Review of Quantum Chromodynamics (QCD)

*Leonard S. Kisslinger*

## **Abstract**

This is a review of the elementary particles, quantum chromodynamics (QCD), and strong interactions in QCD theory via gluon exchange between quarksantiquarks-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�<sup>4</sup> 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 (Ψð Þ *nS* , n = 1, 2) and bottomonium quarks (ϒð Þ *mS* , m = 1, 2, 3, 4) are partially hybrids. Experiments test the theory.

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 Ψð Þ 2*S* charmonium quark meson and the ϒð Þ 3*S* bottomonium quark mesons are mixed hybrid states, while all the other Ψð Þ *nS* and ϒð Þ *mS* are standard charmonium and bottomonium meson states.

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

the figure below.

interaction.

antiquark *q*.

**85**

Color: Quarks have three colors.

*Review of Quantum Chromodynamics (QCD) DOI: http://dx.doi.org/10.5772/intechopen.91640*

mesons, which have no total color.

which is why the gluon has color = 8.

for today's discussion is the *J=*Ψð Þ 1*S* .

with an active gluon: ∣*ccg*ð Þ 2*S* >.

q (quark)

q (anti−quark)

Strong interactions are produced by quarks exchanging gluons, as illustrated in

g

gluon

(quantum of strong interaction)

color (8=octet)

∣ *J=*Ψð Þ 1*S* > ¼ ∣*cc*ð Þ 1*S* >*:* (1)

<sup>Π</sup>*<sup>A</sup>*ð Þ¼ j *<sup>x</sup>* h i *T J* ½ �j *<sup>A</sup>*ð Þ *<sup>x</sup> JA*ð Þ <sup>0</sup> , (2)

quark

g

quark

QCD (Quantum Chromodynamics): quark force via gluon exchange

STRONG FORCE g ~1~100 x e <sup>2</sup> <sup>2</sup>

Nonperturbative. Diagrams do not converge− single diagram no good

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

gluon

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

Note that in the figure above, the quark and antiquark have a different color,

Antiparticles: All fermions have antiparticles. The antiparticle of the electron *e*� is the positron *e*þ, and a photon can create a *e*�*e*<sup>þ</sup> pair. Similarly, each quark *q* has an

Standard mesons consist of a quark and an antiquark. A meson that is important

As we discuss below, the first excited *cc* state, the Ψð Þ 2*S* has a hybrid component

**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

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

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

*T* ≥*TQCDPT <sup>c</sup>* ≃150 MeV, where *TQCDPT <sup>c</sup>* is the critical temperature for the QCDPT. That matter with *T* ≥ *TQCDPT <sup>c</sup>* is QGP is discussed.

The production of the mixed hybrid states Ψð Þ 2*S* and ϒð Þ 3*S* via Au-Au collisions could detect the production of the QGP in the overlapping material. We conclude that the detection of Ψð Þ 2*S* and ϒð Þ 3*S* produced via RHIC could be a test for the creation of the early universe QGP.

## **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.

It was the method of QCD sum rules that showed [5] that the Ψð Þ 2*S* charmonium quark meson and the ϒð Þ 3*S* bottomonium quark mesons are mixed hybrid states, while all the other Ψð Þ *nS* and ϒð Þ *mS* are standard charmonium and bottomonium

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

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

In our final section, the possible production of the QGP via relativistic heavy ion

The production of the mixed hybrid states Ψð Þ 2*S* and ϒð Þ 3*S* via Au-Au collisions could detect the production of the QGP in the overlapping material. We conclude that the detection of Ψð Þ 2*S* and ϒð Þ 3*S* produced via RHIC could be a test for the

*<sup>c</sup>* is the critical temperature for the QCDPT.

u

d

c

s

t

b

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

*<sup>c</sup>* is QGP is discussed.

Among the elementary particles—fermions and bosons—fermions have

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

e

ν e

μ

νμ

τ

τ ν

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

Au-Au collision the temperature of the overlapping material is

*<sup>c</sup>* ≃150 MeV, where *TQCDPT*

**2. Elementary particles and basic forces**

Second Generation

First Generation

Third Generation

That matter with *T* ≥ *TQCDPT*

quantum spin = 1/2.

charge �1/3.

not need.

**84**

creation of the early universe QGP.

meson states.

*Accelerators and Colliders*

of the QGP.

discussed.

