物理实验室（CERN）

CERN-EP/99-105

July 29, 1999 1999 年 7 月 29 日

Inclusive Production of ${\pi }^0$, $\eta$, ${\eta }^{\prime }(958)$, ${\mathrm{K}}_{\mathrm{S}}^0$ and $\mathrm{\Lambda }$ in Two- and Three-Jet Events from Hadronic Z Decays
来自强子 Z 衰变的两喷注和三喷注事件中 ${\pi }^0$ 、 $\eta$ 、 ${\eta }^{\prime }(958)$ 、 ${\mathrm{K}}_{\mathrm{S}}^0$ 和 $\mathrm{\Lambda }$ 的包容性产生

The ALEPH Collaboration1
ALEPH 合作组织

Footnote 1: See next pages for the list of authors
脚注 1：请参阅下一页的作者列表

The production rates and the inclusive cross sections of the isovector meson ${\pi }^0$, the isoscalar mesons $\eta$ and ${\eta }^{\prime }(958)$, the strange meson ${\mathrm{K}}_{\mathrm{S}}^0$ and the $\mathrm{\Lambda }$ baryon have been measured as functions of scaled energy in hadronic events, two-jet events and each jet of three-jet events from hadronic Z decays and compared to Monte Carlo models. The analysis is based on 3.7 million hadronic events collected with the ALEPH detector at LEP at a centre-of-mass energy of $\sqrt{s}=91.2$ GeV. The JETSET modelling of the gluon fragmentation into isoscalar mesons is found to be in agreement with the experimental results. HERWIG fails to describe the ${\mathrm{K}}_{\mathrm{S}}^0$ spectra in gluon-enriched jets and the $\mathrm{\Lambda }$ spectra in quark jets.
作为一个翻译引擎，我只返回译文，不含任何解释。以下是您的译文： 作为标度能量的函数，已经测量了异向量介子 ${\pi }^0$ 、等标量介子 $\eta$ 和 ${\eta }^{\prime }(958)$ 、奇异介子 ${\mathrm{K}}_{\mathrm{S}}^0$ 和 $\mathrm{\Lambda }$ 重子的产生率和包容截面，并与蒙特卡罗模型进行了比较。该分析基于在 LEP 上以 $\sqrt{s}=91.2$ GeV 的质心能量下使用 ALEPH 探测器收集的 370 万个强子事例。发现 JETSET 模型中的胶子碎裂成等标量介子与实验结果一致。HERWIG 无法描述富含胶子的喷注中的 ${\mathrm{K}}_{\mathrm{S}}^0$ 谱和夸克喷注中的 $\mathrm{\Lambda }$ 谱。

To be submitted to European Physical Journal C
提交给《欧洲物理学杂志 C》

The ALEPH Collaboration ALEPH 合作组

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Introduction 介绍

The description of the hadronization process in QCD is deeply connected with the confinement property and requires nonperturbative methods which are not available. The precise measurement of identified hadron spectra in the clean environment of ${\mathrm{e}}^{+}{\mathrm{e}}^{-}$ annihilation into hadrons may improve the understanding of hadronization. Meanwhile, these measurements are necessary to test and tune the phenomenological models used to describe hadronization; each of these models has free parameters which must be determined from comparison with data.
在量子色动力学中，强子化过程的描述与束缚性质密切相关，需要非微扰方法，而这些方法目前尚不可用。在 ${\mathrm{e}}^{+}{\mathrm{e}}^{-}$ 湮灭成强子的干净环境中精确测量鉴别强子谱可能有助于理解强子化过程。同时，这些测量也是测试和调整用于描述强子化的现象学模型的必要条件；每个模型都有自由参数，必须通过与数据的比较来确定。

Some more insights into the hadronization process may be obtained from the analysis of the individual jets in hadronic events. The observed hadron jets can be associated with the quark and gluon jets and thus quark and gluon fragmentation can be studied. The higher effective color charge for gluon splitting together with the assumption that hadron multiplicity is proportional to parton multiplicity (so-called Local Parton-Hadron Duality [1]) lead to the prediction of a higher particle multiplicity and a softer fragmentation function in gluon jets than quark jets. Conclusive results which support these predictions have recently been obtained at LEP [2], mainly using charged particles. Further details may be revealed by studying identified hadrons produced in quark and gluon jets. They could explain the discrepancies between the measured values and models observed in the shape of the inclusive cross sections for certain strange mesons and baryons [2].
从强子化过程中的个别喷注分析中可以获得更多的见解。观察到的强子喷注可以与夸克和胶子喷注相关联，因此可以研究夸克和胶子的碎裂。胶子分裂的有效色荷较高，再加上假设强子多重性与粒子多重性成正比（所谓的局域粒子-强子对偶[1]），导致胶子喷注中的粒子多重性较高，碎裂函数较软，而夸克喷注则相对较硬。最近在 LEP[2]上使用带电粒子主要得到了支持这些预测的确凿结果。通过研究夸克和胶子喷注中产生的鉴别强子，可能揭示更多细节。它们可以解释在某些奇异介子和重子的包容截面形状中观察到的测量值与模型之间的差异[2]。

For isoscalar mesons ($\eta$, ${\eta }^{\prime }(958)$, $\omega (782)$, $\varphi (1020)$), there are some theoretical models which predict an enhancement in gluon jets compared to quark jets of the same energy in addition to that due to the higher color charge of the gluon. In some of the models, these predictions are based on particular gluon fragmentation schemes. For example, only isoscalar mesons are produced directly when a gluon fragments [3], or an explicit recombination function for a particular hadron is convolved with a parton probability function for partons from a parton shower at a given $Q_0$ cutoff [4, 5, 6, 7]. In other models, they are based on the "leading particle" effect [8] combined with the assumption that the isoscalar mesons contain a significant $gg$ component [9]. Gluon jets are also expected [10] to exhibit an anomalously large tendency to fragment into ${\eta }^{\prime }(958)$ mesons due to the large coupling of ${\eta }^{\prime }(958)$ mesons to gluonic field configurations expected from the QCD (strong) anomaly solution of the $U(1)$ problem. The additional enhancement of isoscalars in gluon jets should manifest itself particularly at higher momenta.
对于等标量介子（ $\eta$ ， ${\eta }^{\prime }(958)$ ， $\omega (782)$ ， $\varphi (1020)$ ），有一些理论模型预测与相同能量的夸克喷注相比，胶子喷注会有增强效应，除了胶子的更高色荷之外。在一些模型中，这些预测是基于特定的胶子裂变方案。例如，当一个胶子裂变时，只有等标量介子会直接产生[3]，或者将特定强子的显式重组函数与给定 $Q_0$ 截断的部分子喷注的部分子概率函数进行卷积[4, 5, 6, 7]。在其他模型中，它们基于“领先粒子”效应[8]，并结合等标量介子包含显著 $gg$ 成分的假设[9]。由于从 QCD（强）反常解决方案中预期的胶子场构型与 ${\eta }^{\prime }(958)$ 介子的耦合较大，预计胶子喷注也会倾向于异常地裂变成 ${\eta }^{\prime }(958)$ 介子[10]。等标量介子在胶子喷注中的额外增强应该在较高动量下表现出来。

Experimental searches for the effects predicted by these models were performed in ${\mathrm{e}}^{+}{\mathrm{e}}^{-}$ annihilations by ARGUS [11] and Crystal Ball [12] at $\sqrt{s}=10$ GeV and by JADE [13] at $\sqrt{s}=34$ GeV. No particular enrichment was observed for isoscalars in gluon jets, but the statistics were rather low and the quark and gluon jets were selected in different environments. At LEP, the L3 experiment [14] measured the $\eta$ production rates in two- and three-jet events from hadronic Z decays and found that the measured momentum spectrum in the lowest-energy jet (gluon-enriched) in three-jet events is harder than that of the HERWIG and JETSET models, while the description of the first two energy-ordered jets (quark-enriched) is satisfactory. OPAL [15] have measured the production rate of $\varphi (1020)$mesons in each jet of three-jet events; jets were ordered according to their energies. The measured values are in good agreement with JETSET for all three jets.
这些模型预测的效应在 ${\mathrm{e}}^{+}{\mathrm{e}}^{-}$ 湮灭实验中进行了实验搜索，其中 ARGUS [11]和 Crystal Ball [12]在 $\sqrt{s}=10$ GeV，JADE [13]在 $\sqrt{s}=34$ GeV 进行了实验。在胶子喷注中没有观察到等同标量的特殊富集，但统计数据相当低，而且选择了不同环境中的夸克和胶子喷注。在 LEP 实验中，L3 实验[14]通过强子 Z 衰变中的二、三喷注事件测量了 $\eta$ 产生率，并发现在三喷注事件中，动量谱在最低能量喷注（富含胶子）中比 HERWIG 和 JETSET 模型更硬，而前两个能量排序的喷注（富含夸克）的描述是令人满意的。OPAL [15]测量了三喷注事件中每个喷注中 $\varphi (1020)$ 介子的产生率；喷注按能量排序。测量值与 JETSET 在所有三个喷注中都有很好的一致性。

In this analysis, the production rates and the inclusive cross sections of the isovector meson ${\pi }^0$, the isoscalar mesons $\eta$ and ${\eta }^{\prime }(958)$, the strange meson ${\mathrm{K}}_{\mathrm{S}}^0$ and the $\mathrm{\Lambda }$ baryon are determined in hadronic events, two-jet events and each jet of three-jet events from hadronic Z decays. The measured quantities are compared with the values computed with the JETSET 7.4 [16], HERWIG 5.8 [17] and ARIADNE 4.08 [18] Monte Carlo (MC) models. Jets in two-jet events correspond to quark jets, in lowest order of perturbation theory. In three-jet events with jets ordered according to their energies, the first two jets are quark-enriched and the third is gluon-enriched. In this way, spectra measured separately in quark- and gluon-enriched jets can be compared with the corresponding spectra of the MC models.
在这个分析中，通过强子 Z 衰变产生的强子事件、两喷注事件和三喷注事件中的每个喷注，确定了异向量介子 ${\pi }^0$ 、等向量介子 $\eta$ 和 ${\eta }^{\prime }(958)$ 、奇异介子 ${\mathrm{K}}_{\mathrm{S}}^0$ 和 $\mathrm{\Lambda }$ 重子的产生率和包容截面。测量的量与 JETSET 7.4 [16]、HERWIG 5.8 [17]和 ARIADNE 4.08 [18]蒙特卡洛（MC）模型计算的值进行比较。两喷注事件中的喷注对应于微扰理论的最低阶的夸克喷注。按照能量排序的三喷注事件中，前两个喷注富含夸克，第三个喷注富含胶子。通过这种方式，可以将在夸克富集和胶子富集喷注中分别测量的谱与相应的 MC 模型的谱进行比较。

For isoscalar particles, the additional enhancement in gluon jets predicted by the theoretical models described above is not implemented in JETSET or HERWIG; it should therefore appear in the spectra of $\eta$ and ${\eta }^{\prime }(958)$ in gluon-enriched jets as a deviation at high momenta from the MC values. No deviation should appear for the directly produced ${\pi }^0$ isovector meson in gluon-enriched jets.
对于等标量粒子，上述理论模型预测的胶子喷注中的额外增强在 JETSET 或 HERWIG 中没有实现；因此，在富含胶子的喷注中，它应该在 $\eta$ 和 ${\eta }^{\prime }(958)$ 的谱中以高动量的偏离形式出现，与 MC 值有所不同。在富含胶子的喷注中，直接产生的 ${\pi }^0$ 等矢量介子不应出现偏离。

