We present a search for pair production of doubly charged Higgs bosons in the processes qq¯→H(++)H(--) decaying through H(±±)→τ(±)τ(±),μ(±)τ(±),μ(±)μ(±). The search is performed in pp¯ collisions at a center-of-mass energy of √s = 1.96 TeV using an integrated luminosity of up to 7.0 fb(-1) collected by the D0 experiment at the Fermilab Tevatron Collider. The results are used to set 95% C.L. limits on the pair production cross section of doubly charged Higgs bosons and on their mass for different H(±±) branching fractions. Models predicting different H(±±) decays are investigated. Assuming B(H(±±)→τ(±)τ(±))=1 yields an observed (expected) lower limit on the mass of a left-handed H(L)(±±) boson of 128 (116) GeV and assuming B(H(±±)→μ(±)τ(±))=1 the corresponding limits are 144 (149) GeV. In a model with B(H(±±)→τ(±)τ(±))=B(H(±±)→μ(±)τ(±))=B(H(±±)→μ(±)μ(±))=1/3, we obtain M(H(L)(±±))>130 (138) GeV.
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