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Application of the on-mass-shell current algebra to the {ie153-1} form factorform factor

Применение алгебры токов на массовой поверхности к {ie153-2} форм-факторуформ-фактору

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Il Nuovo Cimento A (1965-1970)

Summary

We wish to evaluate the {ie153-3} decay amplitudes with a current algebra formalism while keeping the pions on the mass shell. This calculation is done using a technique described previously, in which the axial vector currents are modified and the equal-time commutation relations of the new currents verified. As a result of using these new currents, and for not needing to extrapolate the pion mass, the reduction formula contains some terms which must be evaluated by summing over sets of the intermediate states. In this application we note that dominating intermediate states are the π, K*, A1, ℋ mesons, and the two-particle systems (K*K) and (ℋK). Using the known data for the π, K, K* and A1 mesons we find a surprising sensitivity of the ratio of the decay form factors,i.e. ξ(0) ≡f −(0)/f +(0), to the change of the ℋ mass, width and decay constant. Within the expected ranges of these parameters, values ofξ(0) ranging from −0.1 to −0.85 can be obtained by the present treatment.

Riassunto

Si vogliono calcolare le ampiezze del decadimento {ie172-1} nell’ambito del un formalismo dell’algebra delle correnti mantenendo i pioni sullo strato della massa. Si esegue il calcolo con una tecnica prededentemente descritta, in cui si modificano le correnti vettoriali assiali e si verificano le relazioni di commutazione per tempi uguali delle nuove correnti. Per effetto dell’uso di queste nuove correnti e per non dover estrapolare la massa dei pioni, la formula di riduzione contiene alcuni termini che si devono calcolare sommando su insiemi di stati intermedi. In questa applicazione si nota che i mesoni π, K*, A1, ℋ e i sistemi di due particelle (K*K) e (ℋK) sono gli stati intermedi predominanti. Facento uso dei dati noti relativi ai mesoni π, K, K* e A1 si riscontra una sensibilità sorprendente del rapporto dei fattori di forma del decadimento, cioèξ(0) ≡ ≡f −(0)/f +(0), ai cambiamenti della massa, ampiezza e della costante di decadimento del ℋ. Nei limiti previsti per i valori di questi parametri, col presente procedimento si possono ottenere dei valori diξ(0) che vanno da −0.1 e −0.85.

Реэюме

Предлагается вычисление амплитуд Kl3 распада в рамках формалиэма алгебры токов, причем пионы находятся на массовой поверхности. При вычислении испольэуется ранее раэвитая техника, в которой модифицированы аксиальные векторные токи и проверены равновременные коммутационные соотнощения для новых токов. В реэультате испольэования зтих новых токов и чтобы не зкстраполировать пионную массу, формула приведения содержит некоторые члены, которые должны быть оценены с помошью суммирования системы промежуточных состояний. Мы отмечаем, что доминируюшие промежуточные состояния представляют π, K*, A1, ℋ меэоны и двухчастичные системы (K*K) и (ℋK). Испольэуя иэвестные данные для π, K, K* и A1 меэонов, мы получаем пораэительную чувствительность отнощения форм-факторов распадов, т.е.ξ(0) ≡ f−(0)/f+(0), к иэменениям ℋ массы, щирины и постоянной распада. В настояшем подходе, в предполагаемых областях для зтих параметров, эначения величиныξ(0) могут быть получены в области от −0.1 до −0.85.

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References

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Author notes

  1. A. A. Golestaneh

    Present address: Department of Physics and Astronomy, Mount Union College, Alliance, O. Summer Visitor at the University of Maryland, USA

Authors and Affiliations

  1. The Center for Particle Theory, Department of Physics, The University of Texas, Austin, Tex

    A. A. Golestaneh

  2. Center for Theoretical Physics, Department of Physics and Astronomy, University of Maryland, College Park, Md

    A. A. Golestaneh

  3. Department of Physics, College of William and Mary, Williamsburg, Va

    C. E. Carlson

Authors
  1. A. A. Golestaneh
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  2. C. E. Carlson
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Additional information

Supported in part by the Atomic Energy Commission under Contract No. AT(40-1)3992.

Supported in part by the National Science Foundation under Grant No. NSF GU 2061.

Supported in part by the National Science Foundation.

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Golestaneh, A.A., Carlson, C.E. Application of the on-mass-shell current algebra to the {ie153-1} form factorform factor. Nuov Cim A 23, 153–172 (1974). https://doi.org/10.1007/BF02748299

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