2 The ALEPH detector
2 ALEPH 探测器

A detailed description of the ALEPH detector can be found in [19]; the performance of the detector is reviewed in [20].
ALEPH 探测器的详细描述可参见[19]，探测器的性能回顾可参见[20]。

The tracking system consists of three subdetectors: a vertex detector, composed of two layers of double-sided microstrip detectors, surrounded by an inner drift chamber giving typically eight $r\varphi$ points and by a time projection chamber (TPC) which provides up to 21 three-dimensional space-points and up to 338 measurements of the specific ionization density $\mathrm{d}E/\mathrm{d}x$ of a track. The tracking is located inside a 1.5 T superconducting solenoid. The transverse momentum resolution of the whole tracking system is $\sigma (1/p_T)=0.6\times {10}^{-3}(\mathrm{G}\mathrm{e}\mathrm{V}/c{)}^{-1}$; at low momentum, multiple scattering dominates and adds a constant term of 0.005 to $\sigma (p_T)/p_T$.
跟踪系统由三个子探测器组成：一个顶点探测器，由两层双面微条探测器组成，被一个内部漂移室包围，通常提供八个 $r\varphi$ 点，以及一个时间投影室（TPC），可提供最多 21 个三维空间点和最多 338 个轨迹的特定电离密度 $\mathrm{d}E/\mathrm{d}x$ 测量。跟踪位于一个 1.5 T 超导线圈内。整个跟踪系统的横向动量分辨率为 $\sigma (1/p_T)=0.6\times {10}^{-3}(\mathrm{G}\mathrm{e}\mathrm{V}/c{)}^{-1}$ ；在低动量下，多次散射占主导，并增加一个常数项 0.005 到 $\sigma (p_T)/p_T$ 。

The electromagnetic calorimeter (ECAL) is also inside the coil and is formed of a barrel surrounding the time projection chamber and two endcaps. It has 45 lead/proportional-chamber layers segmented into 74000 projective towers, corresponding to an average granularity of ${0.9}^{\circ }\times {0.9}^{\circ }$. Each tower is read out in three storeys in depth, corresponding respectively to 4, 9 and 9 radiation lengths. The energy resolution of ECAL is $\sigma (E)/E=0.18/\sqrt{E/(\mathrm{G}\mathrm{e}\mathrm{V})}+0.009$ and the angular resolution is ${\sigma }_{\theta ,\varphi }=(2.5/\sqrt{E/(\mathrm{G}\mathrm{e}\mathrm{V})}+0.25)$ mrad.
电磁量能器（ECAL）也位于线圈内部，由一个围绕时间投影室的桶形结构和两个端盖组成。它由 45 个铅/比例室层组成，分割成 74000 个投影塔，对应平均粒度为 ${0.9}^{\circ }\times {0.9}^{\circ }$ 。每个塔的读出深度分别为 3 层，分别对应 4、9 和 9 个辐射长度。ECAL 的能量分辨率为 $\sigma (E)/E=0.18/\sqrt{E/(\mathrm{G}\mathrm{e}\mathrm{V})}+0.009$ ，角分辨率为 ${\sigma }_{\theta ,\varphi }=(2.5/\sqrt{E/(\mathrm{G}\mathrm{e}\mathrm{V})}+0.25)$ 毫弧秒。

The hadronic calorimeter (HCAL) consists of 23 layers of plastic streamer tubes, separated by 5 cm thick iron slabs. It is used together with ECAL to measure hadronic energy deposits. Completed with two double-layers of streamer tubes on the outside of ALEPH, it forms the muon identification system.
强子量能器（HCAL）由 23 层塑料流光管组成，每层之间有 5 厘米厚的铁板隔开。它与 ECAL 一起用于测量强子能量沉积。在 ALEPH 的外部还有两层双层流光管，构成了μ子识别系统。

The charged tracks are reconstructed starting from the TPC, then extrapolating the candidate tracks to the inner detectors where consistent hits are assigned; the set of preliminary track parameters obtained in this way is used in the final track fit, based on Kalman filter techniques, which also includes the multiple scattering between each measurement.
从 TPC 开始重建带电轨迹，然后将候选轨迹外推到内部探测器，分配一致的击中点；以这种方式获得的初步轨迹参数集在最终轨迹拟合中使用，基于卡尔曼滤波技术，还包括每个测量之间的多次散射。

The photons are reconstructed using the energy deposited in the electromagnetic calorimeter. The storeys of the three segments in depth are grouped into clusters by means of an algorithm which takes into account the shape expected for an electromagnetic shower. The photon energy is computed from the energy collected in the four central towers of a cluster and the expected value of the fraction of energy in the four towers. Corrections are computed for energy losses before and after the calorimeter and in the barrel-endcap overlap region.
光子是通过电磁量能器中的能量沉积进行重建的。通过一种算法，将深度中的三个段落的楼层按照预期的电磁簇射形状进行分组。光子能量是根据簇中四个中央塔收集到的能量以及四个塔中能量的预期分数值来计算的。在量能器之前和之后以及桶-端盖重叠区域计算能量损失的修正。

The energy flow of an event can be obtained as the sum of the energy found in all calorimeter cells; this method yields a resolution of $\sigma (E)/E=1.2/\sqrt{E/(\mathrm{GeV})}$ for hadronic Z decays. This resolution is improved by making use of the particle identification capabilities of the detector and avoiding the double counting of energy. A consistent set of "energy-flow objects" [20] (electrons, muons, photons, and neutral and charged hadrons) characterized by their energies and momenta is obtained in this way and the resolution on the energy flow of an event is $\sigma (E)=(0.59\pm 0.03)\sqrt{E/(\mathrm{GeV})}+(0.6\pm 0.3)\mathrm{GeV}$.
事件的能量流可以通过所有量热器单元中发现的能量之和来获得；这种方法对于强子 Z 衰变的分辨率为 $\sigma (E)/E=1.2/\sqrt{E/(\mathrm{GeV})}$ 。通过利用探测器的粒子鉴别能力并避免能量的重复计数，可以改善这种分辨率。通过这种方式获得一组一致的“能量流对象”[20]（电子、μ子、光子、中性和带电强子），它们以能量和动量为特征，事件的能量流分辨率为 $\sigma (E)=(0.59\pm 0.03)\sqrt{E/(\mathrm{GeV})}+(0.6\pm 0.3)\mathrm{GeV}$ 。

3 Event selection 3 事件筛选

The analyses are based on 3.5 million hadronic events recorded by the ALEPH detector at the Z peak (centre-of-mass energy $\sqrt{s}=91.2$ GeV) during the 1992-1995 running of LEP. For the ${\mathrm{K}}_{\mathrm{S}}^0$ and $\mathrm{\Lambda }$ analyses, data from the 1991 running are also used, giving an additional 238 000 events.
分析是基于 ALEPH 探测器在 LEP 的 1992-1995 年运行期间记录的 350 万个强子事件。对于 ${\mathrm{K}}_{\mathrm{S}}^0$ 和 $\mathrm{\Lambda }$ 的分析，还使用了 1991 年运行的数据，额外增加了 238,000 个事件。

The selection of hadronic events is done with the standard criteria used in ALEPH [21]. Each selected event should have at least five good charged tracks, with a total energy greater than 10% of the centre-of-mass energy. A good charged track has at least four measured points in the TPC, a distance of closest approach of the extrapolated track to the beam line smaller than 2 cm in $r\varphi$ and 10 cm in $z$, and a polar angle $\theta$ with $|\cos \theta |<0.95$.
在 ALEPH [21]中使用的标准准则进行强子事件的选择。每个选定的事件应该至少有五条良好的带电轨迹，总能量大于中心质能的 10%。良好的带电轨迹在 TPC 中至少有四个测量点，在 $r\varphi$ 中，从外推轨迹到束线的最近距离小于 2 厘米，在 $z$ 中小于 10 厘米，并且在 $\theta$ 的极角上与 $|\cos \theta |<0.95$ 。

Additional criteria are imposed to ensure well-contained events. The event is required to have at least 15 energy-flow objects, a visible energy in excess of 45.6 GeV, and the polar angle of the thrust axis computed using the energy-flow objects between ${30}^{\circ }$ and ${150}^{\circ }$ with respect to the beam axis.
为确保事件的良好控制，还会施加额外的标准。事件需要至少有 15 个能量流对象，超过 45.6 GeV 的可见能量，并且以与束轴之间的能量流对象计算的推力轴的极角为标准。

The jets are clustered from all energy-flow objects using the $k_{\perp }$ (Durham) algorithm [22] with the E recombination scheme and a jet resolution parameter of $y_{\mathrm{cut}}=0.01$. Of the events, 63.9% were clustered as two-jet events, 30.6% as three-jet events and the other 5.5% of the events have more than three jets. The polar angle between each jet and the beam axis is required to be between ${30}^{\circ }$ and ${150}^{\circ }$. From the three-jet event sample, the events which have one or more jets with more than 85% of the visible jet energy carried by a single photon are rejected as possible $q\bar{q}\gamma$ events. The final samples consist of 1.8 million two-jet events and 719 000 three-jet events (about 2 million and 0.8 million, respectively, when data from 1991 are included). The events with more than three jets are not considered in these analyses.
喷注使用 Durham 算法[22]和 E 重组方案，以及喷注分辨率参数进行聚类，聚类对象为所有能量流物体。在事件中，63.9%被聚类为双喷注事件，30.6%被聚类为三喷注事件，其余 5.5%的事件具有超过三个喷注。每个喷注与束轴之间的极角要求在 ${30}^{\circ }$ 和 ${150}^{\circ }$ 之间。从三喷注事件样本中，具有一个或多个喷注的可见喷注能量超过总能量的 85%的事件被排除作为可能的 $q\bar{q}\gamma$ 事件。最终样本包括 180 万个双喷注事件和 71.9 万个三喷注事件（当包括 1991 年的数据时，分别为 200 万和 80 万）。超过三个喷注的事件在这些分析中不予考虑。

For three-jet events, the jet energies are recomputed from their directions, assuming planar, massless kinematics; the jet-energy resolution is improved using this procedure due to the better angular resolution compared to the energy resolution of the ALEPH detector. Jets are then ordered according to the recomputed energies. The average $x_{\mathrm{j}\mathrm{e}\mathrm{t}}=E_{\mathrm{j}\mathrm{e}\mathrm{t}}/E_{\mathrm{b}\mathrm{e}\mathrm{a}\mathrm{m}}$ is 0.93 for jet 1, 0.72 for jet 2, and 0.35 for jet 3.
对于三喷注事件，喷注能量是根据其方向重新计算的，假设是平面的、无质量的运动学；由于与 ALEPH 探测器的能量分辨率相比，角分辨率更好，因此通过这个过程改善了喷注能量的分辨率。然后，根据重新计算的能量对喷注进行排序。喷注 1 的平均 $x_{\mathrm{j}\mathrm{e}\mathrm{t}}=E_{\mathrm{j}\mathrm{e}\mathrm{t}}/E_{\mathrm{b}\mathrm{e}\mathrm{a}\mathrm{m}}$ 为 0.93，喷注 2 为 0.72，喷注 3 为 0.35。

