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Prog. Theor. Phys. Vol. 98 No. 6 (1997) pp. 1289-1298
Analyses of Multiplicity Distributions by Means of the Modified Negative Binomial Distribution and Its KNO Scaling Function
Takeshi Osada,
Noriaki Nakajima,*
Minoru Biyajima**
and
Naomichi Suzuki***
Department of Physics, Tohoku University, Sendai 980-77
*Research Center for Nuclear Physics (RCNP), Osaka University, Ibaraki 567
**Department of Physics, Shinshu University, Matsumoto 390
***Matsusho Gakuen Junior College, Matsumoto 390-12
(Received July 9, 1997)
Abstract:
We analyze various data of multiplicity distributions by means of the
modified negative binomial distribution (MNBD) and its KNO
scaling function, since the MNBD explains the oscillating
behavior of the cumulant moment observed in
e+e- annihilations, h-h collisions and
e-p collisions.
In the present analyses,
we find that the MNBD (discrete distribution) describes the
data of charged particles in e+e- annihilations
much better than the negative binomial distribution (NBD).
To investigate stochastic properties of the MNBD,
we derive the KNO scaling function from the discrete distribution
by using a straightforward method and the Poisson transform.
This is a new KNO function expressed by the Laguerre polynomials.
In analyses of the data by using the KNO scaling function,
we find that the MNBD describes the data better than the gamma function.
Thus, it can be stated that
the MNBD is a useful formula, as is the NBD.
URL :
http://ptp.ipap.jp/link?PTP/98/1289/
DOI : 10.1143/PTP.98.1289
References:
- I. M. Dremin and V. A. Nechitailo, JETP Lett. 58 (1993), 881.
I. M. Dremin and R. Hwa, Phys. Rev. D49 (1994), 5805[APS].
I. M. Dremin, Phys. Lett. B341 (1994), 95.
-
N. Suzuki, M. Biyajima and N. Nakajima, Phys. Rev. D53 (1996), 3582[APS];
ibid. D54 (1996), 3653[APS].
-
N. Nakajima, M. Biyajima and N. Suzuki, Phys. Rev. D54 (1996), 4333[APS].
- P. V. Chliapnikov and O. G. Tchikilev, Phys. Lett. B242 (1990), 275.
- P. V. Chliapnikov, O. G. Tchikilev and V. A. Uvarov, Phys. Lett. B352 (1995), 461.
- O. G. Tchikilev, Phys. Lett. B382 (1996), 296; 388 (1996), 848.
- N. Suzuki, M. Biyajima and G. Wilk, Phys. Lett. B268 (1991), 447.
- M. Biyajima, N. Suzuki, G. Wilk and Z. Wlodarczyk, Phys. Lett. B386 (1996), 279.
-
HRS collaboration, M. Derrick et al., Phys. Rev. D34 (1986), 3304[APS].
- TASSO collaboration, W. Braunschweig et al., Z. Phys. C45 (1989), 193.
-
AMY collaboration, H. W. Zheng et al., Phys. Rev. D42 (1990), 737[APS].
- ALEPH collaboration, D. Decamp et al., Phys. Lett. B273 (1991), 181.
- ALEPH collaboration, D. Buskulic et al., Z. Phys. C69 (1995), 15.
- DELPHI collaboration, P. Abreu et al., Z. Phys. C52 (1991), 271.
- OPAL collaboration, P. D. Acton et al., Z. Phys. C53 (1992), 539.
- OPAL collaboration, P. D. Acton et al., CERN-PPE/96-47.
-
A. Firestone et al., Phys. Rev. D10 (1974), 2080[APS].
- E743 collaboration, R. Ammer et al., Phys. Lett. B178 (1986), 124.
-
ISR collaboration, A. Breakstone et al., Phys. Rev. D30 (1984), 528[APS].
-
UA5 collaboration, G. J. Alner et al., Phys. Rep. 154 (1987), 247[CrossRef].
UA5 collaboration, R. E. Ansorge et al., Z. Phys. C43 (1989), 357.
- H1 collaboration, S. Aid et al., DESY PREPRINT 96-160.
- M. Biyajima, Prog. Theor. Phys. 69 (1983), 966[PTP]; 70 (1983), 1468A.
- A. Giovannini, S. Lupia and R. Ugoccini, Phys. Lett. B374 (1996), 231.
F. Becattini, A. Giovannini and S. Lupia, Z. Phys. C72 (1996), 491.
- S. Saleh, Photoelectron Statistics (Springer-Verlag, Berlin, 1998).
- R. Szwed, G. Wrochna and A. K. Wróblewski, Mod. Phys. Lett. A6 (1991), 245.
