How natural is a small \barθin left-right SUSY models ?

In the world without an axion the smallness of $\barθ$ may be achieved due to a spontaneously broken discrete left-right symmetry. We analyze the radiatively induced \barθin the context of generic left-right symmetric SUSY models without assuming flavor degeneracy in the squark sector. Left-right symmetry allows to keep \barθwithin its present bound only if the inter-generational mass splitting in the squark sector at the scale of the left-right symmetry breaking is smaller than 0.5%. We also consider the naturalness of m_u=0 solution to the strong CP problem in the context of horizontal flavor symmetries. A strong bound on the combination of the horizontal charges in the Up quark sector is found in this case.

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