*T* ≥*TQCDPT*

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

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

QCD (Quantum Chromodynamics): quark force via gluon exchange STRONG FORCE

g ~1~100 x e <sup>2</sup> <sup>2</sup>

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 *e*� is the positron *e*þ, and a photon can create a *e*�*e*<sup>þ</sup> pair. Similarly, each quark *q* has an antiquark *q*.

Standard mesons consist of a quark and an antiquark. A meson that is important for today's discussion is the *J=*Ψð Þ 1*S* .

$$|f/\Psi(\mathfrak{L})>\rangle = |c\overline{c}(\mathfrak{L})>.\tag{1}$$

As we discuss below, the first excited *cc* state, the Ψð Þ 2*S* has a hybrid component with an active gluon: ∣*ccg*ð Þ 2*S* >.

## **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

$$\Pi^A(\mathbf{x}) = \langle |T[J\_A(\mathbf{x})J\_A(\mathbf{0})]| \rangle,\tag{2}$$

with ∣i the vacuum state and the current *JA*ð Þ *x* creates the states with quantum numbers A. For the charmonium states, *Jc* is

$$J\_c = fJ\_{c\tilde{c}} + \sqrt{\mathbf{1} - f^2}J\_{c\tilde{c}g},\tag{3}$$

y

Υ(2S)

Υ(3S)(hybrid)

y 0

−0.8 0.8

Υ(3S)

Υ(1S)

0 y

−0.8 0.8

ψ (2S)

ψ(2S)(hybrid)

0.035

d /dy σ

**Figure 3.**

**Figure 4.**

**87**

**Figure 2.**

(nb)

0.030

*dσ/dy for E = 200 GeV Cu-Cu collisions producing ϒ*ð Þ 1S *.*

0.0

1.0

d /dy(pb)

σ

*dσ/dy for Cu-Cu collisions producing ϒ*ð Þ 2S , *ϒ*ð Þ 3S *.*

2.0

−0.8

0.040

14.0

11.0

8.0

d /dy σ

(nb)

*Review of Quantum Chromodynamics (QCD) DOI: http://dx.doi.org/10.5772/intechopen.91640*

5.0

2.0

*dσ/dy for E = 200 GeV Cu-Cu collisions producing Ψ*ð Þ 2S *.*

0 0.8

where *Jcc* creates a normal charmonium state and *Jccg* creates a hybrid state with an active gluon. It was shown that *<sup>f</sup>* <sup>≃</sup> � ffiffi 2 <sup>p</sup> for the <sup>Ψ</sup>ð Þ <sup>2</sup>*<sup>S</sup>* and <sup>ϒ</sup>ð Þ <sup>3</sup>*<sup>S</sup>* and *<sup>f</sup>* <sup>≃</sup>1*:*0 for the other charmonium and bottomonium states [5]. Therefore,

$$\begin{aligned} |I/\Psi(\mathfrak{L}\mathfrak{S})> &\simeq |c\overline{c}(\mathfrak{L}\mathfrak{S})> \\ |\Psi(\mathfrak{L}\mathfrak{S})> &-\sqrt{2}|c\overline{c}(\mathfrak{L}\mathfrak{S})> +\sqrt{2}|c\overline{c}\mathfrak{g}(\mathfrak{L}\mathfrak{S})> \\ |\Upsilon(\mathfrak{S}\mathfrak{S})> &-\sqrt{2}|b\overline{b}(\mathfrak{S}\mathfrak{S})> +\sqrt{2}|b\overline{b}\overline{g}(\mathfrak{S}\mathfrak{S})>, \end{aligned} \tag{4}$$

That is *J=*Ψð Þ 1*S* is a standard charmonium meson and all of the ϒð Þ *nS* mesons are standard bottominium mesons except for *n* ¼ 3.

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

Ψ and ϒ production by Cu-Cu collisions for E = 200 GeV [6] are shown in **Figures 1–4**. The dashed curves are for the standard model.

Tests of the mixed hybrid theory for Ψð Þ 2*S* and ϒð Þ 3*S* states using ratios of cross sections for Cu-Cu collisions at E = 200 GeV: Since the absolute magnitude of dσ/dy for production of Ψð Þ 2*S* states via Cu-Cu collisions is not certain, due to uncertainty in the normalization of the states, the tests of the theory [6] were carried out using ratios of cross sections, which can be compared to experiments.

