baryogenesis

The majority of ordinary matter in the universe is found in atomic nuclei, which are made of neutrons and protons. There is no evidence of primordial antimatter. In the universe about 1 in 10,000 protons are antiprotons, consistent with ongoing production due to cosmic rays. Possible domains of antimatter in other parts of the universe is inconsistent with the lack of measurable of gamma radiation background.{{rp|36}}

Furthermore, accurate predictions of Big Bang nucleosynthesis depend upon the value of the baryon asymmetry factor (see {{slink||Relation to Big Bang nucleosynthesis}}).

The match between the predictions and observations of the nucleosynthesis model constrains the value of this baryon asymmetry factor. In particular, if the model computed with equal amounts of baryons and antibaryons, they annihilate each other so completely that not enough baryons are left to create nucleons.{{rp|37}}

There are two main interpretations for this disparity: either the universe began with a small preference for matter (total baryonic number of the universe different from zero), or the universe was originally perfectly symmetric, but somehow a set of particle physics phenomena contributed to a small imbalance in favour of matter over time. The goal of cosmological theories of baryogenesis is to explain the baryon asymmetry factor using quantum field theory of elementary particles.{{rp|37}}

{{Anchor|Sakharov conditions}}

In 1967, Andrei Sakharov proposed{{cite journal

| author = A. D. Sakharov

| year = 1967

| title = Violation of CP invariance, C asymmetry, and baryon asymmetry of the universe

| journal = Journal of Experimental and Theoretical Physics Letters

| volume = 5

| pages = 24–27

| url = http://www.jetpletters.ac.ru/ps/1643/article_25089.shtml

| doi =

| author-link = Andrei Sakharov

}} and in Russian, {{cite journal

| author = A. D. Sakharov

| year = 1967

| title = Violation of CP invariance, C asymmetry, and baryon asymmetry of the universe

| journal = ZhETF Pis'ma

| volume = 5

| pages = 32–35

| url = http://www.jetpletters.ac.ru/ps/808/article_12459.shtml

| doi =

| author-link = Andrei Sakharov

| access-date = 2017-09-28

| archive-date = 2019-06-06

| archive-url = https://web.archive.org/web/20190606082623/http://www.jetpletters.ac.ru/ps/808/article_12459.shtml

| url-status = dead

}} republished as {{cite journal

| author = A. D. Sakharov

| year = 1991

| title = Violation of CP invariance, C asymmetry, and baryon asymmetry of the universe

| journal = Soviet Physics Uspekhi

| volume = 34

| pages = 392–393

| language = Russian, English

| doi = 10.1070/PU1991v034n05ABEH002497

| url = https://ufn.ru/en/articles/1991/5/h/

| bibcode = 1991SvPhU..34..392S

| issue = 5

| url-access = subscription

}} a set of three necessary conditions that a baryon-generating interaction must satisfy to produce matter and antimatter at different rates. These conditions were inspired by the recent discoveries of the cosmic microwave background

{{cite journal

| author = A. A. Penzias |author2=R. W. Wilson

| year = 1965

| title = A Measurement of Excess Antenna Temperature at 4080 Mc/s

| journal = Astrophysical Journal

| volume = 142 | pages = 419–421

| doi = 10.1086/148307

| bibcode=1965ApJ...142..419P

|author-link=Arno Allan Penzias

|author2-link=Robert Woodrow Wilson

| doi-access = free

}} and CP-violation in the neutral kaon system.

{{cite journal

| author = J. W. Cronin |author2=V. L. Fitch

| year = 1964

| title = Evidence for the 2π decay of the {{PhysicsParticle|K|BR=2|TR=0}} meson

| journal = Physical Review Letters

| volume = 13 | pages = 138–140

| doi = 10.1103/PhysRevLett.13.138

| bibcode=1964PhRvL..13..138C

| issue = 4

|display-authors=etal|author-link=James Watson Cronin

|author2-link=Val Logsdon Fitch

| doi-access = free

}} The three necessary "Sakharov conditions" are:

• Baryon number $B$ violation.
• C-symmetry and CP-symmetry violation.
• Interactions out of thermal equilibrium.

