HREPHAH 0H3HKA, 2004, moM 67, № 1, c. 4-12
VERY HIGH MULTIPLICITY PHYSICS
ON THE STATUS OF VERY HIGH MULTIPLICITY PHYSICS
© 2004 A. N. Sissakian*
Joint Institute for Nuclear Research, Dubna, Russia Received April 30, 2003
The paper contains the description of the main trends in the very high multiplicity physics. The incident energy dissipation into the secondaries is considered as the thermalization phenomenon. The experimental fact that the particle production process is stopped at such an early stage that the mean multiplicity is nothing but the logarithm of incident energy. This phenomenon is considered as the indication of the absence of complete thermalization in the mostly probable inelastic processes. The quantitative definition of thermalization phenomenon is offered and the very high multiplicity domain where the thermalization must occur is discussed. The physical consequences and model predictions of the thermalization effect are considered. The short review of the last publications on the very high multiplicity physics is also offered.
1. INTRODUCTION
The interest in the very high multiplicity (VHM) hadron processes becomes so many-sided that it is time to give a general description of the situation in this field. The trends can be divided into the three sectors. They are pure theoretical, experimental, and intermediate where the theoretical efforts are directed to the VHM experiment.
The paper is based mainly on the talks presented at the VHM Physics Workshops held in Dubna during 2000—2002 years [1]. It must be mentioned from the very beginning that there is not any experimental information concerning VHM high energy hadron reactions till now. Moreover, there are not either theory predictions for such processes even on the model level. For this reasons the spectrum of efforts presented in [1] is wide.
We would like to start from the well known experimental fact that the high energy hadron collisions are, for the most part, inelastic, see Fig. 1, where the experimental value of total and elastic cross sections are shown.
Having the multiparticle state the idea to introduce thermodynamical methods for hadron interactions description seems fruitful. It is important to notice here that the thermalization means the possibility to use the equilibrium thermodynamics phenomenology. Actually one must be careful with the above mentioned idea. The reason why this is not trivial will be the main subject of the discussion.
Attempts to introduce the thermodynamical notions into the multiple production physics have a long history. The first so-called "thermodynamical
E-mail: sisakian@jinr.ru
model" was offered by Fermi and Landau in 50th of the preceding century [2, 3]. It was assumed that particles production may be considered as the process of cooling of the incident high-temperature state. The reason of cooling is a tendency to equilibrium with the environment. Indeed, the considered process takes place in the "zero-temperature" vacuum and, therefore, the results of cooling should be the state with zero-momentum particles. In this case the hadron mean multiplicity would be approximately equal to the incident total energy and, therefore, the multiplicity would have culminated its maximal value nmax = t/s/m, where y/s is the total CM energy and m ~ 0.2 GeV is the characteristic hadron mass.
But we know that the mean hadron multiplicity is only a logarithm or the second power of the logarithm of incident total energy, see Fig. 2, where the best fit of the power dependence, n(s) ~ y/s, is shown for comparison.
Therefore, something prevents the dissipation of the incident energy into the produced particle masses and, for this reason, the thermalization does not taken place. Here the term "thermalization" means the uniform distribution of perturbation over all degrees of freedom. At the same time, fluctuations must have the Gaussian character.
In otherwords, we would like to offerfor discussion the most important question of hadron dynamics from our point of view: why is the process of incident energy dissipation stopped at such an early stage that the mean multiplicity is comparably small and, for this reason, the complete thermalization does not occur?
a, mb
102
101
Total
Elastic
fS I ^ f+ ! ?
10
1-1
101
103
105
107 p, GeV/c
1.9 2
101
102
Js, GeV
103
104
Fig. 1. Total cross section. It is remarkable that atot is approximately constant in the interval of 10—100 GeV. The Froissart constrain: atot < ln2 s.
1.1. Role of Symmetry Constrains
We know, at least qualitatively, the answer to this question: the reason why the mean hadron multiplicity is much smaller than nmax is hidden in the symmetry constrains. Namely, one may hope that this is an effect of underlying non-Abelian gauge symmetry recorded in the Yang—Mills field theory.
