Review the Evolution of the Universe

I review elementary particles and basic forces. I review the differential rapidity cross sections for $J\mathrm{<mo>/</mo>}\Psi ,\Psi \mathrm{<mo\; stretchy="false">(</mo>2}S\mathrm{<mo\; stretchy="false">)</mo>},\Upsilon \mathrm{<mo\; stretchy="false">(</mo>1}S\mathrm{<mo\; stretchy="false">)</mo>},\Upsilon \mathrm{<mo\; stretchy="false">(</mo>2}S\mathrm{<mo\; stretchy="false">)</mo>},\Upsilon \mathrm{<mo\; stretchy="false">(</mo>3}S\mathrm{<mo\; stretchy="false">)</mo>}$ , production via p-p, Xe-Xe and O-O collisions, at proton-proton energy $\equiv \sqrt{s_{ppi}}=\text{ 5}.\text{44 TeV}.$ . I review the production and suppression via Xe-Xe collisions. I review the QCDPT, the Quark Plasma (QGP), the production and potential detection of QGP via Au-Au collisions and magnetic fields produced during the EWPT. In the final section Sterile Neutrinos as Dark Matter is reviewed.

1. Introduction

This review of Xe-Xe collisions is based on the heavy quark state production formalism [1] and the mixed hybrid theory [2]. We also review the suppression scenario [3].

My review is based on the methods used in heavy quark state production in Cu-Cu and Au-Au collisions at $\sqrt{s_{pp}}=\text{2}00\text{ GeV}$ [5] which used the color octet model [6-8]. Prior to the article [3] Ψ(2S) and ϒ(3S) suppression in p-Pb collisions was estimated [9] and reviewed [10]. The ALICE collaboration studied J/Ψ production [11]

In section 2, The Evolution of the Universe, including quarks and gluons, is reviewed.

In section 3 and subsection 3.1, I review Elementary Particles, Basic Forces, and. Quantum Chromodynamics.

In section 4 and subsections 4.1, 4.2, and 4.3 Ψ and ϒ production via p-p, Xe-Xe, and O-O collisions with $\sqrt{s_{pp}}=\text{ 5}.\text{44 TeV}$ are reviewed.

In section 5 and subsection 5.1 Ψ and ϒ suppression, mixed hybrid theory, and Ψ suppression in Xe-Xe collisions is reviewed.

In section 6, the QCDPT and the Quark Gluon Condensate are reviewed.

In section 7, the EWPT and the generation of magnetic fields during phase transitions is reviewed.

In section 8, Galaxy Rotation and Dark Matter are reviewed.

In section 9, Sterile Neutrinos as Dark Matter is reviewed.

Section 10 gives Results and Conclusions, ending with the References.

2. The evolution of the universe

The evolution of the Universe is shown in the figure below. The time goes from the Big Bang at 10-35 seconds to 14 billion years when we have our present Universe. Recent results are

From Figure 1 at 10-35 seconds after the Universe began to inflate due to about 70% of the universe being dark energy, which is anti-gravity. About 27% of the Universe is Dark Matter. Dark Matter particles have no interaction but gravity.

Note that at 10-11 during the EWPT, magnetic fields were created, and during the Quantum Chromodynamics Phase Transition (QCDPT) at 10-5 Quarks were bound by gluons to create protons and neutrons.

3. Elementary particles and basic forces

Elementary particles: Fermions and Bosons. Fermions have Quantum spin =1/2

The elementary Fermions 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), (t,b).

There are also three anti-leptons. The electron e- has electric charge -1 while the anti-electron, e+, has an electric charge +1.

The elementary bosons include the gluon and photon with quantum spin 1.

The production of a photon via coupling to e-+ e+ is shown below in Figures 1,2.

4. Quantum Chromodynamics (QCD): Strong interaction field theory

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

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

$g^2\simeq 100g_e^2\mathrm{,}\text{ (1)}$

`` where g is the quark-gluon coupling constant and g_e is the electromagnetic charge [12]. For $\sqrt{s_{pp}}=\text{5}.\text{44 TeV}$ the gluon distribution function fg [13,14] is

$f_g\mathrm{<mo\; stretchy="false">(</mo>}\overline{x}\mathrm{<mo\; stretchy="false">(</mo>}y\mathrm{<mo\; stretchy="false">)</mo>,2}m\mathrm{<mo\; stretchy="false">)</mo><mo>=</mo>1334.21}-67056.5\overline{x}\mathrm{<mo\; stretchy="false">(</mo>}y\mathrm{<mo\; stretchy="false">)</mo>}+\mathrm{887962.0<mo\; stretchy="false">(</mo>}\overline{x}\mathrm{<mo\; stretchy="false">(</mo>}y{\mathrm{<mo\; stretchy="false">)</mo><mo\; stretchy="false">)</mo>}}^2\mathrm{.}\text{ (2)}$

Quarks, which are basic constituents of Quantum Chromo-Dynamics (QCD), interact via the exchange of gluons. QCD is a well-established theory of strong interactions.