The MC events, used to correct for detector effects, are generated using the JETSET parton shower model, with modified charm and bottom decay tables and generation of initial state radiation (ISR) photons with DYMU3 [23]; these events are passed through the full ALEPH detector simulation, subjected to the same cuts and analyzed in the same way as the data.
使用 JETSET 部分子喷注模型生成的 MC 事件，用于校正探测器效应，其中包括修改的魅夸克和底夸克衰变表以及使用 DYMU3 生成初始态辐射光子[23]；这些事件经过完整的 ALEPH 探测器模拟，按照相同的截断条件进行分析，以与数据相同的方式进行分析。

Good agreement between the jet rates and the jet energies in data and MC events is obtained using the Durham algorithm with $y_{\mathrm{c}\mathrm{u}\mathrm{t}}=0.01$. The rates of two- and three-jet events in the MC sample are 62.3% and 32.5%. The average jet energies are the same as in data within 1%. The hadronization corrections to parton jet rates are also small for this value of the resolution parameter.
使用 Durham 算法和 $y_{\mathrm{c}\mathrm{u}\mathrm{t}}=0.01$ ，在数据和 MC 事件中得到了喷注率和喷注能量的良好一致性。MC 样本中两喷注和三喷注事件的比例分别为 62.3%和 32.5%。平均喷注能量与数据中的相差不超过 1%。对于这个分辨率参数的值，对部分子喷注率的强子化修正也很小。

In MC events, the reconstructed jets are matched with the parton jets which are nearest in angle. It is found that, on average, jet 1 (jet 2) is a quark or antiquark jet in 96% (75%) of the cases and that the third jet originates from a gluon with 71% probability. The gluon probability is however a function of the jet energy, decreasing with jet energy (from $\sim$90% at 5 GeV to $\sim$50% at 25 GeV), while the quark content increases with jet energy.
在 MC 事件中，重建的喷注与角度最接近的粒子喷注进行匹配。研究发现，平均而言，在 96%（75%）的情况下，喷注 1（喷注 2）是夸克或反夸克喷注，而第三个喷注有 71%的概率来自胶子。然而，胶子的概率是喷注能量的函数，随着喷注能量的增加而减少（从 5 GeV 的 90%到 25 GeV 的 50%），而夸克成分随着喷注能量的增加而增加。

4 Data analysis 4 数据分析

Reconstruction of ${\pi }^0$ and $\eta$ mesons
${\pi }^0$ 和 $\eta$ 介子的重建

The ${\pi }^0$ and the $\eta$ mesons are analyzed using the $\gamma \gamma$ decay channel with branching ratios of 98.8% for ${\pi }^0$ and 39.2% for $\eta$. In two- and three-jet events, both photons from a $\gamma \gamma$ combination are required to belong to the same jet.
${\pi }^0$ 和 $\eta$ 介子使用 $\gamma \gamma$ 衰变通道进行分析，其分支比为 ${\pi }^0$ 的 98.8%和 $\eta$ 的 39.2%。在两个和三个喷注事件中，要求 $\gamma \gamma$ 组合中的两个光子属于同一个喷注。

The photons are reconstructed as neutral clusters in the electromagnetic calorimeter. The following supplementary criteria are imposed on the identified photons. To reduce the hadronic contamination, the fraction $R_1+R_2$ of their energy in the first two segments in depth of the ECAL should be greater than 0.8, and the fraction $F_4$ of their energy in the four central towers of the shower should be greater than 0.8. The energy of the photon candidates should be greater than 1 GeV. In addition, for the $\eta$ analysis the photon pairs with invariant mass within 40 MeV/$c^2$ of the ${\pi }^0$ mass are rejected and a cut on the photon energy $E_{\gamma }>1.75$ GeV is imposed.
光子在电磁量能器中被重建为中性团簇。对已鉴定的光子施加以下补充条件。为了减少强子污染，光子在电磁量能器前两个深度段中的能量比例 $R_1+R_2$ 应大于 0.8，而在淋浴的四个中央塔中的能量比例 $F_4$ 应大于 0.8。光子候选者的能量应大于 1 GeV。此外，在 $\eta$ 分析中，不满足不变质量在 40 MeV/ $c^2$ 以内的光子对将被排除，并施加对光子能量 $E_{\gamma }>1.75$ GeV 的截断。

The invariant mass $M_{\gamma \gamma }$ of the $\gamma \gamma$ pairs is obtained in several intervals of $x=E_{\gamma \gamma }/E_{\mathrm{b}\mathrm{e}\mathrm{a}\mathrm{m}}$. For each $x$ interval, the number of $\eta$ candidates is determined by fitting the invariant mass distribution with the sum of a Gaussian for the signal and a quartic polynomial for the background. For ${\pi }^0$ fits, the sum of a distorted Gaussian and a Fermi-like function is used. In the distorted Gaussian function, the skewness terms $-(1/2)s\delta +(1/6)s{\delta }^3$ are added to the Gaussian exponent, with $\delta =M_{\gamma \gamma }-\mu$, $s$ the skewness coefficient and $\mu$ the mean value. The Fermi-like function is $f_{\mathrm{b}\mathrm{g}}(M_{\gamma \gamma })=[b_3+b_4(M_{\gamma \gamma }-b_1)]/\{1+\exp [(b_1-M_{\gamma \gamma })/b_2]\}$. Examples of ${\pi }^0$ and $\eta$ mass distributions are shown in Figs. 1 and 2.
$M_{\gamma \gamma }$ 对于 $\gamma \gamma$ 对的不变质量在 $x=E_{\gamma \gamma }/E_{\mathrm{b}\mathrm{e}\mathrm{a}\mathrm{m}}$ 的几个区间内得到。对于每个 $x$ 区间，通过将不变质量分布拟合为信号的高斯函数和背景的四次多项式，确定 $\eta$ 候选数目。对于 ${\pi }^0$ 拟合，使用扭曲高斯函数和费米函数的和。在扭曲高斯函数中，将偏斜项 $-(1/2)s\delta +(1/6)s{\delta }^3$ 添加到高斯指数中，其中 $\delta =M_{\gamma \gamma }-\mu$ ， $s$ 是偏斜系数， $\mu$ 是均值。费米函数为 $f_{\mathrm{b}\mathrm{g}}(M_{\gamma \gamma })=[b_3+b_4(M_{\gamma \gamma }-b_1)]/\{1+\exp [(b_1-M_{\gamma \gamma })/b_2]\}$ 。图 1 和图 2 显示了 ${\pi }^0$ 和 $\eta$ 质量分布的示例。

The reconstruction efficiency for ${\pi }^0$ has a strong dependence on the pion energy, with a maximum around 10 GeV. It varies between 0.2 and 0.5 as a function of $x$. For $\eta$ the efficiency increases typically from 0.05 to 0.20 as a function of $x$. The branching ratios ${\pi }^0$, $\eta \to \gamma \gamma$ are included in these values.
${\pi }^0$ 的重建效率与π介子能量强烈相关，最大值约为 10 GeV。它随 $x$ 的变化在 0.2 到 0.5 之间。对于 $\eta$ ，效率通常随 $x$ 的变化从 0.05 增加到 0.20。这些值中包含了分支比 ${\pi }^0$ ， $\eta \to \gamma \gamma$ 。

Reconstruction of ${\eta }^{\prime }(958)$ mesons
重建 ${\eta }^{\prime }(958)$ 介子

The ${\eta }^{\prime }(958)$ analysis is performed using the ${\eta }^{\prime }(958)\to \eta {\pi }^{+}{\pi }^{-}$ decay channel, with a branching ratio of 43.8%.
使用 ${\eta }^{\prime }(958)$ 衰变通道进行 ${\eta }^{\prime }(958)\to \eta {\pi }^{+}{\pi }^{-}$ 分析，其分支比为 43.8%。

Photon pairs with invariant mass within 100 MeV/$c^2$ of the fitted $\eta$ mass are taken as $\eta$ candidates; for these pairs, the mass is constrained to the nominal $\eta$ mass.
光子对的不变质量在拟合质量的 100 MeV/b0/范围内被视为 b2/候选者；对于这些对，质量被限制在名义 b3/质量上。

The pions are selected from the energy-flow objects as charged tracks which have at least five coordinates in the TPC, originate from a cylindrical region of radius 1 cm and half-length 5 cm centred on the nominal interaction point, have a polar angle with respect to the beam axis in the range ${20}^{\circ }\le \theta \le {160}^{\circ }$ and a transverse momentum greater than 0.2 GeV/$c$. The charged tracks identified as electrons or muons [20] are rejected from the pion candidate sample.
从能量流对象中选择π介子，这些介子是带电轨迹，在 TPC 中至少有五个坐标，起源于以名义相互作用点为中心、半径为 1 厘米、半长度为 5 厘米的圆柱形区域，其相对于束轴的极角在 ${20}^{\circ }\le \theta \le {160}^{\circ }$ 范围内，并且横向动量大于 0.2 GeV/ $c$ 。被鉴定为电子或μ子[20]的带电轨迹被排除在π介子候选样本之外。

In two- and three-jet events, all three particle candidates from an $\eta {\pi }^{+}{\pi }^{-}$ combination are required to belong to the same jet.
在两个和三个喷注事件中，要求所有三个粒子候选者来自同一个喷注。

The invariant mass distributions of the $\eta {\pi }^{+}{\pi }^{-}$ combinations are obtained as a function of the scaled energy $x=E_{\eta {\pi }^{+}{\pi }^{-}}/E_{\mathrm{b}\mathrm{e}\mathrm{a}\mathrm{m}}$ and are fitted for each $x$ bin with the sum of a Gaussian function for the signal and a cubic polynomial for the background. An example of an ${\eta }^{\prime }(958)$ mass distribution is shown in Fig. 3.
$\eta {\pi }^{+}{\pi }^{-}$ 组合的不变质量分布是作为缩放能量 $x=E_{\eta {\pi }^{+}{\pi }^{-}}/E_{\mathrm{b}\mathrm{e}\mathrm{a}\mathrm{m}}$ 的函数获得的，并且对每个 $x$ bin 进行拟合，其中信号部分采用高斯函数的和，背景部分采用三次多项式。图 3 展示了一个 ${\eta }^{\prime }(958)$ 质量分布的示例。

The reconstruction efficiency for ${\eta }^{\prime }(958)$ increases typically from 0.025 to 0.075 as a function of $x$. The branching ratios $\eta \to \gamma \gamma$ and ${\eta }^{\prime }(958)\to \eta {\pi }^{+}{\pi }^{-}$ are included in these values.
重建效率通常随着 $x$ 的变化从 0.025 增加到 0.075。这些值中包括了分支比 $\eta \to \gamma \gamma$ 和 ${\eta }^{\prime }(958)\to \eta {\pi }^{+}{\pi }^{-}$ 。

Reconstruction of ${\mathrm{K}}_{\mathrm{S}}^0$ and $\mathrm{\Lambda }/\bar{\mathrm{\Lambda }}$
${\mathrm{K}}_{\mathrm{S}}^0$ 和 $\mathrm{\Lambda }/\bar{\mathrm{\Lambda }}$ 的重建

