Il Nuovo Cimento A (1965-1970)

, Volume 61, Issue 1, pp 105–113 | Cite as

General distribution of hadron transverse-momentum Gaussian cross-sections that are asymptotic exponentials

  • M. M. Nieto


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) x2] with a distribution functionG(m) exp [−g(m)] will yield an asymptotic exponential inx ifg(m)=K2/f(m). Experimental and theoretical implications are discussed.


Transverse Momentum Quark Model Gaussian Width Naam Elastic Data 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Овщее распределение гауссовских дифференциальных сечений по поперечному импулясу адроноб, имеющих экспоненциальную асимптотику


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)x2] с функцией распределенияG(m)·exp [−g(m)] дает экспоненциальную асимптотику поx, еслиg(m)=K2/f(m). Обсуждаются экспериментальные и теоретические следствия.


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)x2] con una funzione di distribuzioneG(m) exp [−g(m)] fornisce un esponenziale asintotico inx seg(m)=K2/f(m). Si discutono le implicazioni sperimentali e teoriche.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. (1).
    Aachen-Berlin-CERN Collaboration:Phys. Lett.,19, 608 (1965).CrossRefGoogle Scholar
  2. (2).
    G. Cocconi:Nuovo Cimento,57 A, 837 (1968).ADSCrossRefGoogle Scholar
  3. (3).
    G. Cocconi, J. Koester andD. H. Perkins: UCRL-10022 (1961).Google Scholar
  4. (4).
    A. D. Krisch:Phys. Rev. Lett.,19, 1149 (1967).ADSCrossRefGoogle Scholar
  5. (5).
    J. Orear:Phys. Rev. Lett.,12, 112 (1964);Phys. Lett.,13, 190 (1964).ADSCrossRefGoogle Scholar
  6. (6).
    F. Cerulus andA. Martin:Phys. Lett.,8, 80 (1964).ADSMathSciNetCrossRefGoogle Scholar
  7. (7).
    H. Fleming, A. Giovannini andE. Predazzi:Nuovo Cimento,56 A, 1131 (1968).ADSCrossRefGoogle Scholar
  8. (8).
    Aachen-Berlin-CERN Collaboration andAachen-Berlin-CERN-London (LC)-Vienna Collaboration:Phys. Lett.,27 B, 336 (1968).Google Scholar
  9. (9).
    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.Google Scholar
  10. (10).
    T. T. Chou andC. N. Yang:Phys. Rev.,170, 1591 (1968).ADSCrossRefGoogle Scholar
  11. (11).
    N. T. Dean:Nucl. Phys., B7, 311 (1968).ADSCrossRefGoogle Scholar
  12. (13).
    I. S. Gradsteyn andI. M. Ryzhik:Table of Integrals, Series and Products (New York, 1965).Google Scholar
  13. (14).
    A. Erdelyi:Asymptotic Expansions (New York, 1956).Google Scholar
  14. (15).
    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.Google Scholar
  15. (16).
    L. Van Hove: CERN report Ref. TH. 917, lecture delivered at theInternational Symposium on Contemporary Physics, Trieste, June, 1968.Google Scholar

Copyright information

© Società Italiana di Fisica 1969

Authors and Affiliations

  • M. M. Nieto
    • 1
  1. 1.The Niels Bohr InstituteUniversity of CopenhagenCopenhagen

Personalised recommendations