Summary
Reviews of elastic and inelastic hadron scattering data are discussed; they indicate (dσ/dt) is universally in the form of a superposition of Gaussians (in a transverse-momentum variablex) that is an asymptotic exponential. After discussing two previous models, we use the method of asymptotic exapansions to show that a massm. superposition (dσ/dt) m -F(x) exp [−f(m) x 2] with a distribution functionG(m) exp [−g(m)] will yield an asymptotic exponential inx ifg(m)=K 2/f(m). Experimental and theoretical implications are discussed.
Riassunto
Si discutono le analisi dei dati dello scattering elastico ed inelastico degli adroni; essi indicano che dσ/dt è sempre nella forma di una sovrapposizione di gaussiane (nella variabilex della quantità di moto trasversale), e cioè nella forma di un esponenziale asintotico. Dopo aver discusso due modelli precedenti, si usa il metodo dello sviluppo asintotico per dimostrare che una sovrapposizione della massa (m) (dσ/dt)m =F(x) exp [−f(m)x 2] con una funzione di distribuzioneG(m) exp [−g(m)] fornisce un esponenziale asintotico inx seg(m)=K 2/f(m). Si discutono le implicazioni sperimentali e teoriche.
Резюме
Проводится обзор данных по упругому и неупругому рассеянию адронов; данные указывают, что dσ/dt в наиболее общем виде представляется как суперпозиция гауссовских членов (по величине поперечного импульсаx), асимптотически представляюшая экспоненту. После обсуждения двух предыдущих моделей, используется метод асимптотических разложений, чтобы показатя, что суперпозиция масс (m) (dσ/dt)m=F(x) exp [−f(m)x 2] с функцией распределенияG(m)·exp [−g(m)] дает экспоненциальную асимптотику поx, еслиg(m)=K 2/f(m). Обсуждаются экспериментальные и теоретические следствия.
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References
Aachen-Berlin-CERN Collaboration:Phys. Lett.,19, 608 (1965).
G. Cocconi:Nuovo Cimento,57 A, 837 (1968).
G. Cocconi, J. Koester andD. H. Perkins: UCRL-10022 (1961).
A. D. Krisch:Phys. Rev. Lett.,19, 1149 (1967).
J. Orear:Phys. Rev. Lett.,12, 112 (1964);Phys. Lett.,13, 190 (1964).
F. Cerulus andA. Martin:Phys. Lett.,8, 80 (1964).
H. Fleming, A. Giovannini andE. Predazzi:Nuovo Cimento,56 A, 1131 (1968).
Aachen-Berlin-CERN Collaboration andAachen-Berlin-CERN-London (LC)-Vienna Collaboration:Phys. Lett.,27 B, 336 (1968).
R. J. Glauber: inBoulder Lectures in Theoretical Physics, edited byW. E. Brittin et al., vol.1 (New York, 1959); inHigh Energy Physics and Nuclear Structure, edited byG. Alexander (Amsterdam, 1967), p. 311.
T. T. Chou andC. N. Yang:Phys. Rev.,170, 1591 (1968).
N. T. Dean:Nucl. Phys., B7, 311 (1968).
I. S. Gradsteyn andI. M. Ryzhik:Table of Integrals, Series and Products (New York, 1965).
A. Erdelyi:Asymptotic Expansions (New York, 1956).
In the general case, there will be more than one solution to (29). Then there will be a sum of terms in (28), one for each solution of (29). However, usually one term will dominate the others. See ref (14)A. Erdelyi:Asymptotic Expansions (New York, 1956). for a more detailed discussion.
L. Van Hove: CERN report Ref. TH. 917, lecture delivered at theInternational Symposium on Contemporary Physics, Trieste, June, 1968.
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Nieto, M.M. General distribution of hadron transverse-momentum Gaussian cross-sections that are asymptotic exponentials. Nuovo Cimento A (1965-1970) 61, 105–113 (1969). https://doi.org/10.1007/BF02760017
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DOI: https://doi.org/10.1007/BF02760017