Mysteries of Physics: Baryonic Asymmetry - Sakharov Conditions

Oscar Eatwell
May 18
5 min read

Updated: May 24

Have you ever wondered what is still left to be discovered? At first glance it seems like science has answered all our questions, just look it up on Google or Chat GPT. Yet there remains a plethora of mysteries which are yet to be uncovered. This series of articles seeks to explore the current issues being tackled by physicists, and the theories which could explain potentially everything.

The Standard Model of Particle Physics is considered by many physicists as the most complete theory of physics, as it entirely describes our world as we know it.

Four different categories of particles exist. First are leptons (such as electrons), next quarks (up quarks and down quarks for example), then bosons (such as Z or photons) and finally neutrinos (particles which have extremely low rates of interaction). They make up the basis of everything which surrounds us.

These particles interact with each other due to four main forces mediated by their corresponding bosons. These forces include the electromagnetic, nuclear weak, nuclear strong and gravitational forces, although the latter is yet to be fully described by the Standard Model.

The aim of this article is to focus on the issues surrounding modern physics, notably the Standard Model, not the theory itself. In this article I explore the Sakharov Conditions

Baryonic Asymmetry - Introduction

The Standard Model, despite its great success, does not answer certain fundamental questions about the Universe. One of the greatest mysteries which yet remains is the observed baryon asymmetry between matter and antimatter.

According to the Standard Model’s predictions, the amount of matter and antimatter at the creation of the universe should have been equal, and stayed as such, which is far from being the case. Indeed, the creation of an equal amount of matter and antimatter could either result in the destruction of all matter (through matter antimatter annihilation) or a separation between “clumps” of matter and antimatter.

However, matter still exists -it cannot have all disappeared- and astronomers have found no evidence of galaxies dominated by antimatter. Thus, the question holds: where did all the antimatter go? The Standard Model provides no explanation to this.

Sakharov Conditions (1976)

The Sakharov Conditions are a set of requirements for baryonic asymmetry to happen. The first is Baryon (B) number violation.

The first Sakharov condition is Baryon number violation. Baryon number is a net count of baryons and antibaryons in a system. Each baryon (proton/neutron) has a +1 B number and each antibaryon (antiproton) has a -1 B number while all other particles have a 0 baryonic number.

The Standard Model approximately conserves B number, with only certain rare processes (such as sphaleron processes which I will discuss later) potentially violating it. Also the universe started with an equal amount of matter and antimatter, thus an equal number of baryons and antibaryons, as such the B number should approximately stay constant at B = 0 in the universe. This prediction does not stand empirically due to the obvious predominance of matter. As such, there must have been in the first moments after the Big Bang a B number violating process.

The next Sakharov condition is Charge Parity (CP) symmetry violation. Charge Parity symmetry refers to the fundamental principle that the laws of physics are identical for a particle and its antiparticle (Charge conjugation) in flipped spatial coordinates (Parity). In other words, a particle and its antiparticle behave in the same way, and will decay in the same way (producing the antiparticle to the particle produced by the decay) if their spatial coordinates are flipped (mirror image). Moreover, CP symmetry implies that these decays will happen at the same rate.

Take for example the hypothetical decay of a proton (this does not actually happen in nature since the proton is a stable baryon but is predicted by Grand Unifying Theories -GUTs):

And the equivalent antiparticle decay:

CP symmetry would imply that the rate of these reactions (𝚪) is the same, such that:

CP violation would imply that:

Since this decay violates baryon number - a proton/antiproton (baryon) turns into a positron/electron (lepton) - a CP violation would entail a definitive B number violation (if the third Sakharov Condition is also verified), since either protons or antiprotons decay at a faster rate than their antiparticle.

CP violation is incorporated in the Standard Model in weak force interactions, such as Kaon decays shown in 1964. However, this effect is too small to explain the baryon asymmetry. CP symmetry, and overall the Standard Model, implies that if a particle decays in a B number violating process, its antiparticle will decay at an equal rate in a B number violating process, thus compensating for the B number discrepancy, thus resulting in overall B number conservation.

One could say that CP symmetry ensures that any B number violation happens both for matter and antimatter at equal rates, thus producing a global net zero change to B number. If a process violates CP symmetry, however, these rates could differ, and a heavy particle might decay more often into baryons than its antiparticle decays into antibaryons, causing baryon asymmetry. As such, a combination of both B number violation and CP symmetry violation is necessary to create a baryonic asymmetry.

The third Sakharov condition is departure from thermal equilibrium. Indeed, even in a system with decays which violate both B number and CP symmetry, which thus have decays producing an asymmetry in the amount of matter, if the system is in thermal equilibrium it will produce reverse reactions which compensate for this asymmetry.

For example, if we go back to our hypothetical proton decay present in Beyond the Standard Model (BSM) theories, even if the decay -which violates B number conservation- also violates CP symmetry, in an environment of thermal equilibrium its inverse reaction would compensate for the discrepancy between protons and antiprotons:

If the decay of protons happens at a faster rate than the decay of antiprotons due to CP violation, the reaction above -its reverse reaction- would compensate, and there would be no baryon asymmetry. As such, it is necessary to be in an environment which is out of thermal equilibrium for baryon asymmetry to occur.

For a departure from thermal equilibrium to happen, the interaction rate of a particle must be lower than the expansion rate of the universe (H - hubble expansion rate):

This means that a departure from thermal equilibrium could only have occurred in the early universe. In the early universe, as the universe expands and cools, some particle interaction rates drop below the Hubble expansion rate, making reverse reactions inefficient and leading to a breakdown of equilibrium.

The Particle Hunt

Thus, by analysing the Sakharov conditions, we can deduce that particle decays must satisfy three specific conditions simultaneously to generate baryon asymmetry: it must be a decay which violates B number conservation, and must happen in a context where CP symmetry is violated and it must be out of thermal equilibrium. As such, theoretical physicists have been hunting for decays which could both have violated B number and CP all the while during the period of the early universe where there could have been departure from thermal equilibrium.

“Religion is a culture of faith; science is a culture of doubt.”

― Richard P. Feynman

Beyond the Model

Mysteries of Physics: Baryonic Asymmetry - Sakharov Conditions

Baryonic Asymmetry - Introduction

Sakharov Conditions (1976)

The Particle Hunt

Further Reading

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