4.1. Quark-Gluon Plasma (QGP)

A form of matter, which is called the Quark-Gluon Plasma (QGP), is a thermalized system where the properties of the system are ruled by the quarks and gluons' degrees of freedom. QGP is the QCD analogue of the plasma state of ordinary atomic matter, but the deconfined state, where the deconfined quanta of QGP cannot be observed directly due to the confining property of the QCD vacuum. The only scope to probe such high and dense nuclear matter like QGP, in our laboratories, is possible via relativistic heavy ion collisions.

The QGP is reviewed in section: The QCDPT and the Quark Plasma (QGP).

4.2 Mixed heavy quark hybrid states

The starting point of the method of QCD sum rules [15] is the correlator

${\Pi }^A\mathrm{<mo\; stretchy="false">(</mo>}x\mathrm{<mo\; stretchy="false">)</mo><mo>=</mo>}\langle \mathrm{<mo>|</mo>}T\mathrm{<mo\; stretchy="false">[</mo>}{J}_A\mathrm{<mo\; stretchy="false">(</mo>}x\mathrm{<mo\; stretchy="false">)</mo>}{J}_A\mathrm{<mo\; stretchy="false">(</mo>0<mo\; stretchy="false">)</mo><mo\; stretchy="false">]</mo><mo>|</mo>}\rangle \mathrm{,}\text{ (3)}$

With $\mathrm{<mo>|</mo>}\rangle$ the vacuum state and the current JA(x) creates the states with quantum numbers A.

With $c,\overline{c}$ and g a charm quark, an anti-charm quark, and a gluon, for the charmonium states, J_c is

$J_c\mathrm{<mo>=</mo>}f{J}_{c\overline{c}}+\sqrt{1-f^2}{J}_{c\overline{c}g}\mathrm{,}\text{ (4)}$

where $J_{c\overline{c}}$ creates a normal charmonium state and $J_{c\overline{c}g}$ creates a hybrid state with an active gluon.

The charm quark C needed, with mass [12] $m_c\simeq \text{1}.\text{27 GeV}.$

Using QCD sum rules, it was shown that $f\simeq -\sqrt{2}$ for the Ψ(2S) and ϒ(3S) heavy quark meson states and $f\simeq 1.0$ for the other charmonium and bottomonium states [2]. vspace4mm

Therefore,

$\begin{array}{l}\mathrm{<mo>|</mo>}J\mathrm{<mo>/</mo>}\Psi \mathrm{<mo\; stretchy="false">(</mo>1}S\mathrm{<mo\; stretchy="false">)</mo><mo>></mo>}\simeq \mathrm{<mo>|</mo>}c\overline{c}\mathrm{<mo\; stretchy="false">(</mo>1}S\mathrm{<mo\; stretchy="false">)</mo><mo>></mo>}\\ \mathrm{<mo>|</mo>}\Psi \mathrm{<mo\; stretchy="false">(</mo>2}S\mathrm{<mo\; stretchy="false">)</mo><mo>></mo>}\simeq -\sqrt{2}\mathrm{<mo>|</mo>}c\overline{c}\mathrm{<mo\; stretchy="false">(</mo>1}S\mathrm{<mo\; stretchy="false">)</mo><mo>></mo>}+\sqrt{2}\mathrm{<mo>|</mo>}c\overline{c}g\mathrm{<mo\; stretchy="false">(</mo>2}S\mathrm{<mo\; stretchy="false">)</mo><mo>></mo>}\mathrm{,}\text{ (5)}\end{array}$

with the $\Psi \mathrm{<mo\; stretchy="false">(</mo>2}S\mathrm{<mo\; stretchy="false">)</mo>}$ being a mixed hybrid meson.

Similarly, it was shown with b and $\overline{b}$ a bottom and anti-bottom quark, with mass [12] $m_b\simeq \text{4}.\text{18 GeV},$ that $\Upsilon \mathrm{<mo\; stretchy="false">(</mo>3}S\mathrm{<mo\; stretchy="false">)</mo>}$ It is also a mixed hybrid meson with

$\mathrm{<mo>|</mo>}\Upsilon \mathrm{<mo\; stretchy="false">(</mo>3}S\mathrm{<mo\; stretchy="false">)</mo><mo>></mo>}\simeq -\sqrt{2}\mathrm{<mo>|</mo>}b\overline{b}\mathrm{<mo\; stretchy="false">(</mo>3}S\mathrm{<mo\; stretchy="false">)</mo><mo>></mo>}+\sqrt{2}\mathrm{<mo>|</mo>}b\overline{b}g\mathrm{<mo\; stretchy="false">(</mo>3}S\mathrm{<mo\; stretchy="false">)</mo><mo>></mo>}\mathrm{.}\text{ (6)}$

We need these results for Ψ and production via p-p, Xe-Xe, and O-O collisions are reviewed in the next three subsections.