From **Figures 1** and **2**, the ratios of Ψð Þ 2*S* to *J=*Ψð Þ 1*S* for the standard model (st) and the mixed hybrid theory (hy) for A-A (including Cu-Cu) collisions are

**Figure 1.** *dσ/dy for E = 200 GeV Cu-Cu collisions producing* J*=Ψ.*

*Review of Quantum Chromodynamics (QCD) DOI: http://dx.doi.org/10.5772/intechopen.91640*

with ∣i the vacuum state and the current *JA*ð Þ *x* creates the states with quantum

q

where *Jcc* creates a normal charmonium state and *Jccg* creates a hybrid state with

2

<sup>p</sup> <sup>∣</sup>*cc*ð Þ <sup>1</sup>*<sup>S</sup>* <sup>&</sup>gt; <sup>þ</sup> ffiffi

<sup>p</sup> <sup>∣</sup>*bb*ð Þ <sup>3</sup>*<sup>S</sup>* <sup>&</sup>gt; <sup>þ</sup> ffiffi

That is *J=*Ψð Þ 1*S* is a standard charmonium meson and all of the ϒð Þ *nS* mesons are

**3.1 Experimental verification that the Ψ**ð Þ **2***S* **and ϒ**ð Þ **3***S* **are mixed hybrid heavy**

Ψ and ϒ production by Cu-Cu collisions for E = 200 GeV [6] are shown in

Tests of the mixed hybrid theory for Ψð Þ 2*S* and ϒð Þ 3*S* states using ratios of cross sections for Cu-Cu collisions at E = 200 GeV: Since the absolute magnitude of dσ/dy for production of Ψð Þ 2*S* states via Cu-Cu collisions is not certain, due to uncertainty in the normalization of the states, the tests of the theory [6] were carried out using ratios of cross sections, which can be compared to

From **Figures 1** and **2**, the ratios of Ψð Þ 2*S* to *J=*Ψð Þ 1*S* for the standard model (st) and the mixed hybrid theory (hy) for A-A (including Cu-Cu) collisions are

> 0 y

−0.8 0.8

J/ ψ

2 <sup>p</sup> <sup>∣</sup>*ccg*ð Þ <sup>2</sup>*<sup>S</sup>* <sup>&</sup>gt;

2 <sup>p</sup> <sup>∣</sup>*bbg*ð Þ <sup>3</sup>*<sup>S</sup>* <sup>&</sup>gt;,

ffiffiffiffiffiffiffiffiffiffiffiffiffi 1 � *f* 2

*Jccg* , (3)

(4)

<sup>p</sup> for the <sup>Ψ</sup>ð Þ <sup>2</sup>*<sup>S</sup>* and <sup>ϒ</sup>ð Þ <sup>3</sup>*<sup>S</sup>* and *<sup>f</sup>* <sup>≃</sup>1*:*0 for

*Jc* ¼ *f Jcc* þ

2

2

the other charmonium and bottomonium states [5]. Therefore,

∣ *J=*Ψð Þ 1*S* > ≃ ∣*cc*ð Þ 1*S* >

<sup>∣</sup>Ψð Þ <sup>2</sup>*<sup>S</sup>* <sup>&</sup>gt; <sup>≃</sup> � ffiffi

<sup>∣</sup>ϒð Þ <sup>3</sup>*<sup>S</sup>* <sup>&</sup>gt; <sup>≃</sup> � ffiffi

**Figures 1–4**. The dashed curves are for the standard model.

standard bottominium mesons except for *n* ¼ 3.

140.0

130.0

120.0

d /dy

σ

**Figure 1.**

**86**

 (nb)

110.0

100.0

*dσ/dy for E = 200 GeV Cu-Cu collisions producing* J*=Ψ.*

**quark mesons**

*Accelerators and Colliders*

experiments.

numbers A. For the charmonium states, *Jc* is

an active gluon. It was shown that *<sup>f</sup>* <sup>≃</sup> � ffiffi

**Figure 2.** *dσ/dy for E = 200 GeV Cu-Cu collisions producing Ψ*ð Þ 2S *.*

**Figure 3.** *dσ/dy for E = 200 GeV Cu-Cu collisions producing ϒ*ð Þ 1S *.*

**Figure 4.** *dσ/dy for Cu-Cu collisions producing ϒ*ð Þ 2S , *ϒ*ð Þ 3S *.*

$$\begin{aligned} \sigma(\Psi(\text{2S}))/\sigma(f/\Psi(\text{1S}))|\_{\text{st}-A-A} &\simeq 0.27\\ \sigma(\Psi(\text{2S}))/\sigma(f/\Psi(\text{1S}))|\_{\text{hy}-A-A} &\simeq 0.52 \pm 0.05, \end{aligned} \tag{5}$$

while the experimental result [7] is

$$
\sigma(\Psi(\mathsf{2S}))/\sigma(\mathsf{J}/\Psi(\mathsf{1S})\simeq\mathsf{0}.\mathsf{59},\tag{6}
$$

