Abstract
We extend the Standard Model (SM) with parity symmetry, motivated by the strong CP problem and dark matter. In our model, parity symmetry is conserved at high energy by introducing a mirror sector with the extra gauge symmetry, SU(2)R × U(1)R. The charges of SU(2)R × U(1)R are assigned to the mirror fields in the same way as in the SM, but the chiralities of the mirror fermions are opposite to respect the parity symmetry. The strong CP problem is resolved, since the mirror quarks are also charged under the SU(3)c in the SM. In the minimal setup, the mirror gauge symmetry leads to stable colored particles which would be inconsistent with the observed data, so that we introduce two scalars in order to deplete the stable colored particles. Interestingly, one of the scalars becomes stable because of the gauge symmetry and therefore can be a good dark matter candidate. We especially study the phenomenology relevant to the dark matter, i.e. thermal relic density, direct and indirect searches for the dark matter. The bounds from the LHC experiment and the Landau pole are also taken into account. As a result, we find that a limited region is viable: the mirror up quark mass is around [600 GeV, 3 TeV] and the relative mass difference between the dark matter and the mirror up quark or electron is about mathcal{O} (1–10%). We also discuss the neutrino sector and show that the right-handed neutrinos in the mirror sector can increase the effective number of neutrinos or dark radiation by 0.14.
Highlights
Another issue of the Standard Model (SM) is the so-called strong CP problem
Scalar fields are introduced in addition to the above minimal parity-symmetric model, otherwise one of the mirror quarks or leptons would be stable as a result of the gauge symmetry, since there is no portal coupling between the SM and the mirror sector [23]
Even if we introduce some scalar fields charged under SU(2)R and/or U(1)R gauge symmetry to break the U(1)Rem symmetry spontaneously, the remnant symmetry from U(1)Rem would guarantee the stability of the U(1)Rem-charged particles
Summary
We shall construct an extended model with SU(3)c × SU(2)L × U(1)L × SU(2)R × U(1)R which respects the parity symmetry. The gauge interaction should respect the parity symmetry: Lg. where FμIν is the field strength composed by AIμ. We can find the gauge kinetic term in the U(1) gauge symmetry case Based on this generic argument, we extend the SM to the parity conserving model. The Yukawa couplings among the mirror fields are written down as follows: LR = −Ydij QRiHRdLj − Yuij QRiHRuLj − Yeij lRiHReLj + h.c. Note that the Yukawa couplings are defined to respect the parity symmetry, that corresponds to the following exchange: QiL(t, x) ↔ QRi(t, −x), lLi (t, x) ↔ lRi(t, −x), uiR(t, x) ↔ uLi(t, −x), eiR(t, x) ↔ eLi(t, −x), diR(t, x) ↔ dLi(t, −x), HR(t, x) ↔ HL(t, −x). We propose one extension to avoid these stable charged particles
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