Baryon number violation is a necessary condition to produce an excess of baryons over anti-baryons. But C-symmetry violation is also needed so that the interactions which produce more baryons than anti-baryons will not be counterbalanced by interactions which produce more anti-baryons than baryons. CP-symmetry violation is similarly required because otherwise equal numbers of left-handed baryons and right-handed anti-baryons would be produced, as well as equal numbers of left-handed anti-baryons and right-handed baryons.

{{cite journal

|author1=A. Riotto |author2=M. Trodden | year = 1999

| title = Recent progress in baryogenesis

| journal = Annual Review of Nuclear and Particle Science

| volume = 49 | pages = 46

| doi = 10.1146/annurev.nucl.49.1.35 | doi-access=free

|arxiv = hep-ph/9901362 |bibcode = 1999ARNPS..49...35R |s2cid=10901646 }} Finally, the last condition, known as the out-of-equilibrium decay scenario, states that the rate of a reaction which generates baryon-asymmetry must be less than the rate of expansion of the universe. This ensures the particles and their corresponding antiparticles do not achieve thermal equilibrium due to rapid expansion decreasing the occurrence of pair-annihilation. The interactions must be out of thermal equilibrium at the time of the baryon-number and C/CP symmetry violating decay occurs to generate the asymmetry.{{rp|46}}

The Standard Model can incorporate baryogenesis, though the amount of net baryons (and leptons) thus created may not be sufficient to account for the present baryon asymmetry. There is a required one excess quark per billion quark-antiquark pairs in the early universe in order to provide all the observed matter in the universe. This insufficiency has not yet been explained, theoretically or otherwise.

Baryogenesis within the Standard Model requires the electroweak symmetry breaking to be a first-order cosmological phase transition, since otherwise sphalerons wipe out any baryon asymmetry that happened up to the phase transition. Beyond this, the remaining amount of baryon non-conserving interactions is negligible.

{{cite journal

| author = V. A. Kuzmin |author2=V. A. Rubakov |author3=M. E. Shaposhnikov

| year = 1985

| title = On anomalous electroweak baryon-number non-conservation in the early universe

| journal = Physics Letters B

| volume = 155 |issue=1–2 | pages = 36–42

| doi = 10.1016/0370-2693(85)91028-7

|bibcode = 1985PhLB..155...36K |author-link=Vadim Kuzmin (physicist) }}

The phase transition domain wall breaks the P-symmetry spontaneously, allowing for CP-symmetry violating interactions to break C-symmetry on both its sides. Quarks tend to accumulate on the broken phase side of the domain wall, while anti-quarks tend to accumulate on its unbroken phase side.

{{cite journal

|author1=M. E. Shaposhnikov |author2=G. R. Farrar | year = 1993

| title = Baryon Asymmetry of the Universe in the Minimal Standard Model

| journal = Physical Review Letters

| volume = 70 | pages = 2833–2836

| doi = 10.1103/PhysRevLett.70.2833

|pmid=10053665 | arxiv = hep-ph/9305274

|bibcode = 1993PhRvL..70.2833F

| issue = 19 |s2cid=15937666 }} Due to CP-symmetry violating electroweak interactions, some amplitudes involving quarks are not equal to the corresponding amplitudes involving anti-quarks, but rather have opposite phase (see CKM matrix and Kaon); since time reversal takes an amplitude to its complex conjugate, CPT-symmetry is conserved in this entire process.

Though some of their amplitudes have opposite phases, both quarks and anti-quarks have positive energy, and hence acquire the same phase as they move in space-time. This phase also depends on their mass, which is identical but depends both on flavor and on the Higgs VEV which changes along the domain wall.{{Cite journal|last1=Croon|first1=Djuna|last2=Howard|first2=Jessica N.|last3=Ipek|first3=Seyda|last4=Tait|first4=Timothy M. P.|date=2020-03-31|title=QCD Baryogenesis|arxiv=1911.01432|journal=Physical Review D|volume=101|issue=5|pages=055042|doi=10.1103/PhysRevD.101.055042|bibcode=2020PhRvD.101e5042C|issn=2470-0010|doi-access=free}} Thus certain sums of amplitudes for quarks have different absolute values compared to those of anti-quarks. In all, quarks and anti-quarks may have different reflection and transmission probabilities through the domain wall, and it turns out that more quarks coming from the unbroken phase are transmitted compared to anti-quarks.