From this, one finds, using t <sup>≃</sup><sup>5</sup> � <sup>10</sup>�<sup>5</sup> s, at the time of the QCDPT the critical

bubbles of our universe nucleated within the QGP, as shown in **Figure 5**.

**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

Δ*QGP* ≃1 � *e*

where Δ*QGP* is the magnitude of the jet quenching and Θ*jet* and Θ*<sup>c</sup>* are the

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

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�<sup>5</sup> s after the Big Bang, when the universe was too hot for protons or neutrons and consisted of quarks and gluons (the constituents of

As **Figure 7** illustrates for Au-Au collisions with sufficient energy that the temperature T tð Þ≥150 MeV where the Au-Au nuclei merge, the emission of mixed

p−p

Pb−Pb

40 50 60 70 80 90 100 110

pz (GeV/c)

*x = (jet/Z) momentum vs. pz = the momentum of the Z boson for p-p and Pb-Pb collisions.*

As can be seen from the figure and Eq. (9), the theoretical prediction of jet

Theoretial studies of jet quenching due to the formation of the QGP in highenergy Pb-Pb collisions [11] help motivate experimental studies. The theoretical

�Θ*jet*

*<sup>c</sup>* <sup>≃</sup>150 MeV. During the time that *<sup>T</sup>* <sup>¼</sup> *<sup>T</sup>QCDPT*

<sup>Θ</sup>*<sup>c</sup>* , (9)

*c* ,

temperature for the QCDPT *TQCDPT*

*Review of Quantum Chromodynamics (QCD) DOI: http://dx.doi.org/10.5772/intechopen.91640*

equation predicting jet quenching [11] is

results are shown in **Figure 6**.

aperature of the jet and emitted gluons, respectively.

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

proton and nucleons)—the quark-gluon plasma (QGP).

1.1

1.0

0.9

x

**Figure 6.**

**89**

0.8

0.7

0.6

quenching due to the QGP has been verified by experiments.

carried out.

which shows that the mixed hybrid theory for the Ψð Þ 2*S* state is consistent with experiment, while the standard ∣*cc*ð Þ 2*S* > is not. From studies of heavy quark state production in p-p collisions, theoretical results for the nature of ϒð Þ 3*S* state found [8]

$$
\begin{aligned}
\sigma(\Upsilon(\text{3S}))/\sigma(\Upsilon(\text{1S})) & \simeq 0.04 \text{ standard} \\
\sigma(\Upsilon(\text{3S}))/\sigma(\Upsilon(\text{1S})) & \simeq 0.14\text{7} - 0.22 \text{ hybrid}
\end{aligned}
\tag{7}
$$

compared to the experimental result of about 0.12–0.16 [9]. Therefore, the ϒð Þ 3*S* state, as well as the Ψð Þ 2*S* state, has been shown to be a heavy quark mixed hybrid state.

## **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 <sup>t</sup>≃10�<sup>5</sup> � <sup>10</sup>�<sup>4</sup> s; one can estimate the temperature of the universe at time T(t) using the equations from Einstein's General Theory of Relativity.

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

$$T(t) \simeq \frac{1\text{ MeV}}{\sqrt{t(\text{in s})}} \cdot \tag{8}$$

**Figure 5.** *Hadron phase forming within the QGP during the QCDPT.*

*<sup>σ</sup>*ð Þ <sup>Ψ</sup>ð Þ <sup>2</sup>*<sup>S</sup> <sup>=</sup>σ*ð Þj *<sup>J</sup>=*Ψð Þ <sup>1</sup>*<sup>S</sup> st*�*A*�*<sup>A</sup>* <sup>≃</sup>0*:*<sup>27</sup>

which shows that the mixed hybrid theory for the Ψð Þ 2*S* state is consistent with experiment, while the standard ∣*cc*ð Þ 2*S* > is not. From studies of heavy quark state production in p-p collisions, theoretical results for the nature of ϒð Þ 3*S* state found [8]

*σ*ð Þ ϒð Þ 3*S =σ*ð Þ ϒð Þ 1*S* ≃0*:*04 *standard*

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

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

using the equations from Einstein's General Theory of Relativity.

