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Supersymmetric D-term Twin Higgs
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We propose a new type of supersymmetric Twin Higgs model where the SU(4) invariant quartic term is provided by a D-term potential of a new U(1) gauge symmetry. In the model the 125 GeV Higgs mass can be obtained for stop masses below 1 TeV, and a tuning required to obtain the correct electroweak scale can be as low as 20 %. A stop mass of about 2 TeV is also possible with tuning of order O(10) %.
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Freeze-Twin Dark Matter
Twin electrons and positrons, frozen in via a massive twin photon, can be the dark matter in mirror twin Higgs models with asymmetric reheating, with the required kinetic mixing matching loop-level expectations.
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