U(1)B1+B2−2L1 mediation for the natural SUSY and the anomalous muon g−2

We propose a U(1)′ mediated supersymmetry (SUSY) breaking, in which U(1)′ is identified with U(1)B1+B2−2L1. The U(1)B1+B2−2L1 gauge symmetry, which is anomaly-free with the field contents of the minimal supersymmetric standard model, assigns ±1/3 charges to the first and second generations of the quarks, and ∓2 to the first generation of the leptons. As a result, the first two generations of squarks acquire masses of about 7 TeV, and the first generation of the sleptons do those of 40 TeV, respectively, in the presence of one or three pairs of extra vector-like matter {5,5¯}. Non-observation on extra colored particles below 1 TeV at the large hadron collider, and also the flavor violations such as μ−→e−γ are explained. By virtue of such a gauge symmetry, proton stability can be protected. The other squarks and sleptons as well as the gauginos can obtain masses of order 102−3 GeV through the conventional gravity or gauge mediated SUSY breaking mechanism. The relative light smuon/sneutrino and the neutralino/chargino could be responsible for the (g−2)μ deviated from the standard model prediction. The stop mass of ∼500GeV relieves the fine-tuning problem in the Higgs sector. Two-loop effects by the relatively heavy sfermions can protect the smallness of the stop mass from the radiative correction by the heavy gluino (≳1TeV). Extra vector-like matter can enhance the radiative corrections to the Higgs mass up to 126 GeV, and induce the desired mixing among the chiral fermions after U(1)B1+B2−2L1 breaking.