Friedman's equations, one can find an approximation to T(t) [10].

QGP

*Hadron phase forming within the QGP during the QCDPT.*

Hadron Phase

compared to the experimental result of about 0.12–0.16 [9]. Therefore, the ϒð Þ 3*S* state, as well as the Ψð Þ 2*S* state, has been shown to be a heavy quark mixed hybrid state.

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

From astrophysical studies, it is known that the QCDPT occured at a time <sup>t</sup>≃10�<sup>5</sup> � <sup>10</sup>�<sup>4</sup> s; one can estimate the temperature of the universe at time T(t)

*T t*ð Þ<sup>≃</sup> <sup>1</sup> *MeV*

ffiffiffiffiffiffiffiffiffiffiffiffiffi

*<sup>t</sup>*ð Þ in <sup>s</sup> <sup>p</sup> *:* (8)

A simpler form of Einstein's equations are Friedman's equations. From

while the experimental result [7] is

*Accelerators and Colliders*

detection of the QGP.

**Figure 5.**

**88**

*<sup>σ</sup>*ð Þ <sup>Ψ</sup>ð Þ <sup>2</sup>*<sup>S</sup> <sup>=</sup>σ*ð Þj *<sup>J</sup>=*Ψð Þ <sup>1</sup>*<sup>S</sup> hy*�*A*�*<sup>A</sup>* <sup>≃</sup>0*:*<sup>52</sup> � <sup>0</sup>*:*05, (5)

*<sup>σ</sup>*ð Þ <sup>ϒ</sup>ð Þ <sup>3</sup>*<sup>S</sup> <sup>=</sup>σ*ð Þ <sup>ϒ</sup>ð Þ <sup>1</sup>*<sup>S</sup>* <sup>≃</sup>0*:*<sup>147</sup> � <sup>0</sup>*:*<sup>22</sup> *hybrid* (7)

*σ*ð Þ Ψð Þ 2*S =σ*ð*J=*Ψð Þ 1*S* ≃0*:*59, (6)

From this, one finds, using t <sup>≃</sup><sup>5</sup> � <sup>10</sup>�<sup>5</sup> s, at the time of the QCDPT the critical temperature for the QCDPT *TQCDPT <sup>c</sup>* <sup>≃</sup>150 MeV. During the time that *<sup>T</sup>* <sup>¼</sup> *<sup>T</sup>QCDPT c* , bubbles of our universe nucleated within the QGP, as shown in **Figure 5**.

## **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 highenergy Pb-Pb collisions [11] help motivate experimental studies. The theoretical equation predicting jet quenching [11] is

$$
\Delta\_{QGP} \simeq \mathbf{1} - \boldsymbol{\sigma}^{-\frac{\Theta\_{\rm jet}}{\Theta\_{\rm t}}},\tag{9}
$$

where Δ*QGP* is the magnitude of the jet quenching and Θ*jet* and Θ*<sup>c</sup>* are the aperature of the jet and emitted gluons, respectively.

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�<sup>5</sup> 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 T tð Þ≥150 MeV where the Au-Au nuclei merge, the emission of mixed

**Figure 6.** *x = (jet/Z) momentum vs. pz = the momentum of the Z boson for p-p and Pb-Pb collisions.*

**Figure 7.** *Au-Au collisions producing Ψ*ð Þ 2S *and ϒ*ð Þ 3S *from the QGP.*

hybrid mesons, the Ψð Þ 2*S* and ϒð Þ 3*S* as discussed above, with active gluons, could be a signal of the formation of the QGP.

## **5. Conclusions**

The results from comparison of the production of Ψð Þ 2*S* and ϒð Þ 3*S* differential cross sections with experiment confirm the theoretical prediction that the Ψð Þ 2*S* and ϒð Þ 3*S* states are mixed hybrid states.

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 Ψð Þ 2*S* and ϒð Þ 3*S* via relativistic heavy ion collisions as shown in **Figure 7**.

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 *T* ≥*TQCDPT <sup>c</sup>* ≃ 150 MeV, the temperature when the universe was a dense plasma (the QGP), can be a test of the creation of the quark-gluon plasma.