5. Ψ and ϒ production via p-p, Xe-Xe, and O-O collisions with $\sqrt{s_{pp}}=\text{ 5}.\text{44 TeV}$

The differential rapidity cross section for the production of a heavy quark state Φ with helicity λ = 0 (for unpolarized collisions [14]) In the color octet model via Xe-Xe collisions is given by [5]

$\frac{d{\sigma }_{AA\to \Phi \mathrm{<mo\; stretchy="false">(</mo>}\lambda \mathrm{<mo>=</mo>0<mo\; stretchy="false">)</mo>}}}{dy}\mathrm{<mo>=</mo>}{R}_{AA}^E{N}_{bin}^{AA}\mathrm{<mo><</mo>}\frac{d{\sigma }_{pp\to \Phi \mathrm{<mo\; stretchy="false">(</mo>}\lambda \mathrm{<mo>=</mo>0<mo\; stretchy="false">)</mo>}}}{dy}\mathrm{<mo>></mo>}\mathrm{,}\text{ (7)}$

where $R_{AA}^E$ is the product of the nuclear modification factor RAA and SΦ, the dissociation factor after the state Φ is formed (Figure 3 in Ref [16]). RAA is defined in Ref [17] as

$R_{AA}\mathrm{<mo\; stretchy="false">(</mo>}p\mathrm{<mo\; stretchy="false">)</mo><mo>=</mo>}\frac{d^2{N}_{bin}^{AA}\mathrm{<mo>/</mo>}dpd\eta }{T_{AA}{d}^2{\sigma }^{NN}\mathrm{<mo>/</mo>}dpd\eta }\mathrm{.}\text{ (8)}$

For Xe-Xe collisions we use $R_{XeXe}^E=0.\text{5}$ as $R_{AA}^E\simeq 0.5$ both for Cu-Cu [16,18] and Au-Au [19-21] and $R_{PbPb}^E=0.\text{5}$ was used in Ref [1].

For p-p collisions we use $R_{pp}^E=0.00\text{5}$ For O-O collisions we use $R_{OO}^E=0.\text{25}$

5.1. Ψ and ϒ production via p-p collisions with $\sqrt{s_{pp}}=\text{ 5}.\text{44 TeV}$

The differential rapidity cross section for pp collisions in terms of f g [14], the gluon distribution function is

$\frac{d{\sigma }_{pp\to \Phi \mathrm{<mo\; stretchy="false">(</mo>}\lambda \mathrm{<mo>=</mo>0<mo\; stretchy="false">)</mo>}}}{dy}\mathrm{<mo>=</mo>}{A}_{\Phi }\frac{1}{x\mathrm{<mo\; stretchy="false">(</mo>}y\mathrm{<mo\; stretchy="false">)</mo>}}{f}_g\mathrm{<mo\; stretchy="false">(</mo>}\overline{x}\mathrm{<mo\; stretchy="false">(</mo>}y\mathrm{<mo\; stretchy="false">)</mo>,2}m\mathrm{<mo\; stretchy="false">)</mo>}{f}_g\mathrm{<mo\; stretchy="false">(</mo>}a\mathrm{<mo>/</mo>}\overline{x}\mathrm{<mo\; stretchy="false">(</mo>}y\mathrm{<mo\; stretchy="false">)</mo>,2}m\mathrm{<mo\; stretchy="false">)</mo>}\frac{dx}{dy}\mathrm{,}\text{ (9)}$

where from Ref [14] AΦ = 1.26×10^-6 nb for Φ = J/ and 3.4×10-8 nb for Φ = ϒ(1S); and a = 4m2/s = 3.6×10^-7 for charmonium and 4.0×10^-6 for bottomonium.

The function $\overline{x}$ , the effective parton x in a nucleus (A), is given in Refs [22,23]:

$x\mathrm{<mo\; stretchy="false">(</mo>}y\mathrm{<mo\; stretchy="false">)</mo><mo>=</mo>0.5<mo\; stretchy="false">[</mo>}\frac{m}{\sqrt{s_{pp}}}\mathrm{<mo\; stretchy="false">(</mo>}\exp y-\exp \mathrm{<mo\; stretchy="false">(</mo>}-y\mathrm{<mo\; stretchy="false">)</mo><mo\; stretchy="false">)</mo>}+\sqrt{{\mathrm{<mo\; stretchy="false">(</mo>}\frac{m}{\sqrt{s_{pp}}}\mathrm{<mo\; stretchy="false">(</mo>}\exp y-\exp \mathrm{<mo\; stretchy="false">(</mo>}-y\mathrm{<mo\; stretchy="false">)</mo><mo\; stretchy="false">)</mo><mo\; stretchy="false">)</mo>}}^2+4a}\mathrm{<mo\; stretchy="false">]</mo>}$

$\overline{x}\mathrm{<mo\; stretchy="false">(</mo>}y\mathrm{<mo\; stretchy="false">)</mo><mo>=</mo><mo\; stretchy="false">(</mo>1}+\frac{{\xi }_g^2\mathrm{<mo\; stretchy="false">(</mo>}{A}^{\mathrm{1<mo>/</mo>3}}-\mathrm{1<mo\; stretchy="false">)</mo>}}{Q^2}\mathrm{<mo\; stretchy="false">)</mo>}x\mathrm{<mo\; stretchy="false">(</mo>}y\mathrm{<mo\; stretchy="false">)</mo>.}\text{ (10)}$

With Ψ(2S), ϒ(3S) enhanced by Π2/4 [14] the differential rapidity cross sections are shown in the following figures. The absolute magnitudes are uncertain, and the shapes and relative magnitudes are our main predictions. In Eq m = mc = 1.5 GeV for charmonium and m = mb = 5 GeV for bottomonium quarks.

