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Register a new userThe DFSZ axion in the CMB
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We perform for the first time a dedicated analysis of cosmological constraints on DFSZ QCD axion models. Such constructions are especially interesting in light of the recent Xenon-1T excess and of hints from stellar cooling. In DFSZ models, for $m_agtrsim 0.1$ eV, scatterings of pions and muons can produce a sizable cosmic background of thermal axions, that behave similarly to massive neutrinos. However, the pion coupling depends on the alignment between the vevs of two Higgs doublets, and can be significantly suppressed or enhanced with respect to the KSVZ scenario. Using the latest Planck and BAO data, we find $m_aleq 0.2~text{eV}$ at $95%$ C.L., when the axion coupling to pions $c_{api}$ is maximal. Constraints on $m_a$, instead, can be significantly relaxed when $c_{api}$ is small. In particular, we point out that in the so-called DFSZ-II model, where the axion coupling to leptons does not vanish simultaneously with $c_{api}$, production via muons gives $m_aleq 0.6~text{eV}$ at $95%$ C.L., whereas in the DFSZ-I model bounds on $m_a$ can be fully lifted. We then combine cosmological data with recent hints of a DFSZ axion coupled to electrons from the Xenon-1T experiment, finding in this case that the axion mass is constrained to be in the window $0.07 ~text{eV} lesssim m_a lesssim 1.8, (0.3)~text{eV}$ for the DFSZ-I (DFSZ-II) model. A similar analysis with stellar cooling hints gives $3 ~text{meV} lesssim m_a lesssim 0.2 ~text{eV}$ for DFSZ-II, while no constraint arises in the DFSZ-I case. Forthcoming CMB Stage 4 experiments will be able to further test such scenarios; for instance the Xenon-1T window should be fully probed at $2sigma$ for a DFSZ-I axion.
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Among many possibilities, solar axion has been proposed to explain the electronic recoil events excess observed by Xenon1T collaboration, although it has tension with astrophysical observations. The axion couplings, to photon $g_{agamma}$ and to electron $g_{ae}$ play important roles. These couplings are related to the Peccei-Quinn (PQ) charges $X_f$ for fermions. In most of the calculations, $g_{agamma}$ is obtained by normalizing to the ratio of electromagnetic anomaly factor $E = TrX_f Q^2_f N_c$ ($N_c$ is 3 and 1 for quarks and charged leptons respectively) and QCD anomaly factor $N = TrX_q T(q)$ ($T(q)$ is quarks $SU(3)_c$ index). The broken PQ symmetry generator is used in the calculation which does not seem to extract out the components of broken generator in the axion which are eaten by the $Z$ boson. However, using the physical components of axion or the ratio of anomaly factors should obtain the same results in the DFSZ for $g_{agamma}$. When going beyond the standard DFSZ models, such as variant DFSZ models, where more Higgs doublets and fermions have different PQ charges, one may wonder if the results are different. We show that the two methods obtain the same results as expected, but the axion couplings to quarks and leptons $g_{af}$ (here f indicates one of the fermions in the SM) are more conveniently calculated in the physical axion basis. The result depends on the values of the vacuum expectation values leading to a wider parameter space for $g_{af}$ in beyond the standard DFSZ axion. We also show explicitly how flavor conserving $g_{af}$ couplings can be maintained when there are more than one Higgs doublets couple to the up and down fermion sectors in variant DFSZ models at tree level, and how flavor violating couplings can arise.
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