THE FEYNMAN RULES OF COLLECTIVE BAG-QUARK CURRENT AND HADRON TIME-LIKE STRUCTURE FUNCTIONS

WANG Xing-Min

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2024年10月30日

Chinese Physics C> 1984, Vol. 8> Issue(2) : 148-157

THE FEYNMAN RULES OF COLLECTIVE BAG-QUARK CURRENT AND HADRON TIME-LIKE STRUCTURE FUNCTIONS

WANG Xing-Min ^,

Hangzhou University

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Abstract：
In this article some Feynman rules in the method of collective bag-quark current are given, and, by use of these rules, the zeroth-order transition matrix elements of various photon-hadron processes are obtained. Then the structure functions of nucleons and pions in the processes of deep-inelastic electron-positron annihilation are calculated. The time-like structure functions thus obtained have Bjorken scaling, satisfy Collan-Gross relation, vanish when x=q²/2p﹒q<1, and F₁≡W₁≥0, F₂≡v/M W₂≤0 when x≥1. All these characteristics are required by definition. Besides, a counting rule is obtained for the time-like structure functions, i.e., F₁(x~1)∝(x－1)^3N-2, which is quite symmetric with the one we obtained for the space-like structure functions.

References

[1]

汪醒民、宋孝同、殷鹏程, 高能物理与核物理, 6(1982), 560.[2] 同上, 6(1983), 160.[3] A. Chodos et al., Phys. Rev., D10(1974), 2599.[4] T. DeGrand et al., Phys. Rev., D12(1975), 2060.[5] M. V. Barnhill III, Phys. Rev., D20(1979), 723.[6] R. L. Jaffe, Phys. Rev., D11(1975), 1953.[7] S. D. Drell, D. J. Lery and T. M. Yan, Phys. Rev., 187(1969), 2159; D1(1970), 1035; Dl(1970).1617.[8] F. E. Close, in Fundamentals of Quark Model SUGSP (1977).[9] J. F. Donoghue and K. Johson, Phys. Rev., D21(1980), 1975.

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WANG Xing-Min. THE FEYNMAN RULES OF COLLECTIVE BAG-QUARK CURRENT AND HADRON TIME-LIKE STRUCTURE FUNCTIONS[J]. Chinese Physics C, 1984, 8(2): 148-157.

WANG Xing-Min. THE FEYNMAN RULES OF COLLECTIVE BAG-QUARK CURRENT AND HADRON TIME-LIKE STRUCTURE FUNCTIONS[J]. Chinese Physics C, 1984, 8(2): 148-157. shu

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Received: 1900-01-01
Revised: 1900-01-01

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沈阳化工大学材料科学与工程学院沈阳 110142

THE FEYNMAN RULES OF COLLECTIVE BAG-QUARK CURRENT AND HADRON TIME-LIKE STRUCTURE FUNCTIONS

WANG Xing-Min ^,

Corresponding author: WANG Xing-Min,

Hangzhou University

Received Date: 1900-01-01
Accepted Date: 1900-01-01
Available Online: 1984-04-05

Abstract: In this article some Feynman rules in the method of collective bag-quark current are given, and, by use of these rules, the zeroth-order transition matrix elements of various photon-hadron processes are obtained. Then the structure functions of nucleons and pions in the processes of deep-inelastic electron-positron annihilation are calculated. The time-like structure functions thus obtained have Bjorken scaling, satisfy Collan-Gross relation, vanish when x=q²/2p﹒q<1, and F₁≡W₁≥0, F₂≡v/M W₂≤0 when x≥1. All these characteristics are required by definition. Besides, a counting rule is obtained for the time-like structure functions, i.e., F₁(x~1)∝(x－1)^3N-2, which is quite symmetric with the one we obtained for the space-like structure functions.