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

## **Acknowledgements**

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

**Author details**

**91**

Leonard S. Kisslinger

Department of Physics, Carnegie Mellon University, Pittsburgh, PA, USA

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

\*Address all correspondence to: kissling@andrew.cmu.edu

provided the original work is properly cited.

*Review of Quantum Chromodynamics (QCD) DOI: http://dx.doi.org/10.5772/intechopen.91640* *Review of Quantum Chromodynamics (QCD) DOI: http://dx.doi.org/10.5772/intechopen.91640*

## **Author details**

hybrid mesons, the Ψð Þ 2*S* and ϒð Þ 3*S* as discussed above, with active gluons, could

Au Au

Υ(3S)

Quark Gluon Plasma

The results from comparison of the production of Ψð Þ 2*S* and ϒð Þ 3*S* differential cross sections with experiment confirm the theoretical prediction that the Ψð Þ 2*S*

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 Ψð Þ 2*S* and ϒð Þ 3*S* via relativistic heavy ion collisions as shown in

From this, one can conclude that the production of these states via RHIC with

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

dense plasma (the QGP), can be a test of the creation of the quark-gluon plasma. This would be an important result for particle theory as well as astrophysics.

*<sup>c</sup>* ≃ 150 MeV, the temperature when the universe was a

sufficient energy that part of the matter during the collision has reached

be a signal of the formation of the QGP.

*Au-Au collisions producing Ψ*ð Þ 2S *and ϒ*ð Þ 3S *from the QGP.*

and ϒð Þ 3*S* states are mixed hybrid states.

**5. Conclusions**

**Figure 7.**

Ψ(2S)

*Accelerators and Colliders*

**Figure 7**.

a temperature *T* ≥*TQCDPT*

**Acknowledgements**

National Laboratory,

**90**

Leonard S. Kisslinger Department of Physics, Carnegie Mellon University, Pittsburgh, PA, USA

\*Address all correspondence to: kissling@andrew.cmu.edu

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

## **References**

[1] Cheng T-P, Li L-F. Gauge Theory of Elementary Particle Physics. New York: Oxford University Press; 1985

[2] Kronfeld AS. Annual Review of Nuclear and Particle Science. 2012;**62**: 265

[3] Callaway DJE, Rahman A. Physical Review D. 1983;**28**:1506

[4] Shifman MA, Vainstein AI, Zakharov VI. Nuclear Physics B. 1979; **147**:385, 448

[5] Kisslinger LS. Physical Review D. 2009;**79**:114026

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[9] Moreno G et al. Physical Review D. 1991;**43**:2815

[10] Kolb EW, Turner MS. The Early Universe. United States of America: Westview Press; 1990

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[12] Sirunyan AM et al. Physical Review Letters. 2017;**119**:082301

[13] Kisslinger LS, Das D. International Journal of Modern Physics A. 2016;**31**: 1630010

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Oxford University Press; 1985

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[6] Kisslinger LS, Liu MX,

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**147**:385, 448

2009;**79**:114026

2012;**85**:092004

**89**:024914

**84**:114020

1991;**43**:2815

1630010

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Westview Press; 1990

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[4] Shifman MA, Vainstein AI,

[2] Kronfeld AS. Annual Review of Nuclear and Particle Science. 2012;**62**:

[3] Callaway DJE, Rahman A. Physical

Zakharov VI. Nuclear Physics B. 1979;

[5] Kisslinger LS. Physical Review D.

McGaughey P. Physical Review C. 2014;

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[9] Moreno G et al. Physical Review D.

[10] Kolb EW, Turner MS. The Early Universe. United States of America:

[11] Casaiderry-Solana et al. Physical

[12] Sirunyan AM et al. Physical Review

[13] Kisslinger LS, Das D. International Journal of Modern Physics A. 2016;**31**:

[7] Adare A et al. Physical Review D.

## *Edited by Ozan Artun*

Since the mid-twentieth century, accelerators and colliders have been at the forefront of science and technology in the fields of space, medicine, energy, and others. This book presents sophisticated knowledge about accelerators and colliders and their crucial technological applications.

With six chapters, the book presents information about currently available accelerators and colliders as well as novel schemes for future systems. Other topics covered include vacuum systems, elementary particles, and quantum chromodynamics.

Published in London, UK © 2020 IntechOpen © Naeblys / iStock

Accelerators and Colliders

Accelerators and Colliders

*Edited by Ozan Artun*