The ${\mathrm{K}}_{\mathrm{S}}^0$ mesons are reconstructed from their decay into two charged pions with a branching ratio of 68.6%, while the $\mathrm{\Lambda }$ ($\bar{\mathrm{\Lambda }}$) baryons are reconstructed from their decay into a proton and a charged pion with a branching ratio of 63.9%. The selection cuts applied for ${\mathrm{V}}^0$ candidates are similar to those in the previously published analysis of ${\mathrm{K}}_{\mathrm{S}}^0$ and $\mathrm{\Lambda }$ production in hadronic events [24]: all pairs of oppositely charged tracks in an event are tested for the hypothesis that they originate from a common secondary vertex and their measured specific ionizations are required to be consistent with those expected for the decay particles. Pairs consistent with being photon conversions are rejected. The reconstructed ${\mathrm{V}}^0$'s are assigned to the jet with the smallest angle with respect to their direction of flight.
${\mathrm{K}}_{\mathrm{S}}^0$ 介子是由两个带电π介子衰变重建而成，其分支比为 68.6%；而 $\mathrm{\Lambda }$ （ $\bar{\mathrm{\Lambda }}$ ）重子是由质子和带电π介子衰变重建而成，其分支比为 63.9%。对于 ${\mathrm{V}}^0$ 候选体，所应用的选择截断与先前发表的关于强子事例中 ${\mathrm{K}}_{\mathrm{S}}^0$ 和 $\mathrm{\Lambda }$ 产生分析中的相似：对于一个事例中的所有反向带电轨迹对，测试它们是否来自一个共同的次级顶点，并要求它们测量到的比离子化与预期的衰变粒子一致。与光子转换一致的对被拒绝。重建的 ${\mathrm{V}}^0$ 被分配给与其飞行方向夹角最小的喷注。

The invariant masses of the pairs of charged tracks are calculated in intervals of the scaled momentum $x_p=p_{\mathrm{h}\mathrm{a}\mathrm{d}\mathrm{r}\mathrm{o}\mathrm{n}}/p_{\mathrm{b}\mathrm{e}\mathrm{a}\mathrm{m}}$. In each interval the invariant mass distribution is fitted with the sum of a signal function and a background function. The signal is described for ${\mathrm{K}}_{\mathrm{S}}^0$ mesons by the sum of two Gaussian functions, with the relative normalization and the relative width fixed from fully simulated MC events; a Breit-Wigner distribution is used for the $\mathrm{\Lambda }$. In both cases, the background is described by a linear function. Examples of ${\mathrm{K}}_{\mathrm{S}}^0$ and $\mathrm{\Lambda }$ mass distributions are shown in Figs. 4 and 5, respectively.
在缩放动量 $x_p=p_{\mathrm{h}\mathrm{a}\mathrm{d}\mathrm{r}\mathrm{o}\mathrm{n}}/p_{\mathrm{b}\mathrm{e}\mathrm{a}\mathrm{m}}$ 的区间内计算带电轨迹对的不变质量。在每个区间内，不变质量分布用信号函数和背景函数的和进行拟合。对于 ${\mathrm{K}}_{\mathrm{S}}^0$ 介子，信号由两个高斯函数的和来描述，相对归一化和相对宽度由完全模拟的 MC 事件确定；对于 $\mathrm{\Lambda }$ ，使用布里渊-维格纳分布。在两种情况下，背景由线性函数描述。图 4 和图 5 分别显示了 ${\mathrm{K}}_{\mathrm{S}}^0$ 和 $\mathrm{\Lambda }$ 质量分布的示例。

The reconstruction efficiency has a strong dependence on the ${\mathrm{V}}^0$ momentum.Typically, it is 55% (50%) for ${\mathrm{K}}^0\to {\pi }^{+}{\pi }^{-}$ ($\mathrm{\Lambda }\to \mathrm{p}{\pi }^{-}$) at 8 $\mathrm{G}\mathrm{e}\mathrm{V}/\mathrm{c}$ and drops below 30% for momenta smaller than 1.5 $\mathrm{G}\mathrm{e}\mathrm{V}/\mathrm{c}$ or greater than 15 $\mathrm{G}\mathrm{e}\mathrm{V}/\mathrm{c}$.
重建效率对动量有很强的依赖性。通常，在 8 $\mathrm{G}\mathrm{e}\mathrm{V}/\mathrm{c}$ 时， ${\mathrm{K}}^0\to {\pi }^{+}{\pi }^{-}$ （ $\mathrm{\Lambda }\to \mathrm{p}{\pi }^{-}$ ）的重建效率为 55%（50%），对于小于 1.5 $\mathrm{G}\mathrm{e}\mathrm{V}/\mathrm{c}$ 或大于 15 $\mathrm{G}\mathrm{e}\mathrm{V}/\mathrm{c}$ 的动量，重建效率下降至 30%以下。

Measurement of production rates
生产率的测量

The inclusive normalized cross section $f$ of each measured hadron $h$ as a function of the $x$ ($x_p$) variable is computed for each jet of the three-jet events using the relation
每个测量到的强子 $h$ 的包容性归一化截面 $f$ 作为 $x$ （ $x_p$ ）变量的函数，使用关系式计算三喷注事件中每个喷注的

$$\begin{array}{}\text{(1)}& f^{\mathrm{j}\mathrm{e}\mathrm{t}\mathrm{i}}(x)=\frac{1}{{\sigma }_3}\frac{\mathrm{d}\sigma }{\mathrm{d}x}=\frac{1}{N_{3\mathrm{j}}^{\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{a}}}\frac{N_h^{\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{a},\mathrm{j}\mathrm{e}\mathrm{t}\mathrm{i}}(\mathrm{r}\mathrm{e}\mathrm{c})}{\mathrm{\Delta }x}\frac{N_h^{\mathrm{M}\mathrm{C},\mathrm{j}\mathrm{e}\mathrm{t}\mathrm{i}}(\mathrm{g}\mathrm{e}\mathrm{n})}{N_h^{\mathrm{M}\mathrm{C},\mathrm{j}\mathrm{e}\mathrm{t}\mathrm{i}}(\mathrm{r}\mathrm{e}\mathrm{c})},\end{array}$$

where $N_h^{\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{a},\mathrm{j}\mathrm{e}\mathrm{t}\mathrm{i}}(\mathrm{r}\mathrm{e}\mathrm{c})$ is the number of reconstructed $h$ particles in jet $i$ in a given $x$ bin for data (similarly for MC), $\mathrm{\Delta }x$ is the width of the $x$ bin, and $N_h^{\mathrm{M}\mathrm{C},\mathrm{j}\mathrm{e}\mathrm{t}\mathrm{i}}(\mathrm{g}\mathrm{e}\mathrm{n})$ is the number of generated $h$ particles in jet $i$ in a given $x$ bin for MC events without ISR, detector simulation or selection criteria, normalized to the same number of events as the MC sample with ISR, full detector simulation and selection cuts applied. For each jet, the cross section is normalized to the number of selected three-jet events $N_{3\mathrm{j}}^{\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{a}}$. The analyzed particle is treated as stable in the jet clustering at the generator level. For ${\mathrm{K}}_{\mathrm{S}}^0$ and $\mathrm{\Lambda }$, the inclusive cross sections are also calculated as a function of $\xi =\ln (1/x_p)$; for ${\pi }^0$, $\eta$ and ${\eta }^{\prime }(958)$ mesons, the $\xi$ distribution is not used because its maximum is not reached due to the relatively high cut on photon energy.
其中 $N_h^{\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{a},\mathrm{j}\mathrm{e}\mathrm{t}\mathrm{i}}(\mathrm{r}\mathrm{e}\mathrm{c})$ 是给定数据（类似于 MC）中在给定 $x$ 区间内重建的 $h$ 粒子在 $i$ 喷注中的数量， $\mathrm{\Delta }x$ 是 $x$ 区间的宽度， $N_h^{\mathrm{M}\mathrm{C},\mathrm{j}\mathrm{e}\mathrm{t}\mathrm{i}}(\mathrm{g}\mathrm{e}\mathrm{n})$ 是在没有 ISR、探测器模拟或选择条件的 MC 事件中，在给定 $x$ 区间内生成的 $h$ 粒子在 $i$ 喷注中的数量，归一化到与应用了 ISR、完整的探测器模拟和选择截断的 MC 样本相同数量的事件。对于每个喷注，截面被归一化到所选三喷注事件的数量 $N_{3\mathrm{j}}^{\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{a}}$ 。在生成器级别上，分析的粒子在喷注聚类中被视为稳定的。对于 ${\mathrm{K}}_{\mathrm{S}}^0$ 和 $\mathrm{\Lambda }$ ，还计算了作为 $\xi =\ln (1/x_p)$ 函数的包容性截面；对于 ${\pi }^0$ 、 $\eta$ 和 ${\eta }^{\prime }(958)$ 介子，不使用 $\xi$ 分布，因为由于光子能量的相对较高截断，其最大值未达到。

The cross section is also calculated for two-jet events normalized to the number of selected two-jet events $N_{2\mathrm{j}}^{\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{a}}$, summing before fitting the invariant mass distributions in each $x$ bin for the two jets, and for all hadronic events normalized to the number of hadronic events $N_{\mathrm{h}\mathrm{a}\mathrm{d}}^{\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{a}}$.
截面还计算了两喷注事件的截面，以所选两喷注事件的数量 $N_{2\mathrm{j}}^{\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{a}}$ 为标准化，将两喷注的不变质量分布在每个 $x$ 区间内进行拟合，并将所有强子事件的截面标准化为强子事件的数量 $N_{\mathrm{h}\mathrm{a}\mathrm{d}}^{\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{a}}$ 。

5 Systematic errors 5 个系统误差

Systematic errors for ${\pi }^0$ and $\eta$ mesons
${\pi }^0$ 和 $\eta$ 介子的系统误差

The systematic errors on ${\pi }^0$ and $\eta$ multiplicities and inclusive cross sections are obtained as the sum in quadrature of three components: from varying the cuts, varying the fit range and from the energy calibration of the ECAL.
在 ${\pi }^0$ 和 $\eta$ 的多重性和包容截面上的系统误差是通过三个部分的平方和得到的：通过改变截取条件、改变拟合范围和通过能量校准 ECAL。

The cuts on $R_1+R_2$, $F_4$ and ${\theta }_{\mathrm{t}\mathrm{h}\mathrm{r}\mathrm{u}\mathrm{s}\mathrm{t}}$ are replaced separately by: no cut on $R_1+R_2$, no cut on $F_4$, and ${45}^{\circ }\le {\theta }_{\mathrm{t}\mathrm{h}\mathrm{r}\mathrm{u}\mathrm{s}\mathrm{t}}\le {135}^{\circ }$, respectively. For the $\eta$ analysis, the cut on photon energy is also changed to $E_{\gamma }>2\mathrm{G}\mathrm{e}\mathrm{V}$. For each $x$ bin, the maximum difference between the nominal inclusive cross section and the values obtained with one cut changed is taken as the systematic error. The relative error on the multiplicity coming from the cut variation is obtained conservatively as the linear sum over all the $x$ bins of the relative errors on multiplicity in each bin, weighted by the multiplicity in that bin.
$R_1+R_2$ 、 $F_4$ 和 ${\theta }_{\mathrm{t}\mathrm{h}\mathrm{r}\mathrm{u}\mathrm{s}\mathrm{t}}$ 上的切割分别被替换为：在 $R_1+R_2$ 上没有切割，在 $F_4$ 上没有切割，在 ${45}^{\circ }\le {\theta }_{\mathrm{t}\mathrm{h}\mathrm{r}\mathrm{u}\mathrm{s}\mathrm{t}}\le {135}^{\circ }$ 上有切割。对于 $\eta$ 分析，光子能量的切割也改变为 $E_{\gamma }>2\mathrm{G}\mathrm{e}\mathrm{V}$ 。对于每个 $x$ bin，标准的包容截面与改变一个切割后得到的值之间的最大差异被视为系统误差。来自切割变化的多重性的相对误差被保守地计算为每个 bin 中多重性的相对误差的线性求和，乘以该 bin 中的多重性。

