Summary
The most general expression for the spin-averaged Compton amplitude of off-mass-shell photons is briefly discussed and the terms are individuated which, in the low-energy limit and forq 2 → 0, contribute to the electric (α) and magnetic (β) nucleon polarizabilities. These amplitudes are connected with the structure functions usually defined in the deep elastic scattering and, through dispersion relations, sum rules for the polarizabilities are deduced. The well-known forward sum rule forα +β is reobtained and, moreover, a sum rule forα, expressed in terms of the parameterR=σ L /σ T , is proposed. With the available SLAC determinations forR, this rule yields the valueα p ∼ 9.3 · 10−4 fm3, which is in substantial agreement with the valueα p=(12.4 ± 2.5) · 10−4 fm3 obtained with a fit of all the available experimental data. Similarly a backward sum rule forα −β is proposed, even though its numerical evaluation is strongly dependent on thet-channel contribution. Nevertheless, within the present experimental knowledge, this rule gives values compatible with the previous evaluations givingα p>β p.
Riassunto
Si discute brevemente la formula più generale di ampiezza Compton per fotoni fuori dallo strato delle masse e se ne isolano i termini che, nel limite di bassa energia e perq 2 → 0, contribuiscono alla polarizzabilità elettrica (α) e magnetica (β) del uucleone. Si collegano queste ampiezze alle funzioni di struttura definite usualmente nel «deep inelastic scattering» e mediante relazioni di dispersione si ricavano regole di somma per le polarizzabilità. In particolare si riottiene la nota regola di somma in avanti perα +β e se ne deduce una perα espressa in termini del parametroR=σ L /σ T . Tenendo presente le determinazioni diR fatte a SLAC, questa regola fornisceα p ∼ 9.3 · 10−4 fm3, in sostanziale accordo con il valoreα p=(12.4±2.5) · 10−4 fm3, ottenuto analizzando l’insieme dei dati sperimentali disponibili. Con tecnica analoga si ricava anche una regola di somma all’indietro perα −β, ma la sua valutazione numerica risulta criticamente dipendente dalla valutazione del contributo nel canalet. Ciò nonostante si mostra come, nei limiti delle informazioni sperimentali disponibili, tale regola di somma non sia incompatibile con le precedenti stime che fornisconoα p>β p.
Реэюме
Обсуждается наиболее обшее выражение для комптоновской амплитуды, усредненной по спину, для протонов вне массовой поверхности. Выделяются члены, которые в пределе ниэких знергий и дляq 2 → 0 дают вклады в злектрическую (а) и магнитную (β) поляриэуемости нуклонов. Эти амплитуды свяэываются со структурными функциями, обычно определяемыми в глубоко упругом рассеянии. Выводятся правила сумм для поляриэуемостей. Заново получается хорощо иэвестное правило симм для α + β. Кроме того, предлагается правило сумм для α, выраженное череэ параметрR=σL/σT. Испольэуя имеюшиеся SLAC данные для В, зто правило дает величину αp ∼ 9.3 · 10−4 fm3, которая, по сушеству, согласуется с величиной α p =(12.4±2.5)·10−4fm3, полученной при подгонке имеюшихся зкспериментальных данных. Аналогично предлагается правило сумм для α → β, хотя численная оценка его сильно эависит от вкладаt-канала. Тем не менее, испольэия современные зкспериментальные данные, зто правило приводит к величинам, сравнимым с предыдушими оценками, которые дают αp>βp.
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Matone, G., Prosperi, D. Nucleon polarizabilities and deep inelastic electron scattering. Nuov Cim A 38, 471–489 (1977). https://doi.org/10.1007/BF02730017
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DOI: https://doi.org/10.1007/BF02730017