dorsal/arxiv
View SchemaAnatomy of the Soft-Photon Approximation in Hadron-Hadron Bremsstrahlung
| Authors | M. K. Liou, Dahang Lin, B. F. Gibson |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9210006 |
| URL | https://arxiv.org/abs/nucl-th/9210006 |
| DOI | 10.1103/PhysRevC.47.973 |
Abstract
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 $M^{TsTts}_{\mu}$ and a two-u-two-t special amplitude $M^{TuTts}_{\mu}$, where s, t and u are the Mandelstam variables. $M^{TsTts}_{\mu}$ 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 $M^{TuTts}_{\mu}$ depends only on the elastic T-matrix evaluated at four sets of (u,t). In deriving these amplitudes, we impose the condition that $M^{TsTts}_{\mu}$ and $M^{TuTts}_{\mu}$ reduce to $\bar{M}^{TsTts}_{\mu}$ and $\bar{M}^{TuTts}_{\mu}$, respectively, their tree level approximations. The amplitude $\bar{M}^{TsTts}_{\mu}$ represents photon emission from a sum of one-particle t-channel exchange diagrams and one-particle s-channel exchange diagrams, while the amplitude $\bar{M}^{TuTts} _{\mu}$ represents photon emission from a sum of one-particle t-channel exchange diagrams and one-particle u-channel exchange diagrams. The precise expressions for $\bar{M}^{TsTts}_{\mu}$ and $\bar{M}^{TuTts}_{\mu}$ 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 $M^{TsTts}_{\mu}$, not $M^{Low(st)}_{\mu}$, should be used. For processes with strong u-channel exchange effects, the amplitude $M^{TuTts}_{\mu}$ should be the first choice.
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"abstract": "A modified Low procedure for constructing soft-photon amplitudes has been\nused to derive two general soft-photon amplitudes, a two-s-two-t special\namplitude $M^{TsTts}_{\\mu}$ and a two-u-two-t special amplitude\n$M^{TuTts}_{\\mu}$, where s, t and u are the Mandelstam variables.\n$M^{TsTts}_{\\mu}$ depends only on the elastic T-matrix evaluated at four sets\nof (s,t) fixed by the requirement that the amplitude be free of derivatives\n($\\partial$T/$\\partial$s and /or $\\partial$T/$\\partial t$). Likewise\n$M^{TuTts}_{\\mu}$ depends only on the elastic T-matrix evaluated at four sets\nof (u,t). In deriving these amplitudes, we impose the condition that\n$M^{TsTts}_{\\mu}$ and $M^{TuTts}_{\\mu}$ reduce to $\\bar{M}^{TsTts}_{\\mu}$ and\n$\\bar{M}^{TuTts}_{\\mu}$, respectively, their tree level approximations. The\namplitude $\\bar{M}^{TsTts}_{\\mu}$ represents photon emission from a sum of\none-particle t-channel exchange diagrams and one-particle s-channel exchange\ndiagrams, while the amplitude $\\bar{M}^{TuTts} _{\\mu}$ represents photon\nemission from a sum of one-particle t-channel exchange diagrams and\none-particle u-channel exchange diagrams. The precise expressions for\n$\\bar{M}^{TsTts}_{\\mu}$ and $\\bar{M}^{TuTts}_{\\mu}$ are determined by using the\nradiation decomposition identities of Brodsky and Brown. We point out that it\nis theoretically impossible to describe all bremsstrahlung processes by using\nonly a single class of soft-photon amplitudes. At least two different classes\nare required: the amplitudes which depend on s and t or the amplitudes which\ndepend on u and t. When resonance effects are important, the amplitude\n$M^{TsTts}_{\\mu}$, not $M^{Low(st)}_{\\mu}$, should be used. For processes with\nstrong u-channel exchange effects, the amplitude $M^{TuTts}_{\\mu}$ should be\nthe first choice.",
"arxiv_id": "nucl-th/9210006",
"authors": [
"M. K. Liou",
"Dahang Lin",
"B. F. Gibson"
],
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"nucl-th"
],
"doi": "10.1103/PhysRevC.47.973",
"title": "Anatomy of the Soft-Photon Approximation in Hadron-Hadron Bremsstrahlung",
"url": "https://arxiv.org/abs/nucl-th/9210006"
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