Baryogenesis from a Majorana fermion coupled to quarks

In the theory with a Majorana fermion (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi mathvariant="script">X</a:mi></a:mrow></a:math>) coupled to quarklike fermions (<d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mi>Q</d:mi></d:math>) via a dimension-six four-fermion vector-vector interaction, we have computed in an earlier work the baryon asymmetry generated in the decay and scattering processes of the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi mathvariant="script">X</f:mi></f:math> with <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>Q</i:mi></i:math>. In this work we consider such processes in the expanding early Universe, set up the Boltzmann equations governing the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi mathvariant="script">X</k:mi></k:math> and net baryon number densities, and numerically solve them in example benchmark points, taking the thermally averaged decay and scattering rates and their temperature dependence from the earlier study. We find that starting from a baryon symmetric universe at early time, the presently observed baryon asymmetry of the universe (BAU) can be explained in this theory over a wide range of mass scales, <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mrow><n:msub><n:mrow><n:mi>M</n:mi></n:mrow><n:mrow><n:mi>χ</n:mi></n:mrow></n:msub><n:mo>∈</n:mo><n:mo stretchy="false">(</n:mo><n:msup><n:mrow><n:mn>10</n:mn></n:mrow><n:mrow><n:mn>4</n:mn></n:mrow></n:msup><n:mo>,</n:mo><n:msup><n:mrow><n:mn>10</n:mn></n:mrow><n:mrow><n:mn>16</n:mn></n:mrow></n:msup><n:mo stretchy="false">)</n:mo><n:mtext> </n:mtext><n:mtext> </n:mtext><n:mi>GeV</n:mi></n:mrow></n:math> for appropriately chosen couplings. We find that scattering processes play a crucial role in generating the baryon asymmetry in this theory. We present our results in a general manner that should be useful not just in our theory, but also in other related theories that share the essential ingredients. Our results should help guide promising ways to probe such new physics in terrestrial experiments. For instance, in regions of parameter space that yield the observed BAU, we present the rate for neutron-antineutron (<r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mi>n</r:mi><r:mo>−</r:mo><r:mover accent="true"><r:mi>n</r:mi><r:mo stretchy="false">¯</r:mo></r:mover></r:math>) oscillation and discuss the prospects for observing this in upcoming experiments.