Summary
Current algebra sum rules for kaon-nucleus elastic-scattering amplitudes are re-written as off-mass-shell, finite-contour forward dispersion relations. Saturating these latter with narrow levels, both in the meson-nucleus continua and in the bound-state spectra, we produce a general formula for the dependence of the real parts of kaon-nucleus scattering lengths on the target quantum numbers. We introduce explicitly a shell-model description of nuclear ground-states, which was instrumental in reproducing with satisfactory accuracy the corresponding pion-nucleus data: most of the effects observed there (up to and including the 2s−1d shell) were consistent with a naive spherical-harmonic-oscillator picture. An output of this analysis is the (average) kaon-nucleon sigma-term: the value derived here stays as large as found in two previous estimates by ourselves, the first from a slightly less sophisticated analysis of (mostly) the same data, the second derived from the dispersion-relation evaluations of the zero-energy, fixed-t kaon-nucleon scattering amplitudes made by Oades. Such a large value (about 640 MeV) confirms the hypothesis, advanced by Donoghue and Nappi, of a large, nonperturbative, strange-quark scalar density in the nucleon.
Riassunto
Si riscrivono le regole di somma dell'algebra delle correnti in forma di relazioni di dispersione su contorno finito per le ampiezze di diffusione in avanti, fuori del “mass-shell”. Saturando poi queste relazioni con livelli stretti, sia nel continuo che sotto soglia, troviamo una formula per esprimere la dipendenza dai numeri quantici del nucleo bersaglio delle parti reali delle lunghezze di diffusione K−-nucleo. Viene esplicitamente introdotta una descrizione di modello “a strati” per gli stati fondamentali dei nuclei, rivelatasi essenziale per riprodurre accuratamente gli stessi dati per la diffusione π--nucleo: gran parte degli effetti osservati erano spiegati con un semplice modello di oscillatore armonico sferico fino allo strato 1d–2s incluso. Un risultato di questa analisi è il valore medio per i nucleoni del termine sigma KN: confermiamo qui il valore abbastanza grande trovato in analisi precedenti degli stessi dati, come pure in un'estrapolazione analitica delle ampiezze elastiche KN ad energia nulla. Un valore cosí grande (circa 640 MeV) conferma l'ipotesi avanzata da Donoghue e Nappi di una apprezzabile densità scalare (non perturbativa) di quark strani nel nucleone.
Резюме
Мы занов записываем правила сумм алгебры токов для амплитуд упругого рассеяния каонов на ядрах в виде дисперсионных соотношений в направлении вперед, вне массовой поверхности. Насыщая последние с узкими уровнями, в непрерывном и дискретном мезон-qjдерных спектрах, мы воспроизводим обшую формулу для зависимости вещественных частей длин каон-ядерного рассеяния от квантовых чисел мишени. Мы явно вводим описание модели оболочек для основных состояний ядер, которое дает удовлетворительнуй точность для соответствующих пион-ядерных данных. Большинство наблюдаемых эффектов согласуется с картиной сферического гармонического осциллятора. Из нашего анализа получается (средний) каон-нуклонный сигма-член. Полученная величина является такой же большой, как и в случае двух предыдущих оценок, проведенных нами сначала из менее сложного анализа тех же данных, а затем из анализа дисперсионных соотношений для амплитуд каон-нуклонного рассеяния при фиксированномt, проведенного Оадсом. такая большая величина (около 600 МэВ) подтверждает гипотезу Донохью и Наппи о больмой, непертурбационной скалярной плотности странных кварков в нуклоне.
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Research supported in part by a grant from Ministero della Pubblica Istruzione (fondi 60%).
Formerly at Dipartimento di Fisica, Università di Lecce, where large portions of this research were carried out.
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Gensini, P.M. A current algebra description of kaon-nucleus scattering lengths. Nuov Cim A 103, 9–32 (1990). https://doi.org/10.1007/BF02902617
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DOI: https://doi.org/10.1007/BF02902617