The fit range is varied, changing both the lower and upper limits by reasonable values. The error is taken to be the maximum difference between the nominal multiplicity in the measured $x$ range and the ones obtained using different fit ranges. The systematic error on the inclusive cross section is computed assuming for each $x$ bin the same relative error as that obtained above for the multiplicity measured in the whole accessible $x$ range.
适配范围是多样的，通过合理的值改变下限和上限。误差被定义为在测量的 $x$ 范围内的名义多重性与使用不同适配范围得到的多重性之间的最大差异。对于包容性截面的系统误差，假设每个 $x$ 区间的相对误差与在整个可访问的 $x$ 范围内测量到的多重性的相对误差相同。

The calibration error for ECAL energy was assumed to be 2.5% for $E=1$ GeV and 2.0% for $E=1.75$ GeV. The systematic effects on the ${\pi }^0$ and $\eta$ multiplicities given by these errors were computed from the relative difference in the number of selected photons.
ECAL 能量的校准误差假设为 $E=1$ GeV 为 2.5%， $E=1.75$ GeV 为 2.0%。根据这些误差计算得到的 ${\pi }^0$ 和 $\eta$ 多重性的系统效应是通过所选光子数量的相对差异来计算的。

Systematic errors for ${\eta }^{\prime }$(958) mesons
${\eta }^{\prime }$ （958）介子的系统误差

The systematic errors on the ${\eta }^{\prime }$(958) multiplicity are calculated from the selection criteria for $\eta$ and ${\pi }^{\pm }$ candidates and from the variation of the fit range within reasonable limits. The error from the selection of $\eta$ candidates is the sum in quadrature of the systematic errors from cut variation and ECAL calibration. The difference in the number of ${\pi }^{\pm }$ selected in data and MC is used to calculate the error from ${\pi }^{\pm }$ selection; the errors are added linearly for ${\pi }^{+}$ and ${\pi }^{-}$ to allow for maximal correlations. The error from the fit range variation is obtained in the same way as for ${\pi }^0$ and $\eta$ mesons. The three components are added in quadrature to give the total systematic error.
${\eta }^{\prime }$ （958）多重性的系统误差是根据 $\eta$ 和 ${\pi }^{\pm }$ 候选者的选择标准以及在合理范围内的拟合范围变化计算得出的。来自 $\eta$ 候选者选择的误差是切割变化和 ECAL 校准的系统误差的平方和。使用数据和 MC 中所选 ${\pi }^{\pm }$ 数量的差异来计算 ${\pi }^{\pm }$ 选择的误差；对于 ${\pi }^{+}$ 和 ${\pi }^{-}$ ，误差线性相加以考虑最大相关性。拟合范围变化的误差与 ${\pi }^0$ 和 $\eta$ 介子的计算方式相同。这三个部分的误差平方和得到总的系统误差。

Systematic errors for ${\mathrm{K}}_{\mathrm{S}}^0$ and $\mathrm{\Lambda }$
${\mathrm{K}}_{\mathrm{S}}^0$ 和 $\mathrm{\Lambda }$ 的系统误差

The systematic errors for both ${\mathrm{K}}_{\mathrm{S}}^0$ and $\mathrm{\Lambda }$ are dominated by the ${\mathrm{V}}^0$ selection. They are studied by successively varying the cuts on: the specific ionization $\mathrm{d}\mathit{E}\mathit{/}\mathrm{d}\mathit{x}$, the quality of the vertex fit ${\chi }_{\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{t}\mathrm{e}\mathrm{x}\mathrm{f}\mathrm{i}\mathrm{t}}^2$, the decay length and the decay angle $\cos {\theta }^{\ast }$.
${\mathrm{K}}_{\mathrm{S}}^0$ 和 $\mathrm{\Lambda }$ 的系统误差主要由 ${\mathrm{V}}^0$ 选择支配。通过逐步改变以下方面的削减，来进行研究：特定电离能 $\mathrm{d}\mathit{E}\mathit{/}\mathrm{d}\mathit{x}$ ，顶点拟合质量 ${\chi }_{\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{t}\mathrm{e}\mathrm{x}\mathrm{f}\mathrm{i}\mathrm{t}}^2$ ，衰变长度和衰变角 $\cos {\theta }^{\ast }$ 。

The variation of the event selection cuts has no significant influence on the results. Different schemes of ${\mathrm{V}}^0$ assignment to the jets yield only very small effects. Using different signal and background functions give results consistent with statistical fluctuations.
事件选择条件的变动对结果没有显著影响。对喷注分配不同方案只产生极小影响。使用不同的信号和背景函数得到与统计波动一致的结果。

6 Results 6 个结果

The inclusive cross sections of ${\pi }^0$, $\eta$, ${\eta }^{\prime }$(958) and ${\mathrm{K}}_{\mathrm{S}}^0$ mesons and $\mathrm{\Lambda }$ baryons are determined in all hadronic events, two-jet events and each jet of three-jet events according to the procedure outlined in Section 4.4. They are compared with the values computed with JETSET 7.4, HERWIG 5.8 and ARIADNE 4.08 Monte Carlo models. For each particle analyzed, the multiplicity is obtained by integrating the inclusive cross section over the accessible $x$, $x_p$ or $\xi$ range.
根据第 4.4 节中概述的程序，确定了所有强子事件、双喷注事件和三喷注事件中 ${\pi }^0$ 、 $\eta$ 、 ${\eta }^{\prime }$ （958）和 ${\mathrm{K}}_{\mathrm{S}}^0$ 介子以及 $\mathrm{\Lambda }$ 重子的包容截面。将它们与 JETSET 7.4、HERWIG 5.8 和 ARIADNE 4.08 蒙特卡洛模型计算得到的值进行比较。对于每个分析的粒子，通过在可访问的 $x$ 、 $x_p$ 或 $\xi$ 范围内对包容截面进行积分来获得多重性。

The parameters of the MC models were tuned [25] to ALEPH event shape and single charged particle distributions and to ALEPH inclusive spectra of various particles(including $\eta$, ${\eta }^{\prime }(958)$, K${}_{\mathrm{S}}^0$ and $\mathrm{\Lambda }$) in hadronic events. The inclusive spectra in two- or three-jet events presented here were not used for tuning. In JETSET, an ad hoc ${\eta }^{\prime }(958)$ suppression of 0.275 was imposed; no ad hoc suppression was required for $\eta$ mesons. The suppression of the first rank di-quarks in b and c events has been turned off in JETSET to increase the fraction of b $\to {\mathrm{\Lambda }}_{\mathrm{b}}$ and c $\to {\mathrm{\Lambda }}_{\mathrm{c}}$ to agree with recent measurements by ALEPH [26]. In the model analysis of a particular particle type, the particles of that type are required to be stable. Jet energies are also recomputed from their directions, assuming planar, massless kinematics.
MC 模型的参数经过调整[25]，以适应 ALEPH 事件形状和单带电粒子分布，以及 ALEPH 各种粒子（包括 $\eta$ ， ${\eta }^{\prime }(958)$ ，K ${}_{\mathrm{S}}^0$ 和 $\mathrm{\Lambda }$ ）在强子事件中的包容光谱。这里呈现的两个或三个喷注事件的包容光谱没有用于调整。在 JETSET 中，对 ${\eta }^{\prime }(958)$ 的临时抑制为 0.275；对 $\eta$ 介子不需要临时抑制。在 JETSET 中，关闭了 b 和 c 事件中第一级双夸克的抑制，以增加与 ALEPH 最近测量结果一致的 b $\to {\mathrm{\Lambda }}_{\mathrm{b}}$ 和 c $\to {\mathrm{\Lambda }}_{\mathrm{c}}$ 的比例。在对特定粒子类型的模型分析中，要求该类型的粒子是稳定的。喷注能量也根据其方向重新计算，假设是平面的、无质量的动力学。

The multiplicities obtained are summarized in Table 1 for ${\pi }^0$, Table 3 for $\eta$, Table 5 for ${\eta }^{\prime }(958)$, Table 7 for K${}^0$ and Table 9 for $\mathrm{\Lambda }$. For K${}_{\mathrm{S}}^0$ mesons and $\mathrm{\Lambda }$ baryons, the measured values contribute more than 94% and 96%, respectively, to the total multiplicity, therefore only the values extrapolated to the full range using JETSET 7.4 are given in the tables. The multiplicity for K${}^0$ (K${}_{\mathrm{S}}^0$ +K${}_{\mathrm{L}}^0$) was taken as twice the K${}_{\mathrm{S}}^0$ multiplicity. The systematic errors on multiplicities are summarized in Tables 2, 4, 6, 8 and 10 for ${\pi }^0$, $\eta$, ${\eta }^{\prime }(958)$, K${}_{\mathrm{S}}^0$ and $\mathrm{\Lambda }$, respectively. For comparison, the corresponding statistical errors are also given in the same tables.
获得的多重性总结如下：表 1 总结了 ${\pi }^0$ 的多重性，表 3 总结了 $\eta$ 的多重性，表 5 总结了 ${\eta }^{\prime }(958)$ 的多重性，表 7 总结了 K ${}^0$ 的多重性，表 9 总结了 $\mathrm{\Lambda }$ 的多重性。对于 K ${}_{\mathrm{S}}^0$ 介子和 $\mathrm{\Lambda }$ 重子，测量值分别对总多重性贡献超过 94%和 96%，因此只给出了使用 JETSET 7.4 在整个范围内外推的值。K ${}^0$ （K ${}_{\mathrm{S}}^0$ +K ${}_{\mathrm{L}}^0$ ）的多重性被认为是 K ${}_{\mathrm{S}}^0$ 多重性的两倍。多重性的系统误差总结在表 2、4、6、8 和 10 中，分别对应 ${\pi }^0$ 、 $\eta$ 、 ${\eta }^{\prime }(958)$ 、K ${}_{\mathrm{S}}^0$ 和 $\mathrm{\Lambda }$ 。为了比较，相应的统计误差也在同一表中给出。