So, the purpose of the present paper is to discuss the most intriguing question of the hadron physics: the dynamical consequence of the non-Abelian gauge symmetry of Yang—Mills field theory. One of the known consequences of this symmetry is the colour charge confinement. The other one is the incomplete thermalization and, as a result, smallness of the total hadron multiplicity.
In the most inelastic hadron processes the ther-malization is not produced and it is impossible to use the methods of thermodynamics for them. But, it can be proved that at the VHM the final state is completely thermalized. So, we would like to provide for the condition where the Fermi—Landau model works. It is evident that such condition is realized in Nature extremely rarely.
This also means that in the VHM region one may use the "rough" thermodynamical parameters, the "temperature", "chemical potential", etc., for the complete description of the system. For instance, in this case one may completely describe the energy
distribution of the system knowing only the mean energy of secondaries [4, 5].
Therefore, the confinement forces, as the symmetry constrains, should not act in the VHM region. This conclusion is crucial in our further considerations since considerably simplifies the multiple production picture.
It is interesting to note that, on the other hand, the system of colour charges must be considered as the plasma state in the case of absence of confinement forces.
Moreover, the thermalized state is calm. This means that the kinetic forces are not important in comparison with the potential ones. This situation is the best to observe the collective phenomena.
1.2. References
The phenomenology of the VHM events was formulated in the papers published in [6]. It includes two basic ideas. The first one gives the classification of asymptotics over multiplicity and the physical interpretation of the classes. The offered interpretation excludes from consideration the final-state interactions, for instance, the Bose—Einstein correlation [7]. The papers [8, 9] fill this deficiency. It was shown [9] that the final-state interaction can cardinally change the multiplicity distribution tail. The experimental
HflEPHÄH OM3MKÄ TOM 67 № 1 2004
Fig. 2. Mean multiplicity. The mean multiplicity in QCD jet n(s)j and in the e+e annihilation processes is relatively high: \nfi(s)j ~ Vln s.
investigation of this prediction will be performed during the experiment at U-70 (Protvino), see [10]. We would also stress the efforts toward the experiment, published in [11].
An idea was offered [12] that the measurements in the VHM region may be performed "roughly", see also [13]. For instance, it is quite possible to have the multiplicity with some, but definite, error. One may also generalize the inclusive approach, combining particles into the groups and considering the group as a "particle", and so on. The effectiveness of such formulation of the experimental programme was shown in [14].
The paper [4] contains a qualitative feature of the VHM physics. The main question is: how much confidence may predictions of the perturbative QCD and existing multiperipheral models in the VHM region have. We have found that pQCD can not be used even if the VHM production process is hard. The experimental investigation of the range of validity of pQCD predictions has been performed
in [15]. The point is that it is hard to use the leading logarithm approximation (LLA) ideology [16] in the VHM region. That is why a new perturbation theory has been built [17-20].
One can hope that the VHM domain is much "simpler" from theoretical point of view than the traditional domain of n ~ n(s) [4]. Nevertheless, the attempts to find new characteristics of inelastic collisions are extremely important. The "wavelet" analysis [21] presents the corresponding example.
2. DEFINITION OF THE VHM REGION
It is natural that just the mean multiplicity defines the scale of multiplicities. Then, generally, we wish to consider the processes with multiplicity
n ^ n(s),
where ns is the mean multiplicity. The VHM domain can be more specified while considering the details of production processes.
HflEPHAH OH3HKA tom 67 № 1 2004
(n)P(n)
100
rs.
10
-2
10
-4
10
-6
10
-8
\
A
B
0
z = n/(n)
Fig. 3. Multiplicity distribution in terms of KNO variables. A — the domain of miltiperipheral models, B — the deep asymptotics over multiplicity, C — the very high multiplicity domain.
One may also introduce the inelasticity coefficient
E 6max
E 1
where E — the total energy in the CM frame, emax — the energy of the fastest particle in the same frame. Then, VHM events mean
1 -
E
<1.
M<n)
II
III
So, the produced particles momentum would be comparatively small.
At the same time, we would like to exclude the influence of the phase space boundaries. For this reason, we would assume that the multiplicity can not be too large:
n << nmax = E/m, m & 0.2 GeV.
From the experimental point of view VHM domain includes extremely rare processes, see Fig. 3. For this reason the B range of multiplicity in Fig. 3 seems to be not atta
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