Dynamical generation of the baryon asymmetry from a scale hierarchy

We propose a novel baryogenesis scenario where the baryon asymmetry originates directly from a hierarchy between two fundamental mass scales: the electroweak scale <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>v</a:mi></a:math> and the Planck scale <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>M</c:mi><c:mi>P</c:mi></c:msub></c:math>, in the form of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:msub><e:mrow><e:mi>Y</e:mi></e:mrow><e:mrow><e:mi>B</e:mi></e:mrow></e:msub><e:mo>∼</e:mo><e:msqrt><e:mrow><e:mfrac><e:mrow><e:mi>v</e:mi></e:mrow><e:mrow><e:msub><e:mrow><e:mi>M</e:mi></e:mrow><e:mrow><e:mi>P</e:mi></e:mrow></e:msub></e:mrow></e:mfrac></e:mrow></e:msqrt><e:mo>.</e:mo></e:mrow></e:math> This relation straightforwardly gives the observed baryon yield today <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>Y</g:mi><g:mi>B</g:mi></g:msub></g:math>, which can be a hint for underlying fundamental physics. We provide an example of baryogenesis models that yield this relation. Our model is based on the neutrino-portal Affleck-Dine mechanism, which generates the asymmetry of the Affleck-Dine sector during the radiation-dominated era and subsequently transfers it to the baryon number before the electroweak phase transition. The observed baryon asymmetry is then a natural outcome of this scenario. The model is testable as it predicts the existence of a Majoron with a keV mass and an electroweak scale decay constant. The impact of the relic Majoron on the effective number of neutrinos (<i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi mathvariant="normal">Δ</i:mi><i:msub><i:mi>N</i:mi><i:mi>eff</i:mi></i:msub></i:math>) can be measured through near-future cosmic microwave background observations.