The differential rapidity cross sections for the production Ψ(1S) and Ψ(2S) via p-p collisions are shown in the Figures 4-6 below.

5.2. The differential rapidity cross section for the production of a heavy quark state via Xe-Xe collisions

The differential rapidity cross section for the production of a heavy quark state Φ with helicity λ = 0 (for unpolarized collisions [14]) in the color octet model via Xe-Xe collisions is given by [5]

$\frac{d{\sigma }_{AA\to \Phi \mathrm{<mo\; stretchy="false">(</mo>}\lambda \mathrm{<mo>=</mo>0<mo\; stretchy="false">)</mo>}}}{dy}\mathrm{<mo>=</mo>}{R}_{AA}^E{N}_{bin}^{AA}\mathrm{<mo><</mo>}\frac{d{\sigma }_{pp\to \Phi \mathrm{<mo\; stretchy="false">(</mo>}\lambda \mathrm{<mo>=</mo>0<mo\; stretchy="false">)</mo>}}}{dy}\mathrm{<mo>></mo>}\mathrm{,}\text{ (11)}$

where $R_{AA}^E$ is the product of the nuclear modification factor R_AA and SΦ, the dissociation factor after the state Φ is formed (see Figure 3 in Ref [16]). R_AA is defined in Ref [17] as

$R_{AA}\mathrm{<mo\; stretchy="false">(</mo>}p\mathrm{<mo\; stretchy="false">)</mo><mo>=</mo>}\frac{d^2{N}_{bin}^{AA}\mathrm{<mo>/</mo>}dpd\eta }{T_{AA}{d}^2{\sigma }^{NN}\mathrm{<mo>/</mo>}dpd\eta }\mathrm{,}\text{ (12)}$

where $N_{bin}^{AA}$ is the number of binary collisions in the AA collision, and η is the pseudo-rapidity [24].

Note that $T_{AA}\mathrm{<mo>=</mo>}{N}_{bin}^{AA}\mathrm{<mo>/</mo>}{\sigma }^{NN}$ , where σ^NN is the cross section for N-N collisions and $\mathrm{<mo><</mo>}\frac{d{\sigma }_{pp\to \Phi \mathrm{<mo\; stretchy="false">(</mo>}\lambda \mathrm{<mo>=</mo>0<mo\; stretchy="false">)</mo>}}}{dy}\mathrm{<mo>></mo>}$ is the differential rapidity cross section for Φ production via nucleon-nucleon collisions in the nuclear medium.

For Xe-Xe collisions we use $R_{XeXe}^E=0.\text{5}$ as $R_{AA}^E\simeq 0.5$ both for Cu-Cu [16,18] and Au-Au [19-21] and $R_{PbPb}^E=0.5$ was used in Ref [1].

$N_{bin}^{XeXe}$ is the number of binary collisions in Xe-Xe collisions, and $\mathrm{<mo><</mo>}\frac{d{\sigma }_{pp\to \Phi \mathrm{<mo\; stretchy="false">(</mo>}\lambda \mathrm{<mo>=</mo>0<mo\; stretchy="false">)</mo>}}}{dy}\mathrm{<mo>></mo>}$ is the differential rapidity cross section for Φ production via nucleon-nucleon collisions in the nuclear medium.

The number of binary collisions for Pb-Pb from Ref [25] used in Ref [1] was $N_{bin}^{PbPb}\simeq \text{26}0.$ The cross sections at $\sqrt{s_{pp}}\simeq \text{5}.0\text{ TeV}$ [26] for PbPb, CuCu, XeXe.

Using $N_{bin}^{PbPb}=260$ , for Cu-Cu collisions $N_{bin}^{CuCu}\simeq \text{51}.\text{5}$ [5,25]. From $N_{bin}^{PbPb}=260$ and the Xe-Xe, Pb-Pb cross sections we estimate $N_{bin}^{XeXe}\simeq \text{216}.$

Therefore in Eq(11) $R_{AA}^E{N}_{bin}^{AA}\to R_{XeXe}^E{N}_{bin}^{XeXe}\simeq 108$ with [27] ${\xi }_g^2\mathrm{<mo>=</mo>.12}Ge{V}^2$ and Q2 defined in Ref [22]. Therefore for Xe with $A\simeq 132,Q^2\simeq 10.18Ge{V}^2$

$\overline{x}\mathrm{<mo\; stretchy="false">(</mo>}y\mathrm{<mo\; stretchy="false">)</mo><mo>=</mo>1.048}x\mathrm{<mo\; stretchy="false">(</mo>}x\mathrm{<mo\; stretchy="false">)</mo>}\mathrm{.}\text{ (13)}$

With Ψ(2S), ϒ(3S) enhanced by Π²/4 [15] the differential rapidity cross sections are shown in the following figures. The absolute magnitudes are uncertain, and the shapes and relative magnitudes are our main predictions. In Eq(13) m = mc = 1.5 Gev for charmonium and m = mb = 5 Gev for bottomonium quarks (Figures 7-10 ).

Note that the differential rapidity cross section for the ϒ(3S) (hybrid) is larger than the differential rapidity cross section for the ϒ(3S).

