Log-normal and Negative Binomial Distributions of DONUT Data

Year 2022, , 181 - 184, 30.06.2021

Çağın Kamışcıoğlu

https://doi.org/10.18466/cbayarfbe.986699

Abstract

There are several parametric models to describe the charged particle multiplicity distributions in literature. Among them, log-normal distribution and negative binomial distribution are the most well-known parametric models. In this study, negative binomial and log-normal distributions are compared and tested in neutrino interactions produced in DONUT experiment. This analysis was carried out using the real experimental results of the DONUT Collaboration. The results of the analysis show that the neutrino data, reported by DONUT collaboration, is well described by negative binomial and log-normal distribution. In terms of fit parameters, the χ/ndf value of the both distribution NBD and LND are close to unity but log-normal distribution data slightly better than negative binomial distribution.

Keywords

Negative binomial, log-normal, multiplicity

References

• 1. Ansorge RE., Åsman B., Burow L., Carlson P., DeWolf RS. et al, 1989. Charged Particle Multiplicity Distributions at 200-GeV and 900-GeV Center-Of-Mass Energy Z. Phys. C.; 43, 357. doi: 10.1007/BF01506531.
• 2. Berger Ch., Lackas W., Raupach F., Wagner W., Alexander G. et al., 1978. A study of jets in electron positron annihilation into hadrons in the energy range 3.1 to 9.5 GeV (PLUTOColl.) Phys. Lett. B; 78,176. doi:10.1016/0370-2693(78)90377-5.
• 3. Brandelik RW, Braunschweig K, Gather V, Kadansky K, Lübelsmeyer et al, 1980. (TASSOColl.) Rapid growth of charged particle multiplicity in high energy e+e− annihilations. Physics Letters B; 89 (3-4): 418-422. doi:10.1016/0370- 2693(80)90156-2.
• 4. Allen P, Blietschau J, Grassler H, Lanske D, Schulte R, et al, 1981. Multiplicity distributions in neutrino-hydrogen interactions. Nuclear Physics B; 181 (3): 385-402. doi:10.1016/0550-3213(81)90532-0.
• 5. Kayis-Topaksu A, Önengüt G, Dantzig van R, Jong de M, Oldeman RGC et al., 2007. (CHORUS Coll.) Charged Particle Multiplicities in Charged-Current Neutrino and Anti-Neutrino Nucleus Interactions. The European Physical Journal C; 51: 775-785. doi:10.1140/epjc/s10052-007-0366-8.
• 6. Agafonova N, Aleksandrov A, Anokhina A, AokiS, Ariga A et al., 2018. (OPERA Coll.). Study of Charged Hadron Multiplicities in Charged-Current Neutrino-Lead Interactions in the OPERA Dedector. The European Physical Journal C; 78: 62. doi:10.1140/epjc/s10052-017-5509-y
• 7. Kamışcıoğlu Ç., 2020. Study of KNO scaling in the emulsion based neutrino experiments. Turkish Journal of Physics;44:222-228. doi: 10.3906/fiz-1912-12.
• 8. Carius S. and Ingelman G., 1990. The log-normal distribution for cascade multiplicities in hadron collisions.Physics Letters B; 252:657. doi:10.1016/0370-2693(90)90500-6.
• 9. Huberman BA. 1988. The Ecology of Computation.North Holland (March 15, 1988).342 pages.
• 10. Szwed R.,Wrochna G., Wroblewski AK., 1991. New AMY and DELPHI multiplicity data and the lognormal distribution. Mod.Phys.Lett. A;6: 245-258. doi:10.1142/S021773239100021X.
• 11. Szwed R.,Wrochna G., Wroblewski AK., 1990. Genesis Of The Lognormal Multiplicity Distribution In The e+ e- Collisions And Other Stochastic Processes. Mod.Phys.Lett.A;5:1851-1870. doi:10.1142/S0217732390002110.
• 12. Decamp D., Deschizeaux B, Goy C, Lees JP, Minard N et al., 1991. Measurement of the charged particle multiplicity distribution in hadronic Z decays. Phys.Lett.B 273(1-2):181-192. doi:https://doi.org/10.1016/0370-2693(91)90575-B.
