Abstract
We show that spontaneous baryogenesis occurs automatically in relaxion models if the reheating temperature is larger than the weak scale, provided the Standard Model fields are charged under the U(1) of which the relaxion is a pseudo-Nambu-Goldstone boson. During the slow roll, the relaxion breaks CPT, biasing the thermal equilibrium in favor of baryons, with sphalerons providing the necessary baryon number violation. We calculate the resulting baryon asymmetry, explore the possible constraints on this scheme and show that there is a swath of parameter space in which the current observations are matched. Successful baryogenesis can be achieved for a range of relaxion masses between $10^{-10}$ and $10^{-5}$ eV. The mechanism operates precisely in the region of parameter space where recent work has shown relaxion oscillations to be a dark matter candidate.
Highlights
An interesting scenario has been suggested [1] to explain why the Higgs mass is much smaller than the fundamental scale
Adapting a long-standing idea of Abbott that attempted to explain the smallness of the cosmological constant [2], the “relaxion” mechanism incorporates an interplay of two explicit/ anomalous breakings of a Goldstone shift symmetry, to relax the Higgs mass dynamically to values close to the weak scale
The smaller breaking drives the pseudoNambu-Goldstone mode (PNGB), the so-called relaxion, which samples over Higgs masses, while the larger breaking comes in the form of a periodic axionlike potential that is proportional to the Higgs vacuum expectation value (VEV): the dynamical evolution of the relaxion stops as soon as the Higgs VEV turns on
Summary
An interesting scenario has been suggested [1] to explain why the Higgs mass is much smaller than the fundamental scale. The term in Eq (1) is invariant, a time derivative of φ yields a CPT violating chemical potential for baryon number [11] This biases sphaleron transitions for temperatures around the electroweak scale where they are active and dominant [4,5,6,7,8]. After reheat until the temperature drops below Tsph ∼ Tew ∼ 130 GeV [13], B þ L violating transitions (blue) are active in the plasma, dying away exponentially fast below Tsph During this period the relaxion rolls (green) towards its final value which it reaches at temperature Tc. one has to satisfy the constraint Tr > Tsph > Tc, which can be done. The baryon asymmetry and the dark-matter relic density are correct in roughly the same region of parameter space
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