5.3. The differential rapidity cross section for the production of a heavy quark state Φ via O-O collisions

This review of heavy quark state production was motivated in part by the article:

Opportunities of O-O Collisions at the LHC [28].

For O-O collisions we use $R_{OO}^E=0.25=R_{XeXe}^E/2$ .

The differential rapidity cross sections are shown in the following Figures 11-14.

Note that the differential rapidity cross section for the ϒ(3S) (hybrid) is larger than the differential rapidity cross section for the ϒ(3S).

6 Ψ and ϒ suppression in Xe-Xe collisions and mixed hybrid theory

The suppression, S_A, of charmonium or bottomonium states is given by the interaction of the meson with nucleons as it traverses the nucleus. From Ref [29]

$S_A\mathrm{<mo>=</mo>}{e}^{-n_o{\sigma }_{\Phi N}L}\mathrm{,}\text{ (14)}$

where Φ is a standard $c\overline{c}$ , hybrid $c\overline{c}g$ charmonium meson, or a standard $b\overline{b},b\overline{b}g$ bottomonium meson. L is the length the path of Φ in nuclear matter, n0 = 0.17 fm-3 is the nuclear matter density, and σΦN is the Φ - N cross section. For Xe-Xe collisions L ≈ 12 fm.

S_A was estimated for Pb-Pb collisions [1] and p-Pb collisions [9]. From Ref [9] σΦN for $\Phi \mathrm{<mo>=</mo>}c\overline{c}\mathrm{,}c\overline{c}g\mathrm{,}b\overline{b}\mathrm{,}b\overline{b}g$ were estimated to be (with a mb → fm correction)

$\begin{array}{l}{\sigma }_{c\overline{c}N}\simeq 3.2\times {10}^{-2}{\text{fm}}^2\\ {\sigma }_{c\overline{c}gN}\simeq {6.5}^2{\text{fm}}^2\\ {\sigma }_{b\overline{b}N}\simeq 2.9\times {10}^{-3}{\text{fm}}^2\text{ (15)}\\ {\sigma }_{b\overline{b}gN}\simeq 0.59{\text{fm}}^2\mathrm{.}\end{array}$

Note that the present results for $n_o{\sigma }_{\Phi N}L$ differ from those in Ref [9] for Pb-Pb suppression by a factor of about 1.25 as $L\simeq \text{15 fm}$ for Pb and 12 fm for Xe.

6.1 Ψ suppression in Xe-Xe collisions

From Eq. for $J\mathrm{<mo>/</mo>}\Psi \mathrm{<mo>=</mo>}\Psi \mathrm{<mo\; stretchy="false">(</mo>1}S\mathrm{<mo\; stretchy="false">)</mo><mo>=</mo><mo>|</mo>}c\overline{c}\mathrm{<mo>;</mo>1}S\mathrm{<mo>></mo>}$

$\begin{array}{l}{n}_o{\sigma }_{c\overline{c}N}L\simeq 0.065\\ S_A^{c\overline{c}}\mathrm{<mo>=</mo>}{e}^{-n_o{\sigma }_{c\overline{c}N}L}\simeq 1.0\mathrm{,}\text{ (16)}\end{array}$

thus the $J\mathrm{<mo>/</mo>}\Psi \mathrm{<mo>=</mo>}\Psi \mathrm{<mo\; stretchy="false">(</mo>1}S\mathrm{<mo\; stretchy="false">)</mo>}$ meson appears unsuppressed in Xe-Xe collisions. For a charmonium hybrid meson $c\overline{c}g$ with L=12 fm

$\begin{array}{l}{n}_o{\sigma }_{c\overline{c}gN}L\simeq 13.3\\ S_A^{c\overline{c}g}\simeq e^{-13.3}\simeq 0.0\mathrm{.}\text{ (17)}\end{array}$

Since from Eq(1) the Ψ(2S) is 50% standard and 50% hybrid

$S_A^{\Psi \mathrm{<mo\; stretchy="false">(</mo>2}S\mathrm{<mo\; stretchy="false">)</mo>}}\simeq \mathrm{<mo\; stretchy="false">(</mo>1}+\mathrm{0.0<mo\; stretchy="false">)</mo><mo>/</mo>2}\simeq 0.5\mathrm{.}\text{ (18)}$

Using the definition of $R^{\Psi \mathrm{<mo\; stretchy="false">(</mo>2}S\mathrm{<mo\; stretchy="false">)</mo>}-J\mathrm{<mo>/</mo>}\Psi \mathrm{<mo\; stretchy="false">(</mo>1}S\mathrm{<mo\; stretchy="false">)</mo>}}$ of the suppression ratio, the ratio between Ψ(2S) to the Ψ(1S) states, from Eqs.

