Research on parton fragmentation functions of protons
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摘要: 部分子的分布函数和碎裂函数是研究和分析高能物理实验的重要基础.对质子的价夸克分布函数q（x）和价夸克碎裂为质子的碎裂函数D（x）的关系进行了分析，发现D（x）=（1/6）q（x）可以很好地将它们联系起来.因此，可以通过比较成熟的质子的部分子分布函数来构建部分子碎裂为质子的碎裂函数.利用此关系，建立了一组新的碎裂函数的参数式，计算了相应的微分散射截面并与实验进行了比较.此工作可以确定价夸克碎裂为质子的碎裂函数，以减少拟合部分子碎裂函数时的不确定性.Abstract: Parton distribution functions and fragmentation functions are fundamental to analyzing high energy experiments.The relationship between the proton valence quark distribution function q(x) and fragmentation function D(x) is analyzed. We find that the simple function D(x)=(1/6)q(x) for a valence quark is a good approximation to describe the available data. We set up a group of new parameterizations of fragmentation functions for protons. Differential cross section data were calculated and compared with recent research. We hope that our work can diminish uncertainties when fitting parton fragmentation functions of protons.
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Key words:
- distribution function /
- fragmentation function /
- structure function /
- annihilation
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图 1 标度$Q_0^2 =1~{\rm GeV}^2$时不同小组的质子的碎裂函数
Fig. 1 The proton fragmentation function for different types of partons at scale $Q_0^2 =1~{\rm GeV}^2$
图 2 (a) u价夸克在$Q^2=1~{\rm GeV}^2$的碎裂为质子的碎裂函数, 实线是用ZRS分布函数转化之后得到的结果; (b)与(a)类似, 是d夸克的碎裂函数分布
Fig. 2 (a) The u valence quark fragmentation function of a proton at $Q^2=1~{\rm GeV}^2$, the solid curve displays the results transformed from a ZRS parton distribution; (b) is the same as (a) but for a d valence quark
图 3 (a) 正负电子湮灭微分截面, 实线是本文的结果, 实验数据是SLD和ALEPH在$\sqrt s $ = 91.2 GeV的数据[23-24]; (b)与(a)类似, 但是是TASSO[25]在$Q=34$ GeV的实验数据; (c)与其类似, 是TPC[26-27]在$Q=29$ GeV的实验数据
Fig. 3 (a) Differential cross sections in annihilation, the solid curve depicts our results, the experimental results are from ALEPH and SLD at $\sqrt s =91.2$ GeV, the experimental data are taken from ref [23-24]; (b) is same as (a), but with data from TASSO[25] at $Q=34$ GeV; (c) is also the same as (a), but with data from TPC [26-27] at $Q=29$ GeV
图 4 比较本文结果与文献[28]中的碎裂函数的范围; (a)实线是本文的碎裂函数结果, 点线是u$^+$碎裂函数的范围; (b)与(a)相似, 但是是对d$^+$+s$^+$
Fig. 4 Comparison of our results with the range of fragmentation functions from ref [28]; In picture (a), the solid line represents our results for fragmentation functions and the dotted line represents the range of fragmentation functions on u$^+$; The picture (b) is same as (a) but for d$^+$+s$^+$
表 1 动量标度$Q^2 $=1 GeV2时各种部分子碎裂成的质子动量与部分子动量的比值
Tab. 1 Fractions of the parton momentum carried by protons for $Q^2=1~{\rm GeV}^2$
小组 u$_{\rm v}$ d$_{\rm v}$ u$_{\rm s}$ d$_{\rm s}$ s c b gluon HKNS 0.083 9 0.042 0 0.015 8 0.015 8 0.015 8 0.024 1 0.018 0 0.039 3 DSS 0.022 0 0.016 0 0.036 0 0.022 0 0.022 5 0.039 5 0.023 5 0.029 1 NSM 0.000 2 0.021 2 0.043 3 0.048 8 0.017 7 0.019 6 0.014 9 0.029 8 
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