## Abstract

This is a review of the elementary particles, quantum chromodynamics (QCD), and strong interactions in QCD theory via gluon exchange between quarks-antiquarks-producing mesons. Some mesons consist of an active gluon in addition to a quark-antiquark. They are called hybrid mesons. We also review the possible detection of the quark-gluon plasma, the consistuent of the universe until about 10−4 s after the Big Bang, via relativistic heavy ion collisions (RHIC) producing heavy quark hybrid mesons.

### Keywords

- quantum chromodynamics
- elementay particles
- quark-gluon plasma

## 1. Introduction

In this review of quantum chromodynamics (QCD), basic QCD particles and forces, the theory of hybrid mesons, the cosmological quantum chromodynamics phase transition (QCDPT), the quark-gluon plasma (QGP), theoretial studies of jet quenching due to the formation of the QGP, and the possible detection of the QGP via the production of mixed hybrid meson states produced by RHIC are reviewed.

First we review elementary particles, fermions and bosons, and standard QCD theory with the concept of color for the basic fermions (quarks) and bosons (gluons).

In the next section, the structure of standard mesons in terms of quarks and antiquarks is discussed.

Next we review the theory predicting that some mesons consisting of heavy charmonium quarks (

The interactions in quantum chromodynamics are strong, so perturbation theory does not work. Therefore, Feynman diagrams used for quantum electrodynamics cannot be used for quantum chromodynamics [1].

One nonperturbative QCD method involves lattice gauge theory. The articles “Twenty-first Century Lattice Gauge Theory: Results from the QCD Lagrangian” by Kronfelld [2] and “Lattice gauge theory in the microcanonical ensemble” by Calloway and Rahman [3] give a detailed description of how lattice gauge theory can calculate QCD interactions using computers.

Another nonperturbative theory, which is used in our review of mixed hybrid heavy quark mesons, is the method of QCD sum rules. This method, developed by Shifman et al. [4], does not require large computers.

It was the method of QCD sum rules that showed [5] that the

In our final section, we review the early universe QCDPT, with the production of the QGP.

In our second subsection, theoretial studies of jet quenching due to the formation of the QGP and experiments with Pb-Pb collisions verifying the theory are discussed.

In our final section, the possible production of the QGP via relativistic heavy ion collisions (RHIC) with the possible detection of the QGP by the production of mixed heavy quark hybrid mesons is reviewed. That is, we consider the collision of gold (Au) atomic nuclei with the energy of the Au nuclei large enough that after the Au-Au collision the temperature of the overlapping material is

The production of the mixed hybrid states

## 2. Elementary particles and basic forces

Among the elementary particles—fermions and bosons—fermions have quantum spin = 1/2.

The elementary femions are leptons and quarks. There are three generations of leptons: electron, muon, and tau, with electric charge −1, and their neutrinos with no electric charge. There are three generations of quarks: (u, d); (c, s); and (t, b). The (u, c, t) quarks have electric charge 2/3 while the (d, s, b) quarks have electric charge −1/3.

Bosons have quantum spin = 1: photon, quantum of the electromagnetic field; gluon, quantum of the strong field; and W and Z, weak field quanta, which we do not need.

### 2.1 Quantum chromodynamics (QCD): strong interaction field theory

Strong interactions are produced by quarks exchanging gluons, as illustrated in the figure below.

Color: Quarks have three colors.

Color is to the strong interaction as electric charge is to the electromagnetic interaction.

A quark and antiquark can form a gluon, which has color 8.

Note that particles with color, like gluon and quarks, cannot move freely in space. Particles that can move freely are baryons, like the proton and neutron, and mesons, which have no total color.

Note that in the figure above, the quark and antiquark have a different color, which is why the gluon has color = 8.

Antiparticles: All fermions have antiparticles. The antiparticle of the electron *q* has an antiquark

Standard mesons consist of a quark and an antiquark. A meson that is important for today’s discussion is the

As we discuss below, the first excited

## 3. QCD sum rules and mixed heavy quark hybrid meson states

The starting point of the method of QCD sum rules [4] is the correlator

with *Jc *is

where

That is

### 3.1 Experimental verification that the Ψ 2 S and ϒ 3 S are mixed hybrid heavy quark mesons

**–** 4 . The dashed curves are for the standard model.

Tests of the mixed hybrid theory for

From Figures 1 and 2 , the ratios of

while the experimental result [7] is

which shows that the mixed hybrid theory for the

compared to the experimental result of about 0.12–0.16 [9]. Therefore, the

## 4. The cosmological QCDPT and possible detection of the QGP

In this section we first review the temperature of the universe based on the time when the cosmolical quantum chromodynamic phase transition (QCDPT) occured. At that time, the universe consisted of the quark-gluon plasma (QGP). Then we discuss the creation of the QGP via RHIC Au-Au collisions with the possible detection of the QGP.

### 4.1 The quantum chromodynamic phase transition (QCDPT)

From astrophysical studies, it is known that the QCDPT occured at a time

A simpler form of Einstein’s equations are Friedman’s equations. From Friedman’s equations, one can find an approximation to T(t) [10].

From this, one finds, using

### 4.2 Theoretical studies and predictions for the detection of the QGP

Theoretial studies of jet quenching due to the formation of the QGP were carried out.

Theoretial studies of jet quenching due to the formation of the QGP in high-energy Pb-Pb collisions [11] help motivate experimental studies. The theoretical equation predicting jet quenching [11] is

where

Motivated in part by the theoretical study, the CMS collaboration carried out a study [12] of jet quencing via jet+Z boson correlations in Pb-Pb collisions. The results are shown in Figure 6 .

As can be seen from the figure and Eq. (9), the theoretical prediction of jet quenching due to the QGP has been verified by experiments.

### 4.3 Creation and detection of the QGP via RHIC

A main goal of the study of heavy quark state production in relativistic heavy ion collisions (RHIC) is the detection of the quark-gluon plasma [13]. The energy of the atomic nuclei must be large enough so just after the nuclei collide, the temperature is that of the universe about 10^{−5} s after the Big Bang, when the universe was too hot for protons or neutrons and consisted of quarks and gluons (the constituents of proton and nucleons)—the quark-gluon plasma (QGP).

As Figure 7 illustrates for Au-Au collisions with sufficient energy that the temperature

## 5. Conclusions

The results from comparison of the production of

There are tests of the creation of the QGP from jet quenching via experiments using Z-jet correlations, as well as other tests suggested by theoretical studies.

There are also possible tests of the creation and detection of the QGP by the production of

From this, one can conclude that the production of these states via RHIC with sufficient energy that part of the matter during the collision has reached a temperature

This would be an important result for particle theory as well as astrophysics.

## Acknowledgments

Leonard S. Kisslinger acknowledges support in part as a visitor at the Los Alamos National Laboratory,