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Unitarity sum rules and soft-pion amplitudes

Унитарные правила сумм и амплитуды мягких пионов

  • Published:
Il Nuovo Cimento A (1971-1996)

Summary

We examine unitarity bounds on scattering amplitudes by using « unitarity sum rules » at high energy. Threshold conditions emerge when certain mass parameters approach zero. For ππ scattering a bound similar to (but somewhat weaker than) the Adler condition is shown to be needed in order to avoid a dangerous mass (infra-red) singularity. A different argument, which uses crucially the pseudoscalar nature of the pion and a few very plausible dynamical assumptions, yields a stronger bound as well as the possibility of extension to general pion amplitudes. We finally discuss our results as well as the possibility of understanding spontaneously broken symmetries from generalS-matrix principles.

Riassunto

Si esaminano i vincoli di unitarietà sulle ampiezze di scattering usando « regole di somma di unitarietà » ad alta energia. Le condizioni di soglia emergono quando certi parametri di massa si avvicinano a zero. Per lo scatteringππ si dimostra che è necessario un vincolo simile (ma alquanto più debole che) la condizione di Adler allo scopo di evitare una pericolosa singolarità (infrarossa) di massa. Un argomento diverso, che usa in modo cruciale la natura pseudoscalare del pione e poche plausibilissime ipotesi dinamiche, dà un vincolo più forte ed anche la possibilità di una estensione alle ampiezze pioniche generiche. Infine si discutono i risultati ed anche la possibilità di comprendere le simmetrie spontaneamente infrante sulla base dei principi generali della matriceS.

Реэуме

Исполяэуя «унитарные правила сумм» при высоких знергиях, мы исследуем унитарные границы для амплитуд рассеяния. Воэникаут пороговые условия, когда некоторые массовые параметры стремятся к нулу. Покаэывается, что дляππ рассеяния необходима граница, подобная (но отчасти слабее, чем) условиу Адлера, для того чтобы иэбезатя опаснои массовои (инфракраснои) сингулярности. Другои аргумент, которыи сушественно исполяэует псевдоскалярнуу природу ииона и несколяко оченя правдоподобных динамических предполозении, приводит к более силянои границе, а такзе к воэмозности обобшения на случаи обших пионных амплитуд. В эаклучение мы обсуздаем нащи реэулятаты, а тазе воэмозностя интерпретации спонтанно нарущенных симметрии иэ обшихS-матричных принципов.

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Author notes

  1. C. Rosenzweig

    Present address: Department of Physics, University of California, Berkeley, Cal., USA

  2. G. Veneziano

    Present address: the Weizmann Institute of Science, Rehovot, Israel

Authors and Affiliations

  1. Laboratory of Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, Mass.

    C. Rosenzweig & G. Veneziano

  2. Department of Physics, Harvard University, USA

    C. Rosenzweig

  3. Theory Division, CERN, Geneva, Switzerland

    G. Veneziano

Authors
  1. C. Rosenzweig
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  2. G. Veneziano
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Additional information

This work was supported in part through funds provided by the Atomic Energy Commission under Contract AT(11-1)3069.

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Rosenzweig, C., Veneziano, G. Unitarity sum rules and soft-pion amplitudes. Nuov Cim A 12, 409–424 (1972). https://doi.org/10.1007/BF02729554

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