Thus there is a net baryonic flux through the domain wall. Due to sphaleron transitions, which are abundant in the unbroken phase, the net anti-baryonic content of the unbroken phase is wiped out as anti-baryons are transformed into leptons.{{cite journal|last1=Fujikura|first1=Kohei|last2=Harigaya|first2=Keisuke|last3=Nakai|first3=Yuichiro|last4=Wang|first4=Ruoquan|date=2021-03-08|title=Electroweak-like baryogenesis with new chiral matter|journal=Journal of High Energy Physics|volume=2021|issue=7|page=224|doi=10.1007/JHEP07(2021)224|arxiv=2103.05005|bibcode=2021JHEP...07..224F|s2cid=232168718}} However, sphalerons are rare enough in the broken phase as not to wipe out the excess of baryons there. In total, there is net creation of baryons (as well as leptons).

In this scenario, non-perturbative electroweak interactions (i.e. the sphaleron) are responsible for the B-violation, the perturbative electroweak Lagrangian is responsible for the CP-violation, and the domain wall is responsible for the lack of thermal equilibrium and the P-violation; together with the CP-violation it also creates a C-violation in each of its sides.{{Cite journal|last1=Curtin|first1=David|last2=Jaiswal|first2=Prerit|last3=Meade|first3=Patrick|date=2012-08-01|title=Excluding electroweak baryogenesis in the MSSM|url=https://doi.org/10.1007/JHEP08(2012)005|journal=Journal of High Energy Physics|language=en|volume=2012|issue=8|pages=5|doi=10.1007/JHEP08(2012)005|issn=1029-8479|arxiv=1203.2932|bibcode=2012JHEP...08..005C|s2cid=118747227}}

{{see also|Baryon asymmetry}}The central question to baryogenesis is what causes the preference for matter over antimatter in the universe, as well as the magnitude of this asymmetry. An important quantifier is the asymmetry parameter, given by

$$\backslash eta\; =\; \backslash frac\{n\_\backslash text\{B\}\; -\; n\_\{\backslash bar\; \backslash text\{B\}\}\}\{n\_\backslash gamma\}\; ,$$

where {{math|n_B}} and {{math|n_{{{overline|B}}}}} refer to the number density of baryons and antibaryons respectively and {{math|n_γ}} is the number density of cosmic background radiation photons.{{Cite arXiv |arxiv=hep-ph/0609145 |first=James M. |last=Cline |title=Baryogenesis: Lecture at the Les Houches Summer School, Session 86: Particle Physics and Cosmology: the Fabric of Spacetime. |date=2006-11-22}}

According to the Big Bang model, matter decoupled from the cosmic background radiation (CBR) at a temperature of roughly {{val|3000}} kelvin, corresponding to an average kinetic energy of {{val|3000|u=K}} / ({{val|10.08|e=3|u=K/eV}}) = {{val|0.3|u=eV}}. After the decoupling, the total number of CBR photons remains constant. Therefore, due to space-time expansion, the photon density decreases. The photon density at equilibrium temperature {{mvar|T}} is given by

$$\backslash begin\{align\}$$

n_\gamma &= \frac{1}{\pi^2} {\left(\frac{k_\text{B} T}{\hbar c}\right)}^3 \int_0^\infty \frac{x^2}{e^x - 1} dx \\[2pt]

&= \frac{2\zeta(3)}{\pi^2}{\left(\frac{k_\text{B} T}{\hbar c}\right)}^3 \\[2pt]

&\approx 20.3 \left(\frac{T}{\mathrm{1\,K}}\right)^3 \text{cm}^{-3},

\end{align}

with {{math|k_B}} as the Boltzmann constant, {{mvar|ħ}} as the Planck constant divided by {{math|2π}} and {{mvar|c}} as the speed of light in vacuum, and {{math|ζ(3)}} as Apéry's constant. At the current CBR photon temperature of {{val|2.725|u=K}}, this corresponds to a photon density {{math|n_γ}} of around 411 CBR photons per cubic centimeter.