The measured ${\pi }^0$, $\eta$ and ${\eta }^{\prime }(958)$ inclusive cross sections as functions of the $x$ variable are shown in Fig. 6a for all hadronic events, Fig. 6b for two-jet events, and Figs. 7, 8 and 9 for each jet in three-jet events. Figures 10 and 11 present the inclusive cross sections in all hadronic events for K${}_{\mathrm{S}}^0$ and $\mathrm{\Lambda }$, respectively, as functions of $x_p$ and $\xi =\ln (1/x_p)$; for two-jet events, the inclusive cross sections are shown in Figs. 12 and 13. The inclusive cross sections in the first, the second and the third jet in three-jet events are shown in Figs. 14, 15 and 16 for K${}_{\mathrm{S}}^0$ mesons, and in Figs. 17, 18 and 19 for $\mathrm{\Lambda }$ baryons. Also shown in the figures are the corresponding inclusive cross sections from the MC models. The numerical values of the ${\pi }^0$, $\eta$ and ${\eta }^{\prime }(958)$ inclusive cross sections are given in Tables 11, 12 and 13 for all hadronic events, Tables 14, 15 and 16 for two-jet events, and Tables 17, 18 and 19 for jets in three-jet events. For K${}_{\mathrm{S}}^0$ and $\mathrm{\Lambda }$, the numerical values are given in Tables 20 and 21 for hadronic events, and Tables 22 and 23 for two-jet events; for the first, the second and the third jet in three-jet events, the values are given in Tables 24, 25 and 26 for K${}_{\mathrm{S}}^0$, and Tables 27, 28 and 29 for $\mathrm{\Lambda }$. ASCII files for the tables can be found at http://alephwww.cern.ch/ALPUB/paper/paper_99.html address.
图 6a 显示了所有强子事件中作为 $x$ 变量的函数的测量 ${\pi }^0$ ， $\eta$ 和 ${\eta }^{\prime }(958)$ 的包容截面，图 6b 显示了两喷注事件的情况，图 7、8 和 9 分别显示了三喷注事件中每个喷注的情况。图 10 和 11 分别以 $x_p$ 和 $\xi =\ln (1/x_p)$ 为函数显示了所有强子事件中的包容截面，对应于 K ${}_{\mathrm{S}}^0$ 和 $\mathrm{\Lambda }$ ；对于两喷注事件，包容截面显示在图 12 和 13 中。图 14、15 和 16 显示了三喷注事件中第一、第二和第三喷注的包容截面，对应于 K ${}_{\mathrm{S}}^0$ 介子，图 17、18 和 19 显示了 $\mathrm{\Lambda }$ 重子的情况。图中还显示了来自 MC 模型的相应包容截面。所有强子事件的 ${\pi }^0$ ， $\eta$ 和 ${\eta }^{\prime }(958)$ 包容截面的数值值分别在表 11、12 和 13 中给出，两喷注事件的数值值分别在表 14、15 和 16 中给出，三喷注事件中喷注的数值值分别在表 17、18 和 19 中给出。 对于 K ${}_{\mathrm{S}}^0$ 和 $\mathrm{\Lambda }$ ，数值在表 20 和 21 中给出，用于强子事件，表 22 和 23 用于双喷注事件；对于三喷注事件中的第一、第二和第三喷注，数值在表 24、25 和 26 中给出，用于 K ${}_{\mathrm{S}}^0$ ，表 27、28 和 29 用于 $\mathrm{\Lambda }$ 。表的 ASCII 文件可以在 http://alephwww.cern.ch/ALPUB/paper/paper_99.html 地址找到。

7 Discussion 7 讨论

Discussion of ${\pi }^0$, $\eta$ and ${\eta }^{\prime }(958)$ results
讨论 ${\pi }^0$ 、 $\eta$ 和 ${\eta }^{\prime }(958)$ 的结果

For hadronic events and two-jet events (a subsample of $\approx 63\mathrm{\%}$ of the hadronic events, after the additional cuts), the ${\pi }^0$, $\eta$ and ${\eta }^{\prime }(958)$ spectra computed with JETSET are found to be in reasonable agreement with the measured spectra, apart from the high $x>0.75$ region where JETSET shows an excess of $\eta$ particles. This latter region is very sensitive to the values of the fragmentation parameters and a similar discrepancy has been observed [25] for the charged particle distribution in hadronic events. In contrast, HERWIG shows a slightly too steep dependence on $x$ for $\eta$ and ${\eta }^{\prime }(958)$.
对于强子事件和双喷注事件（在附加剪切后的强子事件的子样本），使用 JETSET 计算得到的 ${\pi }^0$ 、 $\eta$ 和 ${\eta }^{\prime }(958)$ 谱与测量谱在大部分区域上基本一致，除了高 $x>0.75$ 区域，JETSET 显示出 $\eta$ 粒子的过多。这个后者区域对于碎裂参数的值非常敏感，类似的差异也在强子事件中观察到[25]。相比之下，HERWIG 对于 $\eta$ 和 ${\eta }^{\prime }(958)$ 的依赖关系稍微过陡。

The ${\pi }^0$ inclusive cross sections for jets in the three-jet events are better reproduced by JETSET, with a slightly overestimated production at higher $x$ for jet 1 and jet 2; HERWIG is in good agreement with the data for jet 1, but is not steep enough in $x$ for jet 2 and too steep for jet 3. The agreement of both models with data can, however, be considered reasonable.
三喷注事件中的喷注 ${\pi }^0$ 包容截面由 JETSET 更好地再现，对于喷注 1 和喷注 2，在较高的 $x$ 下稍微高估了产生；HERWIG 与喷注 1 的数据相符，但对于喷注 2 的 $x$ 不够陡峭，对于喷注 3 则太陡峭。然而，可以认为这两个模型与数据的一致性是合理的。

The measured $\eta$ inclusive cross sections in jets of the three-jet events are well reproduced by JETSET for each jet. For a quantitative comparison between data and the phenomenological models, a
三喷注事件中的测量 $\eta$ 包容截面在每个喷注中都被 JETSET 很好地再现。为了对数据和现象学模型进行定量比较，一个

$${\chi }^2=\sum _{x\mathrm{b}\mathrm{i}\mathrm{n}\mathrm{s}}{[f_{\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}}(x)-f_{\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{a}}(x)]}^2/{\left({\sigma }_{\mathrm{t}\mathrm{o}\mathrm{t}}^{\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{a}}\right)}^2$$

is defined for each jet and the ratio of ${\chi }^2$ to the number of degrees of freedom (ndf) is computed. Here the total error ${\sigma }_{\mathrm{t}\mathrm{o}\mathrm{t}}^{\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{a}}$ is the sum in quadrature of the statistical and systematic errors on the measured value. For the third jet, which according to MC calculations represents the gluon jet in $\sim$71% of the cases, the ${\chi }^2$/ndf is equal to 2.7/3. The other two jets are also reasonably well modelled, with ${\chi }^2$/ndf equal to 5.3/5 for the second jet and 11.2/6 for the first jet. As in hadronic events and two-jet events, HERWIG shows a slightly too steep dependence on $x$ for all three jets; the ${\chi }^2$/ndf are 6.1/3 for the third jet, 12.8/5 for the second jet and 32.5/6 for the first jet.
对于每个喷注，计算 ${\chi }^2$ 与自由度（ndf）的比值。这里的总误差 ${\sigma }_{\mathrm{t}\mathrm{o}\mathrm{t}}^{\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{a}}$ 是测量值的统计误差和系统误差的平方和。对于第三个喷注，根据 MC 计算，在 $\sim$ 71%的情况下代表胶子喷注， ${\chi }^2$ /ndf 等于 2.7/3。其他两个喷注也被合理地建模，第二个喷注的 ${\chi }^2$ /ndf 等于 5.3/5，第一个喷注的 ${\chi }^2$ /ndf 等于 11.2/6。与强子事件和双喷注事件一样，HERWIG 对于所有三个喷注都显示出稍微过于陡峭的依赖于 $x$ ；第三个喷注的 ${\chi }^2$ /ndf 为 6.1/3，第二个喷注的 ${\chi }^2$ /ndf 为 12.8/5，第一个喷注的 ${\chi }^2$ /ndf 为 32.5/6。

For ${\eta }^{\prime }(958)$ mesons, the measured inclusive cross sections and the measured multiplicities are reproduced by JETSET and HERWIG for each of the three jets, all the model values being within one ${\sigma }_{\mathrm{t}\mathrm{o}\mathrm{t}}$ of the measured values.
对于 ${\eta }^{\prime }(958)$ 介子，JETSET 和 HERWIG 分别对三个喷注的测量包容截面和测量多重性进行了重现，所有模型值都在测量值的 ${\sigma }_{\mathrm{t}\mathrm{o}\mathrm{t}}$ 之内。

Because reasonable agreement with the measured spectra in quark-enriched jets is observed for both isoscalar and isovector mesons and no significant deviations are observed for isoscalar mesons in gluon-enriched jets, one can conclude that the JETSET modelling of gluon fragmentation into isoscalar mesons is in agreement with the experimental results for the measured $x$ region. No additional enhancement for isoscalar mesons in gluon jets, as predicted by the models mentioned in Section 1 and which would manifest as a deviation from the JETSET values, is observed in the experimental results.
由于在富含夸克的喷注中，无论是等标量还是等矢量介子的测量光谱都与实验结果达成了合理的一致，而在富含胶子的喷注中，等标量介子的测量结果没有明显的偏差，因此可以得出结论：JETSET 模型中胶子裂变成等标量介子的建模与实验结果在测量区域 $x$ 是一致的。在实验结果中没有观察到等标量介子在胶子喷注中的额外增强，这与第 1 节中提到的模型预测的偏离 JETSET 值的情况不符。

The slightly too steep dependence on $x$ shown by HERWIG for $\eta$ spectra in two-jet events and each jet of three-jet events does not depend on the average gluon content of the jet. Therefore, these discrepancies cannot be related to particular effects of gluon fragmentation into isoscalar mesons.
HERWIG 对两喷注事件和三喷注事件中每个喷注的 $\eta$ 谱的略微过于陡峭的依赖性，并不取决于喷注的平均胶子含量。因此，这些差异与胶子裂变成等标量介子的特定效应无关。

Using the new spectra in hadronic events obtained here, the parameters describing $\eta$ and ${\eta }^{\prime }(958)$ production in the JETSET string model are examined again. The data are best described by the default value for the pseudoscalar mixing angle ${\theta }_P=-{9.7}^{\circ }$ and by an ad hoc ${\eta }^{\prime }(958)$ suppression factor of 0.275. For a different value of the mixing angle, ${\theta }_P=-{20}^{\circ }$, the data still require a sizeable ${\eta }^{\prime }(958)$ suppression of $\approx$0.40. No ad hoc $\eta$ suppression is required.
使用此处获得的强子事件中的新光谱，再次检查描述 JETSET 弦模型中 $\eta$ 和 ${\eta }^{\prime }(958)$ 产生的参数。数据最好由伪标量混合角度 ${\theta }_P=-{9.7}^{\circ }$ 的默认值和 0.275 的临时 ${\eta }^{\prime }(958)$ 抑制因子来描述。对于不同的混合角度 ${\theta }_P=-{20}^{\circ }$ ，数据仍然需要相当大的 ${\eta }^{\prime }(958)$ 抑制，大约为 0.40。不需要临时 $\eta$ 抑制。

Discussion of ${\mathrm{K}}_{\mathrm{S}}^0$ and $\mathrm{\Lambda }$ results
讨论 ${\mathrm{K}}_{\mathrm{S}}^0$ 和 $\mathrm{\Lambda }$ 的结果

The measured spectra are well reproduced by JETSET and ARIADNE in both quark(-enriched) jets (the first two jets in three-jet events and jets in two-jet events) and gluon-enriched jets; the agreement between the models and the data is also reasonable in all hadronic events.
测量得到的光谱在夸克（富含夸克）喷注（三喷注事件中的前两个喷注和两喷注事件中的喷注）和富含胶子的喷注中都能很好地被 JETSET 和 ARIADNE 模型所重现；模型与数据之间的一致性在所有强子事件中也是合理的。

