Summary
An adaptation of the multispinor formalism for evaluating duality diagrams is applied to the scattering of mesons\((6, \bar 6)\) from baryons (56, 1). The prescription automatically provides the «correct»D/F ratios and relative magnitudes of helicity flip/no flip amplitudes at the particle poles, and reproduces Reggeized supermultiplet predictions in the asymptotic region. However, the resonance structure is highly unphysical and consequently the low-energy predictions are very poor.
Riassunto
Si applica un adattamento del formalismo multispinoriale per la valutazione dei diagrammi di dualità allo scattering di mesoni\((6, \bar 6)\) su barioni (56, 1). Le ipotesi forniscono automaticamente i «corretti» rapportiD/F e i moduli relativi delle ampiezze con o senza flip di elicità nei poli delle particelle, e riproducono le previsioni di supermultipletto reggeizzato nella regione asintotica. D’altra parte la struttura della risonanza è altamente non fisica e di conseguenza le previsioni a bassa energia sono scarse.
Резюме
При рассеянии мезонов\((6, \bar 6)\) барионами (56, 1) используется адаптация формализма высших спиноров для вычисления дуальных диаграмм. Это описание автоматически обеспечивает «правильные»D/F отношения и относительные величины для амплитуд с переворачиванием четности к амплитудам без переворачивания четности в полюсах частиц, и воспроизводит реджеизованные супермультиплетные предсказания в асимптотической области. Однако, резонансная структура является очень нефизичной и, следовательно, предсказания при низких энергиях являются очень плохими.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R. Delbourgo andP. Rotelli:Phys. Lett., to be published.
H. Harari:Phys. Rev. Lett.,22, 562 (1969);J. L. Rosner:Phys. Rev. Lett.,22, 689 (1969).
For more conventional Veneziano models ofπ N scattering seeK. Igi:Phys. Lett.,28 B, 330 (1968);S. K. Bose andK. C. Gupta: University of Notre Dame preprint;J. Namyslowski andM. Swiecki: Polish Institute of Nuclear Research preprint;C. Lovelace: CERN preprint TH. 1047 (25th June 1969);A. W. Hendry, S. T. Jones andH. W. Wyld jr.: University of Illinois preprint.
In the case of meson-meson scattering, exchange degeneracy and charge conjugation invariance are alone sufficient to determine theSU 3 structure except for the octet/singlet ratio.
The Pomeron contribution to elastic amplitudes is, as always, outside the scope of duality but must necessarily appear in any reasonable unitarization procedure.
This is a well-known difficulty for supermultiplet schemes but can be circumvented by using momentum spurions, see, for example,F. Hussain andP. Rotelli:Phys. Rev.,142, 1013 (1966).
The vertices used both for isospin 3/2(Δ) and 1/2N are\(g_{\delta or \gamma } \frac{{(p_2 )_\lambda }}{M}\overline {\mathcal{N}_\lambda } (q)(1 or \gamma _5 )\mathcal{N}(p_2 )for J^P = \tfrac{3}{2}^ + or\tfrac{3}{2}^ - ,\), whereM is the mass of the spin-3/2 particle, and projection operator\(\left[ { - g_{\mu \nu } + \frac{1}{3}\gamma _\mu \gamma _\nu + \frac{1}{{3M}}(q_\mu \gamma _\nu - \gamma _\mu q_\nu ) + \frac{2}{{3M^2 }}q_\mu q_\nu } \right](\gamma \cdot q + M)\).
By using «physical» masses (in GeV/c2)m=0.94, μ=0.14, Δ=1.24,m ρ=0.76 and αψ(0)=0.18, αψ(0)=0.5, α′=0.9 (GeV/c)−2 we find, proceeding as in the text, (G M /G E )t=m 2ρ ≃32/3,β ψψ=−2.2 (GeV/c2)−4,g 2ρ =14.0,\(a_{SL}^{\tfrac{3}{2}} = 4a_{SL}^{\tfrac{1}{2}} = - 0.044\mu ^{ - 1} \).β ψψ ≃30.0 (GeV/c2)−4 again producing\(\mathcal{N}_\gamma \Delta _\gamma \mathcal{N}_\delta \) ghosts\(g_\gamma ^2 (\Delta ) \simeq - 54, g_\delta ^2 (\mathcal{N}) \simeq - 266\) and\(g_\gamma ^2 (\mathcal{N}) \simeq - 2.660\).
R. Delbourgo andA. Salam:Phys. Lett.,28 B, 497 (1968) andPhys. Rev. (to be published), which is in the nature of a review paper. The original idea of supermultiplet Reggeization was conceived byA. Salam andJ. Strathdee:Phys. Rev. Lett.,19, 339 (1967).
Author information
Authors and Affiliations
Additional information
To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.
The research reported in this document has been sponsored in part by the Air Force Office of Scientific Research OAR through the European Office of Aerospace Research, United State Air Force.
Traduzione a cura della Redazione.
Переведено редакцией.
Rights and permissions
About this article
Cite this article
Delbourgo, R., Rotelli, P. Veneziano model for the scattering of meson and baryon supermultiplets. Nuovo Cimento A (1965-1970) 69, 412–418 (1970). https://doi.org/10.1007/BF02726481
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02726481