= Solution
A <grand unified theory> embeds the strong and electroweak <gauge groups> in a larger group, for example $SU(3)_c\times SU(2)_L\times U(1)_Y\subset SU(5)$. <quarks> and <leptons> can belong to common representations, while heavy extra gauge or scalar <bosons> connect them. The resulting interactions can violate <baryon number>, unlike ordinary perturbative Standard Model reactions. Running gauge couplings and proton-decay searches test such ideas; unification is a theoretical possibility, not an established observation.<Unified Gauge Theories and the Baryon Number of the Universe by Motohiko Yoshimura>[Abstract, early-universe baryon-number-violating reactions in unified theories; later erratum noted in source record]{ref}
<baryogenesis> must explain why a nearly matter-antimatter-symmetric early state evolves into a surviving <baryon asymmetry>. In the usual local CPT-invariant framework, the <Sakharov conditions> require baryon-number violation, C and <CP violation>, and departure from <thermal equilibrium>. <baryon> conservation would forbid creating a net excess; exact conjugation symmetries would pair baryon-producing processes with equal antibaryon production; equilibrium with no imposed asymmetry would erase a source term through <detailed balance>.
For heavy particles $X$ and $\bar X$, let decay channels carry different <baryon numbers>. CP-violating interference can make their <branching fractions> differ, even though <CPT symmetry> requires equal total widths. Defining the mean <baryon number> produced per decay as $\epsilon$, an out-of-equilibrium abundance can generate $n_B/s$ of order $\epsilon$ times its initial number per <entropy>, reduced by inefficient production and washout. A rough condition is that decays become effective after inverse production has ceased, with the relevant reaction rate compared with the <Hubble parameter>. Complex couplings alone do not guarantee a nonzero rate asymmetry: a relative <absorptive phase> is also needed.
Survival matters as much as production. Electroweak <sphalerons> violate $B+L$ while conserving <baryon-minus-lepton number> $B-L$, so a minimal GUT-generated asymmetry with $B-L=0$ can be washed out if <sphalerons> and the other relevant reactions equilibrate. Generating nonzero $B-L$, as in suitable heavy-Majorana-neutrino <leptogenesis>, can avoid this problem. \b[A viable GUT <baryogenesis> model must generate an asymmetry and demonstrate that subsequent reactions do not erase it.] The <Sakharov conditions> are necessary ingredients under these assumptions, not a numerical prediction of the observed abundance.
Back to article page