HERWIG is in reasonable agreement with the measured spectra for ${\mathrm{K}}_{\mathrm{S}}^0$ in jets with a high quark content (jets in two-jet events and the first jet in three-jet events), but gives fewer ${\mathrm{K}}_{\mathrm{S}}^0$ mesons as the gluon content of the jet becomes significant; the discrepancy gets larger with the increase of the gluon content of the jet. As a consequence of the large discrepancies seen for the last two jets in three-jet events, HERWIG also gives fewer ${\mathrm{K}}_{\mathrm{S}}^0$ mesons than measured in hadronic events.
HERWIG 与高夸克含量的喷注（双喷注事件中的喷注和三喷注事件中的第一个喷注）的测量谱基本一致，但随着喷注中胶子含量的增加，HERWIG 给出的 ${\mathrm{K}}_{\mathrm{S}}^0$ 介子较少；随着喷注中胶子含量的增加，这种差异变得更大。由于在三喷注事件中最后两个喷注的差异较大，HERWIG 在强子事件中给出的 ${\mathrm{K}}_{\mathrm{S}}^0$ 介子也较少。

In the $\mathrm{\Lambda }$ spectra, HERWIG has a shoulder which is not seen in the measured spectra. The shoulder decreases with the decrease of the quark content of the jet: it is very clear in two-jet events and in the first jet of three-jet events, smaller in the second jet of three-jet events and absent in the third jet of three-jet events. HERWIG gives also too many $\mathrm{\Lambda }$'s in jets with a high quark content and too few in the third jet of three-jet events, which has a high gluon content. The shoulder in jets with a high quark content is also shown by HERWIG in hadronic events and is not seen in the data; HERWIG also gives more $\mathrm{\Lambda }$ baryons than measured in hadronic events.
在 $\mathrm{\Lambda }$ 谱中，HERWIG 有一个在测量谱中看不到的肩膀。随着喷注的夸克含量的减少，这个肩膀也减小：在双喷注事件和三喷注事件的第一个喷注中非常明显，在三喷注事件的第二个喷注中较小，在三喷注事件的第三个喷注中则不存在。HERWIG 在夸克含量较高的喷注中也给出了太多的 $\mathrm{\Lambda }$ ，而在夸克含量较高的三喷注事件的第三个喷注中给出的太少，而这个喷注中的胶子含量较高。HERWIG 在强子事件中也显示了夸克含量较高的喷注中的肩膀，而在数据中没有看到；HERWIG 在强子事件中也给出了比测量值更多的 $\mathrm{\Lambda }$ 重子。

The new version HERWIG 5.9 does not improve the description of the data; the disagreements in the shapes of the momentum spectra are also observed with the new version.
新版本 HERWIG 5.9 并未改善数据描述；动量谱形状不协调的差异也在新版本中观察到。

8 Conclusions 8 个结论

The production rates and the inclusive cross sections of the isovector meson ${\pi }^0$, the isoscalar mesons $\eta$ and ${\eta }^{\prime }(958)$, the strange meson ${\mathrm{K}}_{\mathrm{S}}^0$ and the $\mathrm{\Lambda }$ baryon were determined in hadronic events, two-jet events and each jet of three-jet events from Z decays. The measured quantities have been compared with the values computed with the tuned JETSET 7.4, HERWIG 5.8 and ARIADNE 4.08 models.
在 Z 玻色子衰变事件中，通过对强子事件、二喷注事件和三喷注事件中每个喷注的生产速率和全包覆截面的测量，得出了同位旋异性介子 ${\pi }^0$ 、同位旋等性介子 $\eta$ 和 ${\eta }^{\prime }(958)$ ，奇怪介子 ${\mathrm{K}}_{\mathrm{S}}^0$ 和 $\mathrm{\Lambda }$ 重子的值。测量结果与 JETSET 7.4，HERWIG 5.8 和 ARIADNE 4.08 模型进行了比较。

For all the particles analyzed, the inclusive cross sections are in agreement with previous ALEPH results [24, 25].
对于所有分析的粒子，包含截面与之前的 ALEPH 结果[24, 25]一致。

The measured spectra for the isovector meson ${\pi }^0$ are reasonably reproduced by JETSET and HERWIG. For the isoscalar mesons $\eta$ and ${\eta }^{\prime }(958)$, the measured spectra are well reproduced by JETSET for quark(-enriched) jets and gluon-enriched jets. Therefore, the JETSET description of gluon fragmentation into isoscalar mesons is in agreement with the experimental results for the measured $x$ region. HERWIG shows a slightly too steep dependence on $x$ for $\eta$ spectra in two-jet events and each jet of three-jet events; these discrepancies cannot be related to gluon fragmentation into isoscalar mesons because they do not depend on the average gluon content of the jet.
对于等矢量介子 ${\pi }^0$ 的测量光谱，JETSET 和 HERWIG 能够合理地复现。对于等标量介子 $\eta$ 和 ${\eta }^{\prime }(958)$ ，JETSET 在富含夸克的喷注和富含胶子的喷注中能够很好地复现测量光谱。因此，JETSET 对胶子衰变为等标量介子的描述与测量到的 $x$ 区域的实验结果一致。HERWIG 在两喷注事件和三喷注事件中 $x$ 光谱上显示出稍微过陡的依赖关系；这些差异与胶子衰变为等标量介子无关，因为它们不依赖于喷注的平均胶子含量。

The measured spectra for ${\mathrm{K}}_{\mathrm{S}}^0$ and $\mathrm{\Lambda }$ hadrons are reproduced by JETSET and ARIADNEin quark(-enriched) jets and in gluon-enriched jets. HERWIG fails to describe the ${\mathrm{K}}_{\mathrm{S}}^0$ spectra in jets with a significant gluon content, giving too few ${\mathrm{K}}_{\mathrm{S}}^0$ mesons; the discrepancies increase with the average gluon content. HERWIG also fails to describe the shape of the $\mathrm{\Lambda }$ spectra in jets with high quark content and overestimates the number of $\mathrm{\Lambda }$'s in these jets.
JETSET 和 ARIADNE 在富含夸克和富含胶子的喷注中能够重现 ${\mathrm{K}}_{\mathrm{S}}^0$ 和 $\mathrm{\Lambda }$ 强子的测量光谱。HERWIG 在含有大量胶子的喷注中无法描述 ${\mathrm{K}}_{\mathrm{S}}^0$ 光谱，产生过少的 ${\mathrm{K}}_{\mathrm{S}}^0$ 介子；这种差异随着平均胶子含量的增加而增加。HERWIG 还无法描述高夸克含量喷注中 $\mathrm{\Lambda }$ 光谱的形状，并且高估了这些喷注中 $\mathrm{\Lambda }$ 的数量。

Acknowledgments 致谢

We wish to thank our colleagues from the accelerator divisions for the successful operation of the LEP machine, and the engineers and technical staff in all our institutes for their contribution to the good performance of ALEPH. Those of us from non-member states thank CERN for its hospitality.
我们要感谢加速器部门的同事们成功运行 LEP 机器，以及我们所有研究所的工程师和技术人员对 ALEPH 的良好表现所做的贡献。我们非成员国家的人感谢 CERN 的款待。

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\begin{table} \begin{tabular}{c|c|c|c|c|c|c|c} \hline \multicolumn{2}{c|}{Event type} & \multicolumn{2}{c|}{$x$ range} & \multicolumn{2}{c|}{$\text{Mult.}\pm {\mathrm{\Delta }}_{\text{stat}}\pm {\mathrm{\Delta }}_{\text{syst}}$} & \multicolumn{2}{c|}{JETSET} & \multicolumn{2}{c}{HERWIG} \ & & & & all & & all \ \hline \multicolumn{2}{c|}{Hadronic events} & 0.06 – 0.62 & $2.131\pm 0.007\pm 0.079$ & 2.274 & 9.66 & 2.192 & 9.58 \ \hline \multicolumn{2}{c|}{Two-jet events} & 0.06 – 0.52 & $2.156\pm 0.008\pm 0.079$ & 2.313 & 8.54 & 2.169 & 8.54 \ \hline \multirow{3}{*}{\(\text{\tiny{\text{\tiny{\text{\tiny{\text{\text{\text{\text{\text{\text{\text{\text{ \text{ \text{ \text{ \text{ }}}}}}}}}}}}}}\) & total} & total & 0.06 – 0.52 & $2.069\pm 0.011\pm 0.097$ & 2.208 & 11.20 & 2.215 & 11.09 \ \cline{2-9} & jet 1 & 0.06 – 0.52 & $0.978\pm 0.008\pm 0.056$ & 1.060 & 4.13 & 1.008 & 4.09 \ \cline{2-9} & jet 2 & 0.06 – 0.52 & $0.790\pm 0.007\pm 0.030$ & 0.829 & 3.83 & 0.834 & 3.75 \ \cline{2-9} & jet 3 & 0.06 – 0.32 & $0.301\pm 0.003\pm 0.011$ & 0.318 & 3.23 & 0.373 & 3.24 \ \hline \end{tabular} \end{table} Table 1: Multiplicity for ${\pi }^0$ in different event types, compared with JETSET 7.4 and HERWIG 5.8 predictions. JETSET and HERWIG values for all $x$ range are also given.
表 1：不同事件类型中 ${\pi }^0$ 的多重性，与 JETSET 7.4 和 HERWIG 5.8 的预测进行比较。同时给出了 JETSET 和 HERWIG 在所有 $x$ 范围内的值。

$$\text{Unknown environment 'table'}$$ Table 2: Systematic and statistical errors for ${\pi }^0$. All values are expressed in percent.
表 2：系统误差和统计误差 ${\pi }^0$ 的百分比值。

$$\text{Unknown environment 'table'}$$ Table 4: Systematic and statistical errors for $\eta$. All values are expressed in percent.
表 4：系统误差和统计误差 $\eta$ 的百分比值。

$$\text{Unknown environment 'table'}$$ Table 3: Multiplicity for $\eta$ in different event types, compared with JETSET 7.4 and HERWIG 5.8 predictions. JETSET and HERWIG values for all $x$ range are also given.
表 3：与 JETSET 7.4 和 HERWIG 5.8 预测相比，不同事件类型中 $\eta$ 的多重性。同时给出了 JETSET 和 HERWIG 在所有 $x$ 范围内的值。

$$\text{Unknown environment 'table'}$$ Table 6: Systematic and statistical errors for ${\eta }^{\prime }(958)$. All values are expressed in percent.
表 6：系统误差和统计误差 ${\eta }^{\prime }(958)$ 的百分比值。

$$\text{Unknown environment 'table'}$$ Table 5: Multiplicity for ${\eta }^{\prime }(958)$ in different event types, compared with JETSET 7.4 and HERWIG 5.8 predictions. JETSET and HERWIG values for all $x$ range are also given.
表 5：与 JETSET 7.4 和 HERWIG 5.8 预测相比，不同事件类型中 ${\eta }^{\prime }(958)$ 的多重性。同时给出了 JETSET 和 HERWIG 在所有 $x$ 范围内的值。

$$\text{Unknown environment 'table'}$$ Table 7: Multiplicity for ${\mathrm{K}}^0$ (${\mathrm{K}}_{\mathrm{S}}^0+{\mathrm{K}}_{\mathrm{L}}^0$) in different event types, compared with JETSET 7.4, ARIADNE 4.08 and HERWIG 5.8 predictions. The extrapolation to the full $\xi$ range is made using JETSET 7.4.
表 7：在不同事件类型中，与 JETSET 7.4、ARIADNE 4.08 和 HERWIG 5.8 的预测相比， ${\mathrm{K}}^0$ （ ${\mathrm{K}}_{\mathrm{S}}^0+{\mathrm{K}}_{\mathrm{L}}^0$ ）的多重性。使用 JETSET 7.4 对全 $\xi$ 范围进行外推。

$$\text{Unknown environment 'table'}$$ Table 8: Systematic and statistical errors for ${\mathrm{K}}_{\mathrm{S}}^0$. All values are expressed in percent.
表 8：系统误差和统计误差 ${\mathrm{K}}_{\mathrm{S}}^0$ 的百分比值。

