arXiv subjects
Publications and source records attributed to M. K. Liou.
The criteria suggested by Welsh and Fearing (nucl-th/9606040) to judge the validity of certain soft-photon amplitudes are examined. We comment on aspects of their analysis which lead to incorrect conclusions about published amplitudes and point out important criteria which were omitted from their analysis.
A relativistic and manifestly gauge-invariant soft-photon amplitude, which is consistent with the soft-photon theorem and satisfies the Pauli Principle, is derived for the proton-proton bremsstrahlung process. This soft-photon amplitude is the first two-u-two-t special amplitude to satisfy all theoretical constraints. The conventional Low amplitude can be obtained as a special case. It is demonstrated that previously proposed amplitudes for this process, both the (u,t) and (s,t) classes, violate the Pauli principle at some level. The origin of the Pauli principle violation is shown to come from two sources: (i) For the (s,t) class, the two-s-two-t amplitude transforms into the two-s-two-u amplitude under the interchange of two initial-state (or final-state) protons. (ii) For the (u,t) class, the use of an internal emission amplitude determined from the gauge-invariance constraint alone, without imposition of the Pauli principle, causes a problem. The resulting internal emission amplitude can depend upon an electromagnetic factor which is not invariant under the interchange of the two protons.
A novel soft-photon amplitude is proposed to replace the conventional Low soft-photon amplitude for nucleon-nucleon bremsstrahlung. Its derivation is guided by the standard meson-exchange model of the nucleon-nucleon interaction. This new amplitude provides a superior description of $ppγ$ data. The predictions of this new amplitude are in close agreement with potential-model calculations, which implies that, contrary to conclusions drawn by others, off-shell effects are essentially insignificant below pion-production threshold.
A modified Low procedure for constructing soft-photon amplitudes has been used to derive two general soft-photon amplitudes, a two-s-two-t special amplitude $M^{TsTts}_μ$ and a two-u-two-t special amplitude $M^{TuTts}_μ$, where s, t and u are the Mandelstam variables. $M^{TsTts}_μ$ depends only on the elastic T-matrix evaluated at four sets of (s,t) fixed by the requirement that the amplitude be free of derivatives ($\partial$T/$\partial$s and /or $\partial$T/$\partial t$). Likewise $M^{TuTts}_μ$ depends only on the elastic T-matrix evaluated at four sets of (u,t). In deriving these amplitudes, we impose the condition that $M^{TsTts}_μ$ and $M^{TuTts}_μ$ reduce to $\bar{M}^{TsTts}_μ$ and $\bar{M}^{TuTts}_μ$, respectively, their tree level approximations. The amplitude $\bar{M}^{TsTts}_μ$ represents photon emission from a sum of one-particle t-channel exchange diagrams and one-particle s-channel exchange diagrams, while the amplitude $\bar{M}^{TuTts} _μ$ represents photon emission from a sum of one-particle t-channel exchange diagrams and one-particle u-channel exchange diagrams. The precise expressions for $\bar{M}^{TsTts}_μ$ and $\bar{M}^{TuTts}_μ$ are determined by using the radiation decomposition identities of Brodsky and Brown. We point out that it is theoretically impossible to describe all bremsstrahlung processes by using only a single class of soft-photon amplitudes. At least two different classes are required: the amplitudes which depend on s and t or the amplitudes which depend on u and t. When resonance effects are important, the amplitude $M^{TsTts}_μ$, not $M^{Low(st)}_μ$, should be used. For processes with strong u-channel exchange effects, the amplitude $M^{TuTts}_μ$ should be the first choice.