Therefore, the asymmetry parameter {{mvar|η}}, as defined above, is not the "best" parameter. Instead, the preferred asymmetry parameter uses the entropy density {{mvar|s}},

$$\backslash eta\_s\; =\; \backslash frac\{n\_\backslash text\{B\}\; -\; n\_\{\backslash bar\; \backslash text\{B\}\}\}\{s\}$$

because the entropy density of the universe remained reasonably constant throughout most of its evolution. The entropy density is

$$s\; \backslash \; \backslash stackrel\{\backslash mathrm\{def\}\}\{=\}\backslash \; \backslash frac\{\backslash mathrm\{entropy\}\}\{\backslash mathrm\{volume\}\}\; =\; \backslash frac\{p\; +\; \backslash rho\}\{T\}\; =\; \backslash frac\{2\backslash pi^2\}\{45\}g\_\backslash text\{⁎\}(T)\; T^3\; ,$$

with {{mvar|p}} and {{mvar|ρ}} as the pressure and density from the energy density tensor {{mvar|T_μν}}, and {{mvar|g_⁎}} as the effective number of degrees of freedom for "massless" particles at temperature {{mvar|T}} (in so far as {{math|mc² ≪ k_BT}} holds),

$$g\_\backslash text\{⁎\}(T)\; =\; \backslash sum\_\{i=\backslash mathrm\{bosons\}\}\; g\_i\{\backslash left(\backslash frac\{T\_i\}\{T\}\backslash right)\}^3\; +\; \backslash frac\{7\}\{8\}\backslash sum\_\{j=\backslash mathrm\{fermions\}\}\; g\_j\{\backslash left(\backslash frac\{T\_j\}\{T\}\backslash right)\}^3,$$

for bosons and fermions with {{mvar|g_i}} and {{mvar|g_j}} degrees of freedom at temperatures {{mvar|T_i}} and {{mvar|T_j}} respectively. At the present epoch, {{math|1=s = 7.04 n_γ}}.

Another possible explanation for the cause of baryogenesis is the decay reaction of B-mesogenesis. This phenomenon suggests that in the early universe, particles such as the B-meson decay into a visible Standard Model baryon as well as a dark antibaryon that is invisible to current observation techniques.{{cite journal|last1=Alonso-Álvarez|first1=Gonzalo|last2=Elor|first2=Gilly|last3=Escudero|first3=Miguel|date=2021-01-07|title=Collider signals of baryogenesis and dark matter from B mesons: A roadmap to discovery|journal=Physical Review D|volume=104|issue=3|page=035028|doi=10.1103/PhysRevD.104.035028|arxiv=2101.02706|bibcode=2021PhRvD.104c5028A|s2cid=231419063}}

The asymmetric dark matter proposal investigates mechanisms that would explain the abundance of dark matter but lack of dark antimatter as the consequence of the same effect as would explain baryogenesis.{{Cite journal |last=Petraki |first=Kalliopi |last2=Volkas |first2=Raymond R. |date=2013-07-30 |title=Review of asymmetric dark matter |url=https://www.worldscientific.com/doi/abs/10.1142/S0217751X13300287 |journal=International Journal of Modern Physics A |volume=28 |issue=19 |pages=1330028 |doi=10.1142/S0217751X13300287 |issn=0217-751X|arxiv=1305.4939 }}

• Affleck–Dine mechanism
• Anthropic principle
• Big Bang
• Chronology of the universe
• CP violation
• Leptogenesis (physics)
• Lepton

{{reflist}}

• {{cite book

|author1=E. W. Kolb |author2=M. S. Turner

|name-list-style=amp| year = 1994

| title = The Early Universe

| publisher = Perseus Publishing

| isbn = 978-0-201-62674-2

}}

• {{cite journal

|author=A. D. Dolgov

|year=1997

|title=Baryogenesis, 30 Years After

|arxiv=hep-ph/9707419

|doi=10.1080/01422419808240874

|volume=13

|issue=1–3

|journal=Surveys in High Energy Physics

|pages=83–117

|bibcode = 1998SHEP...13...83D |s2cid=119499400

}}

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