1. High-energy scattering amplitudes of Yang-Mills theories in generalized leading-term approximation and eikonal xxxxulas
C. Y. Lo
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In this paper, we study the apparent discrepancy between Feynman diagrams and the eikonal xxxxulas, and the apparent paradox between the eikonal xxxxulas and the s-u crossing symmetry. We analyze the generalized leadingterm approximation (GLA), which generates the terms of the eikonal xxxxulas from Feynman diagrams. This analysis is done through using the techniques of decomposing diagrammatically the isospin factors (or group-theoretical weights in general) of Feynman diagrams. As a result, we modify the GLA into a generalized complex leading-term approximation. We calculate, with this new xxxxalism, the high-energy limit (s→∞ with t fixed) of the vector-meson-vector-meson elastic amplitude of a Yang-Mills theory with SU(2) symmetry through tenth perturbative order. With this new method, we resolve the apparent discrepancy and paradox mentioned above. This method is generalizable to other non-Abelian gauge theories.

Phys. Rev. D 23, 508 (1981)
Cited 4 times
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2. High-energy amplitudes of Yang-Mills theory in arbitrary perturbative orders
Hung Cheng and C. Y. Lo
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In this paper, we give a summary of our work on perturbative calculations of high-energy amplitudes in Yang-Mills theory. Using the model of SU(2) with an isodoublet of Higgs bosons, we calculate the leading real part and the leading imaginary part of the vector-meson-vector-meson scattering amplitude in the 2nd through 10th orders. We also calculate two sets of diagrams to all perturbative orders: the ladder diagrams and the multi-meson-exchange diagrams. The leading terms of the amplitude of I=1 (one unit of isospin exchanged) come from the ladder diagrams only and are shown to add up to a Regge-pole term corresponding to the Reggeization of the vector meson. The above results are shown to generalize easily to other non-Abelian gauge field theories. The extension to the process of fermion-fermion scattering is also straightforward, and we give a proof that these amplitudes are asymptotically proportional to the corresponding ones in vector-meson-vector-meson scattering. The 2nd- through 10th-order calculations show the following features: (i) All factors of lns come from integration over longitudinal momenta. (ii) All divergent integrals over the transverse momenta cance. (This has been explicitly verified up to the 8th order only.) The 2nd- through 10th-order results suggest to us a recursion xxxxula which determines to all perturbative orders the leading terms of the scattering amplitudes. Summing up these leading terms, we found the following: (a) For the amplitude of I=0 (no exchange of isospin), the sum of the leading terms exceeds the Froissart bound, representing a fixed branch point at J0=1+[(2ln2) / π2]g2 in the plane of the angular momentum. (b) For the amplitude of I=2 (two units of isospin exchanged), the sum of leading terms at Δ→=0 has a branch point at J2=2α1(0)-1, where α1 is the Regge trajectory on which the vector meson lies. (c) From (a) and (b) we have ∞>J0>1>α1(0)>J2. The qualitative features of high-energy scattering in Yang-Mills theories are therefore exactly the same as those in QED. In particular, the violation of the Froissart bound by summing leading terms in all these cases indicates the necessity of a calculational program to go beyond summing leading terms.

Phys. Rev. D 15, 2959 (1977)
Cited 25 times
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3. High-energy amplitudes of Yang-Mills theory in the eighth order
C. Y. Lo and Hung Cheng
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We give the asymptotic xxxxs of the eighth-order amplitudes for both fermion-fermion scattering and vector-vector scattering in the Yang-Mills theory with an isospin-1/2 Higgs boson, in the limit s→∞ with t fixed.

Phys. Rev. D 13, 1131 (1976)
Cited 27 times
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4. Diagonalizing Tensor Covariants, Light-Cone Commutators, and Sum Rules
C. Y. Lo
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We derive fixed-mass sum rules for virtual Compton scattering including the nucleon spin and not specializing to the forward direction. We use the methods of both Dicus, Jackiw, and Teplitz (for the absorptive parts) and Heimann, Hey, and Mandula (for the real parts). We find a set of tensor covariants such that the corresponding scalar amplitudes are proportional to simple t-channel parity-conserving helicity amplitudes. We give a relatively complete discussion of the convergence of the sum rules in a Regge model.

Phys. Rev. D 8, 2650 (1973)
Cited 2 times
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