• 13. Jones GT, Jones RWL, Kennedy BW, Morrison DRO, Mobayyen MM. et al., 1992. Multiplicity distributions of charged hadrons in vp and charged current interactions. Zeitschrift für Physik C Particles and Fields. 54:45–54.doi:10.1007/BF01881707.
• 14. Buskulic D, Casper D, Bonis DI, Decamp D, Ghez P et al., 1995. Measurements of the charged particle multiplicity distribution in restricted rapidity intervals.Zeitschrift für Physik C Particles and Fields 69:15–25.doi:/10.1007/BF02907382.
• 15. Acton PD, Alexander G, Allison J, Allport PP, Anderson KJ et al., 1992. A Study of charged particle multiplicities in hadronic decays of the Z0. Z.Phys.C. 53:539-554. doi:10.1007/BF01559731.
• 16. MacKeown PK. and Wolfendale AW., 1966. The interpretation of the charge ratio of cosmic-ray muons. Proc. Phys. Soc. 553.doi:10.1088/0370-1328/89/3/312.
• 17.Alner, GJ, Alpgard K, Anderer P, Ansorge RE, Asman B. et al., 1985.Multiplicity distributions in different pseudorapidity intervals at a CMS energy of 540 GeV. Physics Letters B,160(1-3): 193-198.doi: 10.1016/0370-2693(85)91491-1.
• 18.Alner, GJ, Alpgard K, Anderer P, Ansorge RE, Asman B. et al., 1985.A new empirical regularity for multiplicity distributions in place of KNO scaling. Physics Letters B;160(1-3): 199-206.doi: 10.1016/0370-2693(85)91492-3.
• 19.Alner GJ, Ansorge RE, Asman B, Bockmann K, Booth CN et al., 1986. Scaling Violations in Multiplicity Distributions at 200-GeV and 900-GeV..Phys.Lett.B,167:476-480.doi:10.1016/0370-2693(86)91304-3.
• 20.Chew CK and Lim YK., 1985.Charged-particle multiplicity distributions in $e^+$$e^-$ annihilation and negative binomial distributions.Physics Letters B,163(1-4):257-260. doi:10.1016/0370-2693(85)90233-3.
• 21. Grosse-Oetringhaus JF, Reygers K., 2010.Charged-Particle Multiplicity in Proton-Proton Collisions. J.Phys.G, 37:083001.doi:10.1088/0954-3899/37/8/083001.
• 22. Arneodo M., 1987. Comparison of multiplicity distributions to the negative binomial distribution in muon-proton scattering. Zeitschrift für Physik C Particles and Fields; 35:335–345.doi:10.1007/BF01570769.
• 23. Kamışcıoğlu Ç., 2021. Study of KNO-G scaling in neutrino interactions. Modern Physics Letters A. 36(9):2150062.doi:10.1142/S0217732321500620.
• 24. Kodama K, Ushida N, Andreopoulos C, Saoulidou N, Tzanakos G et al., 2008. Final tau-neutrino results from the DONuT experiment. PHYSICAL REVIEW D;78:052002. doi: 10.1103/PhysRevD.78.052002.
• 25. Kodama K, Saoulidou N, Tzanakos G, Baller B, Lundber B et al., 2002. Detection and analysis of tau–neutrino interactions in DONUT emulsion target. Nuclear Instruments and Methods in Physics Research A. 493:45–66.doi:10.1016/S0168-9002(02)01555-3.
• 26. Kodama K, Ushida N, Andreopoulos C, Saoulidou N, Tzanakos G et al., 2001. Observation of tau neutrino interactions. Physics Letters B; 504: 218–224.doi:10.1016/S0370-2693(01)00307-0.
• 27. Kodama K, Andreopoulos C, Giokaris N, Saoulidou N, Tzanakos G et al., 2004. Identification of neutrino interactions using the DONUT spectrometer. Nuclear Instruments and Methods in Physics Research A.;516 :21–33.doi:10.1016/j.nima.2003.07.035.
• 28. Kittel W., De Wolf EA, 2005. Soft multihadron dynamics.World Scientific Press.
• 29. Szwed R.1986. Proceedings of the XVII international symposium on multiparticle dynamics.pp. 663.
• 30. Wroblewski AK, 1990..High-energy physics. Proceedings, 25th International Conference.pp. 125.Singapore.