$R^{\Psi \mathrm{<mo\; stretchy="false">(</mo>2}S\mathrm{<mo\; stretchy="false">)</mo>}-J\mathrm{<mo>/</mo>}\Psi \mathrm{<mo\; stretchy="false">(</mo>1}S\mathrm{<mo\; stretchy="false">)</mo>}}{\mathrm{<mo>|</mo>}}_{Xe-Xe-theory}\simeq 0.5\mathrm{,}\text{ (19)}$

The experimental result [30] for d-Au collisions and [31] for p-Pb collisions is

$R^{\Psi \mathrm{<mo\; stretchy="false">(</mo>2}S\mathrm{<mo\; stretchy="false">)</mo>}-J\mathrm{<mo>/</mo>}\Psi \mathrm{<mo\; stretchy="false">(</mo>1}S\mathrm{<mo\; stretchy="false">)</mo>}}{\mathrm{<mo>|</mo>}}_{exp}\simeq 0.65\pm 0.1\text{ (20)}$

which is somewhat larger than $R^{\Psi \mathrm{<mo\; stretchy="false">(</mo>2}S\mathrm{<mo\; stretchy="false">)</mo>}-J\mathrm{<mo>/</mo>}\Psi \mathrm{<mo\; stretchy="false">(</mo>1}S\mathrm{<mo\; stretchy="false">)</mo>}}{\mathrm{<mo>|</mo>}}_{Xe-Xe-theory}$ .

6.2 suppression in Xe-Xe collisions

From Eq. for $\Upsilon \mathrm{<mo\; stretchy="false">(</mo>1}s\mathrm{<mo\; stretchy="false">)</mo><mo>=</mo><mo>|</mo>}b\overline{b}\mathrm{<mo>;</mo>1}S\mathrm{<mo>></mo>}$

$\begin{array}{l}{n}_o{\sigma }_{b\overline{b}N}L\simeq 0.0\text{ (21)}\\ S_A^{b\overline{b}}\simeq \mathrm{1.0.}\mathrm{,}\end{array}$

Thus the ϒ(1S) and ϒ(2S) mesons are not suppressed.

For a hybrid bottomonium meson $b\overline{b}g$ from Eq.

$\begin{array}{l}{n}_o{\sigma }_{\overline{b}gNL}\simeq 1.2\text{ (22)}\\ S_A^{b\overline{g}}\simeq 0.3\mathrm{.}\end{array}$

For the mixed hybrid ϒ(3S)

$S_A^{\Upsilon \mathrm{<mo\; stretchy="false">(</mo>3}S\mathrm{<mo\; stretchy="false">)</mo>}}\simeq \mathrm{<mo\; stretchy="false">(</mo>1}+\mathrm{.3<mo\; stretchy="false">)</mo><mo>/</mo>2}\simeq 0.65\mathrm{.}\text{ (23)}$

Therefore for Xe-Xe collisions the ϒ(3S) suppression is moderate and could be measured in future CERN LHC experiments.

7. The QCDPT and the Quark Plasma (QGP)

The QCDPT is the transition from a universe with dense matter called the quark gluon plasma (QGP), to our universe with protons and neutrons and other hadrons.

As the figure below illustrates, for Au-Au collisions the emission of mixed hybrid mesons, the Ψ(2S) and ϒ(3S) as discussed above, with active gluons, could be a signal of the formation of the QGP (Figure 15).

The study of the QGP requires reference measurements from systems in which the QGP is not expected to be formed, such as p+p and p+A collisions. The transverse size of the overlap region is comparable to that of a single proton, in systems like p+p and p+A and hence the formation of a hot and dense fluid-like medium or QGP is not expected.

Control measurements are however needed to characterize the extent to which initial-state effects can be demarcated from the effects due to the final-state interactions in the QGP.

The p+A collisions due to the absence of a produced medium are expected to isolate the nuclear effects from the initial state of the hard-scattering process. Also the system size evolution at freeze-out can be studied from the small systems (like p+p and p+A), along with the rescattering effects. some of these assumptions are being tested and understood carefully both in Large Hadron Collider (LHC) and in Relativistic Heavy Ion Collider (RHIC) data and more can be possible in future at Electron Ion Collider (EIC).

As was reviewed in the first part of this section and the QGP was inferred through the production of Ψ(2S) and (3S) mesons in Au-Au collisions.

8. The Electroweak Phase Transition (EWPT) and magnetic field creation

Particles get mass, magnetic fields created, Baryogenesis–more quarks than anti-quarks

Fermions (spin 1/2 particles) are (e^-, ve) and the µ and τ leptons, and the quarks (qu, qd ) and the other two quark generations.

Gauge bosons (spin 1 particles) are W⁺, W^-, Z⁰ and photon (γ). Scalar boson (spin 0) is Higgs, φH

At the LHC (Large Hadron Collider) one has found the Higgs mass $\simeq \text{125 GeV}$ and CP = Charge-Parity

Production of W⁺, W^-, and is shown in the Figure 16 below

With a First Order (EWPT):

1) Critical Temperature, $T_c\simeq 100-150\text{ GeV}$

2) Latent heat $=\mathrm{<mo><</mo>}{\varphi }_H\mathrm{<mo>></mo>}\equiv v$

3) Bubbles of the new universe form $(\mathrm{<mo><</mo>}{\varphi }_H\mathrm{<mo>></mo>}\equiv v)$ inside the old universe $(\mathrm{<mo><</mo>}{\varphi }_H\mathrm{<mo>></mo>}\equiv 0).$ This gives the Standard Model particles their masses:

$\begin{array}{l}{M}_W\mathrm{<mo>=</mo>}gv\mathrm{<mo>/</mo>}\sqrt{2}g\mathrm{<mo>=</mo>}strongcouplingconstant\\ M_Z\mathrm{<mo>=</mo>}{m}_W\mathrm{<mo>/</mo>}\cos \mathrm{<mo\; stretchy="false">(</mo>}{\theta }_W\mathrm{<mo\; stretchy="false">)</mo>}{\theta }_W\mathrm{<mo>=</mo>}Weinbergangle\text{ (24)}\\ m_e\propto m_u\propto m_d\propto v\mathrm{.}\end{array}$

Standard Model M_W = 80 GeV and M_Z = 90 GeV.

