Properties of color singlet chain states in e+ e- annihilation
Properties of color singlet chain states in e+ e- annihilation
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DOI：
10.1103/physrevd.64.012006
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发表时间：
2000-11
影响因子：
5
通讯作者：
Qun Wang;G. Gustafson;Yi Jin;Q. Xie
中科院分区：
文献类型：
--
作者：
Qun Wang;G. Gustafson;Yi Jin;Q. Xie
We use the method of the color effective Hamiltonian to study the structure of color singlet chain states in ${N}_{c}=3$ and in the large ${N}_{c}$ limit. In order to obtain their total fraction when ${N}_{c}$ is finite, we illustrate how to orthogonalize these nonorthogonal states. We give numerical results for the fraction of orthogonalized states in ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}q\overline{q}\mathrm{gg}.$ With the help of a diagram technique, we derive their fraction up to ${O(1/N}_{c}^{2})$ for the general multigluon process. For large ${N}_{c}$ the singlet chain states correspond to well-defined color topologies. Therefore we may expect that the fraction of non-color-singlet-chain states is an estimate of the fraction of events where color reconnection is possible. In the case of soft gluon bremsstrahlung, we give an explicit form for the color effective Hamiltonian which leads to the dipole cascade formulation for parton showering in leading order in ${N}_{c}.$ The next-to-leading order corrections are also given for ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}q\overline{q}{g}_{1}{g}_{2}$ and ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}q\overline{q}{g}_{1}{g}_{2}{g}_{3}.$
We use the method of the color effective Hamiltonian to study the structure of color singlet chain states in ${N}_{c}=3$ and in the large ${N}_{c}$ limit. In order to obtain their total fraction when ${N}_{c}$ is finite, we illustrate how to orthogonalize these nonorthogonal states. We give numerical results for the fraction of orthogonalized states in ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}q\overline{q}\mathrm{gg}.$ With the help of a diagram technique, we derive their fraction up to ${O(1/N}_{c}^{2})$ for the general multigluon process. For large ${N}_{c}$ the singlet chain states correspond to well-defined color topologies. Therefore we may expect that the fraction of non-color-singlet-chain states is an estimate of the fraction of events where color reconnection is possible. In the case of soft gluon bremsstrahlung, we give an explicit form for the color effective Hamiltonian which leads to the dipole cascade formulation for parton showering in leading order in ${N}_{c}.$ The next-to-leading order corrections are also given for ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}q\overline{q}{g}_{1}{g}_{2}$ and ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}q\overline{q}{g}_{1}{g}_{2}{g}_{3}.$