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Hadron Multiplicity Distribution in Non Extensive Statistics

This study investigates the hadron multiplicity distribution in non-extensive statistics, specifically in the context of Tsallis entropy. It explores the deviation from Poisson distribution and analyzes the negative-binomial distribution generating function, as well as the integral representation for q > 1. The research also examines the integral representation of the partition function and applies it to relativistic ideal and Van der Waals gases. Furthermore, it discusses the Tsallis and Van der Waals corrections, as well as the deviations from Poisson distribution in the context of Bose-Einstein statistics and multiple fireballs.

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Hadron Multiplicity Distribution in Non Extensive Statistics

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  1. Hadron Multiplicity Distribution in Non Extensive Statistics Carlos E. Aguiar Takeshi Kodama UFRJ

  2. Non Extensive Statistics Tsallis entropy: Non extensivity: q-biased probabilities: q-biased averages:

  3. Tsallis Distribution Variational principle: Probability distribution: “Partition function”: Temperature:

  4. Momentum Distribution NA22 250GeV/c

  5. NA22 250GeV/c

  6. NA22 250GeV/c

  7. Multiplicity Distribution Deviation from Poisson

  8. Multiplicity Distribution Deviation from Poisson

  9. Multiplicity Distribution Deviation from Poisson

  10. Multiplicity Distribution Deviation from Poisson

  11. Multiplicity Distribution Deviation from Poisson

  12. Multiplicity Distribution Deviation from Poisson

  13. Negative-Binomial Distribution generating function: average and variance: k =  Poisson distribution k = - N binomial distribution

  14. Multiplicity Distributionin Tsallis Statistics

  15. Integral Representation for q > 1 maximum at x = 1 , width = [q(q-1)]1/2

  16. Integral Representationof the Partition Function

  17. Relativistic Ideal Gas No ideal Tsallis gas for q > 1 N particles:

  18. Relativistic Van der Waals Gas v = “hard-core volume” W(x) = Lambert function: Number of particles < V / v

  19. First Order Correctionsto Ideal Gas (q-1) << 1 and v/V << 1

  20. Tsallis and Van der Waals Corrections Deviation from Poisson:

  21. Tsallis - Van der Waals - Bose - Einstein Corrections Deviation from Poisson:

  22. Multiple Fireballs Nfb <n>  Nfb <n> k  Nfb k

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