Bubbles nucleate, creating electromagnetic fields, and collide, creating magnetic fields. These magnetic fields could explain the mystery of gallactic and inter-gallactic magnetic fields, as discussed below.

EW-MSSM Theory. The MSSM (Minimal Supersymmetry Model) another scalar boson field, the Stop (φs) is added to the Standard Model Fermion and Boson fields. This has been shown to lead to a first order EWPT.

Electroweak Minimal Supersymmetry Model (EW-MSSM)

All Supersymmetry partners of Standard model particles except the top quark, , are integrated out, giving an EW-MSSM Lagrangian:

$\begin{array}{l}{L}^{MSSM}\mathrm{<mo>=</mo>}{L}^1+L^2+L^3\\ +\text{l}eptonicandquarkinteractions\\ L^1\mathrm{<mo>=</mo>}-\frac{1}{4}{W}_{\mu \nu }^i{W}^{i\mu \nu }-\frac{1}{4}{B}_{\mu \nu }{B}^{\mu \nu }\\ L^2\mathrm{<mo>=</mo><mo>|</mo><mo\; stretchy="false">(</mo>}i{\partial }_{\mu }-\frac{g}{2}\tau \cdot W_{\mu }-\frac{g^{\prime }}{2}{B}_{\mu }\mathrm{<mo\; stretchy="false">)</mo>}\Phi {\mathrm{<mo>|</mo>}}^2-V\mathrm{<mo\; stretchy="false">(</mo>}\Phi \mathrm{<mo\; stretchy="false">)</mo>}\\ L^3\mathrm{<mo>=</mo><mo>|</mo><mo\; stretchy="false">(</mo>}i{\partial }_{\mu }-\frac{g_s}{2}{\lambda }^a{C}_{\mu }^a\mathrm{<mo\; stretchy="false">)</mo>}{\Phi }_s{\mathrm{<mo>|</mo>}}^2-V_{hs}\mathrm{<mo\; stretchy="false">(</mo>}{\Phi }_s\mathrm{,}\Phi \mathrm{<mo\; stretchy="false">)</mo>}\mathrm{,}\text{ (25)}\end{array}$

where

$\begin{array}{l}{W}_{\mu \nu }^i\mathrm{<mo>=</mo>}{\partial }_{\mu }{W}_{\nu }^i-{\partial }_{\nu }{W}_{\mu }^i-g{ϵ}_{ijk}{W}_{\mu }^j{W}_{\nu }^k\text{ (26)}\\ B_{\mu \nu }\mathrm{<mo>=</mo>}{\partial }_{\mu }{B}_{\nu }-{\partial }_{\nu }{B}_{\mu }\mathrm{,}\end{array}$

where the W^i,/, with i = (1,2), are the W⁺, W^- fields, $C_{\mu }^a$ is an SU(3) gauge field, (Φ, Φs) are the (Higgs, right-handed Stop fields), (τI, λ^a) are the (SU(2),SU(3) generators, and the electromagnetic and Z fields are defined as

$\begin{array}{l}{A}_{\mu }^{em}\mathrm{<mo>=</mo>}\frac{1}{\sqrt{g^2+g^{\mathrm{<mo>\text{'}</mo>2}}}}\mathrm{<mo\; stretchy="false">(</mo>}{g}^{\prime }{W}_{\mu }^3+g{B}_{\mu }\mathrm{<mo\; stretchy="false">)</mo>}\text{ (27)}\\ Z_{\mu }\mathrm{<mo>=</mo>}\frac{1}{\sqrt{g^2+g^{\mathrm{<mo>\text{'}</mo>2}}}}\mathrm{<mo\; stretchy="false">(</mo>}g{W}_{\mu }^3-g^{\prime }{B}_{\mu }\mathrm{<mo\; stretchy="false">)</mo>}\mathrm{.}\end{array}$

Electromagnetic field creation during EWPT bubble nucleation (due to spatial symmetry, no magnetic field is created)

B (magnetic) field creation via EWPT bubble collisions (Figure 17)

Results for B (magnetic) field creation via EWPT bubble collisions (Figure 18):

The B-field at the end of the EWPT, with the temperature = T_c, was found to be

$B^{EWPT}\mathrm{<mo\; stretchy="false">(</mo>}{T}_c\mathrm{<mo\; stretchy="false">)</mo><mo>=</mo>10}{M}_W^2\text{ with }{M}_W\mathrm{<mo>=</mo>}\text{8}0\text{ GeV}$

$B^{EWPT}\mathrm{<mo\; stretchy="false">(</mo>}{T}_c\mathrm{<mo\; stretchy="false">)</mo>}$ is needed for the estimates of gravitational radiation.

