1 On the quantum nature of a fireball created in ultrarelativistic nuclear collisions V. A. Kizka

2025-04-28 0 0 368.65KB 8 页 10玖币
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On the quantum nature of a fireball created in ultrarelativistic nuclear collisions
V. A. Kizka
V.N. Karazin Kharkiv National University, Kharkiv, 61022, Ukraine
Valeriy.Kizka@karazin.ua
Abstract. In the article, the fireball formed in the collision of relativistic nuclei is considered as a quantum
object. Based on this, an attempt is made to explain the difference in the measurements of hyperon yields in
the two experiments - NA49 and NA57. Using the basic principles of quantum mechanics, it was shown that
a fireball can have two quantum states - with and without ignited Quark-Gluon Plasma (QGP). With an
increase of the collision energy of heavy ions, the probability of QGP ignition increases. At the same time,
the probability of the formation of fireball without QGP ignition also remains nonzero even at nuclear
collision energies that are much higher than the threshold QGP formation energy, which may be erroneously
considered to be fixed and which is intensively sought in modern heavy ion accelerators. Thus, at SPS
energy of heavy ion collisions
NN
s
= 17.3 GeV, which is much higher than the assumed threshold energy
of QGP formation in the region around or slightly above of
NN
s
= 3 GeV, only half of the central collisions
of heavy ions bring to the formation of a fireball consisted of deconfined matter, the remaining half of the
collisions lead to the formation of a fireball from only hadronic matter.
Keywords: Hadronic matter, Quark-Gluon Plasma, heavy-ion collisions, hyperon production, mid-
rapidity multiplicity, nuclear spin.
1. Introduction
The difference between the two experiments - NA49 and NA57 in the strange (hyperon) sector [1]
has not yet been explained. This shows that we have missed something in understanding the nature
of the fireball formed in collisions of relativistic nuclei.
A possible methodological reason for the difference in measurements between the two experiments
is related to the different method for determining the centrality of the collision of two heavy ions
[1], [2]. But so far this issue remains unaddressed. Moving away from this methodological issue, I
consider another possible reason for the mismatch of measurements of NA49 and NA57.
The main goal of experiments on heavy ion collisions is to study the properties of Quark-Gluon
Plasma (QGP). One of the main signals about the formation of QGP is an increase in the yield of
hyperons, due to a decrease in the threshold energy for the formation of hyperons in comparison
with that in the collision of protons [3], [4]. The almost twofold difference in the hyperon yields of
the two experiments, NA49 and NA57, has not yet been discussed from the standpoint of the
fundamental properties of the fireball and the processes occurring in the target when relativistic
heavy ions pass through it.
The work is organized as follows. The second section shows the difference between measurements
in two experiments in which a quantum object is observed. Section III shows the application of the
formulas obtained in section II to the results of NA49 and NA57 in their strange sector. Section IV
discusses possible methods for testing the idea discussed in the article. Section V contains
conclusions.
2. Theoretical justification
Let us consider a quantum system described by wave function
(x), where x is a complete set of
variables from which the wave function depends. Let L be a physical quantity (observable) that
2
characterizes a specific property of a given quantum system. Let L has discrete spectra of
eigenvalues La, Lb and them correspond complete set of eigenfunctions
a(x) and
b(x),
respectively. Then we can write
(x)=a·
a(x)+b·
b(x), where a and b are an amplitudes of partial
states
a(x) and
b(x), respectively. The average value of the observable L, multiple repeated
measurements of which must be processed, is
ˆ(1)L x L x dx
   
Hermitian operator
ˆ
L
is matched to a physical value L. Average value L coincides with average
value Lexp, obtained by statistical processing of the results of experimental measurements. Further
we can write:
* * * * * 2 2
ˆ
( ) ( ) ( ) ( ) ( ) ( ) , (2)
a a a b b b a b
L x L x dx L a a x x dx L b b x x dx L a L b 
 
for normalized and orthogonal eigenfunctions
a(x) and
b(x), respectively. And a2 and b2 are a
square of modules of amplitudes of partial states
a(x) and
b(x), respectively.
Suppose the first experiment "1" measures L in an acceptance area
1 (kinematic and hardware
conditions of the experiment that limit the signal) from which the states
a and
b are visible
without possibility of their separation. The second experiment "2" make measurements in an
acceptance area
2 from which only the state
a is visible. We have the right to assume this if we
assume that each of the states is characterized by its own kinematic, space-time distribution of
particles emitted by the quantum system under study. (Due to the specifics of measurements on
particle detectors at nuclear colliders, I have jumped ahead here, considering a quantum system as a
fireball formed after a collision of nuclei). Suppose we do not know in advance which state exists at
the moment of measurement. Moreover, to make matters worse, we do not even suspect that the
system has two different quantum states.
The result of measurement of L by experiment "1": L1 = Laa2 + Lbb2. The result of measurement
of L by experiment "2": L2 = La, because experimental setting "2" only “sees” one state
a. But
we assumed that we know nothing about the two states of a quantum system. This means that
experiment "2" will measure the physical quantity L even if the system is in a state
b. In this case,
the measurement will give zero. When processing experimental data, we still take this measurement
into account to calculate the average value L2, what will underestimate the real value in the
“visible” state
a. Obviously, we must write the experimental value measured by experiment "2" in
the same way as for the first experiment, but with the second term nulled: L2 = Laa2.
Let us apply to our study a good model M1 that takes into account the existence of only the
b state
for a quantum system. The model will produce the following result for the observable L:
1
M
bb
LL
.
We put an approximate equal sign, because we use a good model that gives the calculation of the
observable very close to the real physical quantity. Difference between measurements of both
experiments:
1
22
12 . (3)
M
bb
L L L b L b 
Therefore, the probability of the state
b:
摘要：

1OnthequantumnatureofafireballcreatedinultrarelativisticnuclearcollisionsV.A.KizkaV.N.KarazinKharkivNationalUniversity,Kharkiv,61022,UkraineValeriy.Kizka@karazin.uaAbstract.Inthearticle,thefireballformedinthecollisionofrelativisticnucleiisconsideredasaquantumobject.Basedonthis,anattemptismadetoexpla...

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