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An extra Abelian gauge symmetry is motivated in many new physics models inboth supersymmetric and nonsupersymmetric cases. Such a new gauge symmetry mayinteract with both the observable sector and the hidden sector. Wesystematically investigate the most general residual discrete symmetries inboth sectors from a common Abelian gauge symmetry. Those discrete symmetriescan ensure the stability of the proton and the dark matter candidate. A hiddensector dark matter candidate (lightest U-parity particle or LUP) interacts withthe standard model fields through the gauge boson Z', which may selectivelycouple to quarks or leptons only. We make a comment on the implications of thediscrete symmetry and the leptonically coupling dark matter candidate, whichhas been highlighted recently due to the possibility of the simultaneousexplanation of the DAMA and the PAMELA results. We also show how to constructthe most general U(1) charges for a given discrete symmetry, and discuss therelation between the U(1) gauge symmetry and R-parity.

Common gauge origin of discrete symmetries in observable sector and hidden sector