9. Galaxy rotation and dark matter

Our galaxy, the Milky Way, is a gargantuan collection of stars, gas, dust, with a massive black hole held together by gravity. Gravity does not collapse due to the centripetal force.

By measuring the galaxy radius, its speed, and the amount of visible mass, the amount of dark matter mass can be estimated. This is illustrated in the Figure 19 below.

From the measurements illustrated in the Figure above it is estimated that about 24% of the Milky Way galaxy mass is Dark Matter and this includes the mass of the supermassive black hole at the center of the galaxy. This is consistent with the Evolution of the Universe reviewed in section 2.

10. Sterile neutrinos as dark matter

Sterile neutrinos are a well-known source of Dark Matter. For many years the MiniBooNE Collaboration has studied neutrino oscillations. The MiniBooNE Collaboration detected a sterile neutrino v₄ using ${\overline{\nu }}_{\mu }\to {\overline{\nu }}_e$ oscillations and, estimated the mass difference between this sterile neutrino and a standard neutrino as

$\Delta m^2\mathrm{<mo>=</mo>}{m}_4^2-m_1^4\simeq 0.06{\text{(}eV\mathrm{<mo\; stretchy="false">)</mo>}}^2\mathrm{,}\text{ (28)}$

which is too small for sterile neutrino v₄ to be a WIMP (Weakly Interacting Massive Particle).

The notation for the three active neutrinos ${\nu }_e\mathrm{<mo>=</mo>}{\nu }_1\mathrm{,}{\nu }_{\mu }\mathrm{<mo>=</mo>}{\nu }_2\mathrm{,}{\nu }_{\tau }\mathrm{<mo>=</mo>}{\nu }_3$ and the three sterile neutrinos are ${\nu }_4\mathrm{,}{\nu }_5\mathrm{,}{\nu }_6$

$\mathrm{<mo\; stretchy="false">(</mo>}{\nu }_{\mu }\to {\nu }_e\mathrm{<mo\; stretchy="false">)</mo><mo>=</mo>}Re\mathrm{<mo\; stretchy="false">[</mo>}{\displaystyle \sum _{i\mathrm{<mo>=</mo>1}}^6}{\displaystyle \sum _{j\mathrm{<mo>=</mo>1}}^6}{U}_{1i}{U}_{1j}^{\mathrm{<mo>*</mo>}}{U}_{2i}^{\mathrm{<mo>*</mo>}}{U}_{2j}{e}^{-i\mathrm{<mo\; stretchy="false">(</mo>}\delta m_{ij}^2\mathrm{<mo>/</mo>}E\mathrm{<mo\; stretchy="false">)</mo>}L}\mathrm{<mo\; stretchy="false">]</mo>}\mathrm{,}\text{ (29)}$

where neutrinos with flavors ${\nu }_e\mathrm{,}{\nu }_{\mu }\mathrm{,}{\nu }_{\tau }$ and three sterile neutrinos, ${\nu }_{s_1}\mathrm{,}{\nu }_{s_2}\mathrm{,}{\nu }_{s_3}$ are related to neutrinos with definite mass by

${\nu }_f\mathrm{<mo>=</mo>}U{\nu }_m\mathrm{,}\text{ (30)}$

Where U is a 6x6 matrix. In Ref [9] the sterile-active neutrino mixing angles were calculated, which should be useful for future searches for sterile neutrinos as Dark Matter particles.

Recently the MiniBooNE Collaboration has carried out a search for sub-Gev Dark Matter at the Fermilab [32], with the estimate

$\text{200}\text{MeV}\mathrm{<mo><</mo>}{M}_{{\nu }_{s3}}\mathrm{<mo><</mo>}\text{1250}\text{MeV}\mathrm{.}\text{ (31)}$

Thus, it is likely that most of the Dark Matter in the Universe consists of sterile neutrinos.

11. Result and Conclusion

The following sections provide a comprehensive review of various topics in physics. Section 2 explores the evolution of the universe, with a focus on quarks and gluons. Section 3, including subsection 3.1, discusses elementary particles, basic forces, and quantum chromodynamics, highlighting the magnitude of the quark-gluon coupling constant. Section 4, along with subsections 4.1 to 4.3, examines differential rapidity cross sections for the production of heavy quark states and their generation in p-p, Xe-Xe, and O-O collisions at 5.44 TeV.

Section 5, with subsection 5.1, analyzes suppression effects, mixed hybrid theory, and suppression phenomena in Xe-Xe collisions, noting that moderate suppression could be measured in future CERN experiments. Section 6 reviews QCDPT, the Quark-Gluon Condensate, and the Quark-Gluon Plasma (QGP), with hybrid meson production via Au-Au collisions potentially signaling QGP formation. Section 7 covers EWPT and magnetic field creation.

Sections 8 and 9 delve into astrophysical phenomena, including galaxy rotation and dark matter, as well as sterile neutrinos as a form of dark matter."

Author L.S.K. acknowledges support in part by a grant from the Pittsburgh Foundation.

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