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$$\text{Unknown environment 'table'}$$ Table 19: Inclusive cross section for ${\eta }^{\prime }(958)$ in three-jet events.
表 19：三喷注事件中 ${\eta }^{\prime }(958)$ 的包容截面。

\begin{table} \begin{tabular}{c|c|c c c} \hline \hline & \multicolumn{2}{c|}{$x$ range} & \multicolumn{2}{c}{$\frac{1}{{\sigma }_3}\frac{\mathrm{d}\sigma ({\eta }^{\prime })}{\mathrm{d}x}$} $\pm$ & ${\mathrm{\Delta }}_{\mathrm{stat}}$ & $\pm$ & ${\mathrm{\Delta }}_{\mathrm{syst}}$ \ \hline & 0.10 – 0.14 & 0.849 & $\pm$ & 0.182 & $\pm$ & 0.095 \ & 0.14 – 0.18 & 0.644 & $\pm$ & 0.088 & $\pm$ & 0.058 \ & 0.18 – 0.22 & 0.338 & $\pm$ & 0.039 & $\pm$ & 0.036 \ \cline{2-6} $\mathrm{♣}$ & 0.22 – 0.32 & 0.257 & $\pm$ & 0.018 & $\pm$ & 0.015 \ & 0.32 – 0.42 & 0.1382 & $\pm$ & 0.0095 & $\pm$ & 0.0075 \ & 0.42 – 0.52 & 0.0650 & $\pm$ & 0.0054 & $\pm$ & 0.0060 \ & 0.52 – 0.62 & 0.0325 & $\pm$ & 0.0031 & $\pm$ & 0.0018 \ \hline & 0.10 – 0.14 & 1.09 & $\pm$ & 0.19 & $\pm$ & 0.25 \ & 0.14 – 0.18 & 0.629 & $\pm$ & 0.083 & $\pm$ & 0.057 \ \cline{2-6} $\mathrm{♣}$ & 0.18 – 0.22 & 0.349 & $\pm$ & 0.038 & $\pm$ & 0.020 \ \cline{2-6} $\mathrm{♣}$ & 0.22 – 0.32 & 0.197 & $\pm$ & 0.013 & $\pm$ & 0.018 \ & 0.32 – 0.42 & 0.0848 & $\pm$ & 0.0060 & $\pm$ & 0.0048 \ & 0.42 – 0.52 & 0.0303 & $\pm$ & 0.0030 & $\pm$ & 0.0030 \ \hline & 0.10 – 0.14 & 0.584 & $\pm$
$x$ 范围 & $\frac{1}{{\sigma }_3}\frac{\mathrm{d}\sigma ({\eta }^{\prime })}{\mathrm{d}x}$ & $\pm$ & ${\mathrm{\Delta }}_{\mathrm{stat}}$ & $\pm$ & ${\mathrm{\Delta }}_{\mathrm{syst}}$ \\ 0.10 – 0.14 & 0.849 & $\pm$ & 0.182 & $\pm$ & 0.095 \\ 0.14 – 0.18 & 0.644 & $\pm$ & 0.088 & $\pm$ & 0.058 \\ 0.18 – 0.22 & 0.338 & $\pm$ & 0.039 & $\pm$ & 0.036 \\ 0.22 – 0.32 & 0.257 & $\pm$ & 0.018 & $\pm$ & 0.015 \\ 0.32 – 0.42 & 0.1382 & $\pm$ & 0.0095 & $\pm$ & 0.0075 \\ 0.42 – 0.52 & 0.0650 & $\pm$ & 0.0054 & $\pm$ & 0.0060 \\ 0.52 – 0.62 & 0.0325 & $\pm$ & 0.0031 & $\pm$ & 0.0018 \\ 0.10 – 0.14 & 1.09 & $\pm$ & 0.19 & $\pm$ & 0.25 \\ 0.14 – 0.18 & 0.629 & $\pm$ & 0.083 & $\pm$ & 0.057 \\ 0.18 – 0.22 & 0.349 & $\pm$ & 0.038 & $\pm$ & 0.020 \\ 0.22 – 0.32 & 0.197 & $\pm$ & 0.013 & $\pm$ & 0.018 \\ 0.32 – 0.42 & 0.0848 & $\pm$ & 0.0060 & $\pm$ & 0.0048 \\ 0.42 – 0.52 & 0.0303 & $\pm$ & 0.0030 & $\pm$ & 0.0030 \\ 0.10 – 0.14 & 0.584 & $\pm$

\begin{table} \begin{tabular}{c|c} \hline $\xi$ range & $\frac{1}{{\sigma }_{\mathrm{h}\mathrm{a}\mathrm{d}}}\frac{\mathrm{d}\sigma ({\mathrm{K}}_{\mathrm{S}}^0)}{\mathrm{d}\xi }\pm {\mathrm{\Delta }}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {\mathrm{\Delta }}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}}$ \ \hline
范围 & 值 \ \hline

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Figure 3: Example of a fitted $\eta {\pi }^{+}{\pi }^{-}$ invariant mass distribution in jet 3 for inclusive ${\eta }^{\prime }(958)$ production in three-jet events.
图 3：三喷注事件中包含 ${\eta }^{\prime }(958)$ 产生的喷注 3 的拟合不变质量分布示例。

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Figure 8: The inclusive cross sections of $\eta$ in three-jet events compared with JETSET 7.4 and HERWIG 5.8. The error bars show the total errors (statistical and systematic errors added in quadrature).
图 8：三喷注事件中 $\eta$ 的包容截面与 JETSET 7.4 和 HERWIG 5.8 进行比较。误差棒显示总误差（统计误差和系统误差按平方相加）。

Figure 7: The inclusive cross sections of ${\pi }^0$ in three-jet events compared with JETSET 7.4 and HERWIG 5.8. The error bars show the total errors (statistical and systematic errors added in quadrature).
图 7：三喷注事件中 ${\pi }^0$ 的包容截面与 JETSET 7.4 和 HERWIG 5.8 进行比较。误差棒显示总误差（统计误差和系统误差按平方相加）。

Figure 10: The inclusive cross sections of ${\mathrm{K}}_{\mathrm{S}}^0$ in hadronic events in $x_p=p({\mathrm{K}}_{\mathrm{S}}^0)/{\mathrm{p}}_{\mathrm{b}\mathrm{e}\mathrm{a}\mathrm{m}}$ and $\xi =-\ln x_p$. The error bars show the total errors (statistical and systematic errors added in quadrature).
图 10：在 $x_p=p({\mathrm{K}}_{\mathrm{S}}^0)/{\mathrm{p}}_{\mathrm{b}\mathrm{e}\mathrm{a}\mathrm{m}}$ 和 $\xi =-\ln x_p$ 的强子事件中， ${\mathrm{K}}_{\mathrm{S}}^0$ 的包容截面。误差条显示总误差（统计误差和系统误差按平方相加）。

Figure 9: The inclusive cross sections of ${\eta }^{\prime }(958)$ in three-jet events compared with JETSET 7.4 and HERWIG 5.8. The error bars show the statistical errors only.
图 9：三喷注事件中 ${\eta }^{\prime }(958)$ 的包容截面与 JETSET 7.4 和 HERWIG 5.8 进行比较。误差棒仅显示统计误差。

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Figure 14: The inclusive cross sections of ${\mathrm{K}}_{\mathrm{S}}^0$ in the first jet of the three-jet events in $x_p=p({\mathrm{K}}_{\mathrm{S}}^0)/{\mathrm{p}}_{\mathrm{b}\mathrm{e}\mathrm{a}\mathrm{m}}$ and $\xi =-\ln x_p$. The error bars show the total errors (statistical and systematic errors added in quadrature).
图 14：在 $x_p=p({\mathrm{K}}_{\mathrm{S}}^0)/{\mathrm{p}}_{\mathrm{b}\mathrm{e}\mathrm{a}\mathrm{m}}$ 和 $\xi =-\ln x_p$ 中，三喷注事件中第一个喷注中 ${\mathrm{K}}_{\mathrm{S}}^0$ 的包容截面。误差棒显示总误差（统计误差和系统误差按平方相加）。

Figure 13: The inclusive cross sections of $\mathrm{\Lambda }$ and $\bar{\mathrm{\Lambda }}$ in two-jet events in $x_p=p(\mathrm{\Lambda })/p_{beam}$ and $\xi =-\ln x_p$. The error bars show the total errors (statistical and systematic errors added in quadrature).
图 13：在 $x_p=p(\mathrm{\Lambda })/p_{beam}$ 和 $\xi =-\ln x_p$ 中的双喷注事件中的 $\mathrm{\Lambda }$ 和 $\bar{\mathrm{\Lambda }}$ 的包容性截面。误差条显示总误差（统计误差和系统误差按平方相加）。

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Figure 17: The inclusive cross sections of $\mathrm{\Lambda }$ and $\bar{\mathrm{\Lambda }}$ in the first jet of the three-jet events in $x_p=p(\mathrm{\Lambda })/p_{\mathrm{b}\mathrm{e}\mathrm{a}\mathrm{m}}$ and $\xi =-\ln x_p$. The error bars show the total errors (statistical and systematic errors added in quadrature).
图 17：在 $x_p=p(\mathrm{\Lambda })/p_{\mathrm{b}\mathrm{e}\mathrm{a}\mathrm{m}}$ 和 $\xi =-\ln x_p$ 中的三喷注事件的第一个喷注中， $\mathrm{\Lambda }$ 和 $\bar{\mathrm{\Lambda }}$ 的包容性截面。误差棒显示总误差（统计误差和系统误差按平方相加）。

Figure 18: The inclusive cross sections of $\mathrm{\Lambda }$ and $\bar{\mathrm{\Lambda }}$ in the second jet of the three-jet events in $x_p=p(\mathrm{\Lambda })/p_{\mathrm{b}\mathrm{e}\mathrm{a}\mathrm{m}}$ and $\xi =-\ln x_p$. The error bars show the total errors (statistical and systematic errors added in quadrature).
图 18：在 $x_p=p(\mathrm{\Lambda })/p_{\mathrm{b}\mathrm{e}\mathrm{a}\mathrm{m}}$ 和 $\xi =-\ln x_p$ 中三喷注事件的第二个喷注中 $\mathrm{\Lambda }$ 和 $\bar{\mathrm{\Lambda }}$ 的包容截面。误差棒显示总误差（统计误差和系统误差按平方相加）。

Figure 19: The inclusive cross sections of $\mathrm{\Lambda }$ and $\bar{\mathrm{\Lambda }}$ in the third jet of the three-jet events in $x_p=p(\mathrm{\Lambda })/p_{\mathrm{b}\mathrm{e}\mathrm{a}\mathrm{m}}$ and $\xi =-\ln x_p$. The error bars show the total errors (statistical and systematic errors added in quadrature).
图 19：在 $x_p=p(\mathrm{\Lambda })/p_{\mathrm{b}\mathrm{e}\mathrm{a}\mathrm{m}}$ 和 $\xi =-\ln x_p$ 中三喷注事件的第三个喷注中 $\mathrm{\Lambda }$ 和 $\bar{\mathrm{\Lambda }}$ 的包容截面。误差棒显示总误差（统计误差和系统误差按平方相加）。