Should Squarks Be Degenerate?

For generic squark masses, box diagrams with squarks and gluinos give unacceptably large contributions to neutral meson (K, B and D) mixing. The standard solution to this problem is to assume that squarks are degenerate to a very good approximation. We suggest an alternative mechanism to suppress squark contributions to flavor changing neutral currents: the alignment of quark with squark mass matrices. This mechanism arises naturally in the framework of Abelian horizontal symmetries. Within the Standard Model, flavor changing neutral current (FCNC) interactions are highly suppressed by the weak coupling constant, by small mixing angles and by small fermion masses. This makes such processes a particularly sensitive probe of new physics at high energy scales. New contributions to FCNC may be comparable to or even dominate over the Standard Model contributions. Thus, measurements of FCNC processes such as neutral meson mixing [1], ∆mK mK = 7× 10, ∆mB mB ≈ 7× 10, ∆mD mD ≤ 7× 10, (1) and radiative B-decay [2], BR(B → Xsγ) ≤ 5.4× 10, (2) put severe constraints on extensions of the Standard Model. Supersymmetric extensions of the Standard Model predict large new contributions to FCNC processes. Squarks and gluinos contribute to (1) through box diagrams and to (2) through penguin diagrams. A possible suppression due to large squark and gluino masses is easily compensated for by three enhancement factors: (i) Matrix elements of new four quark operators are enhanced due to different Lorentz structure; (ii) The weak coupling of the Standard Model diagrams is replaced by the strong coupling; (iii) The GIM mechanism does not operate for generic squark masses. The resulting contributions are so large, even for squark masses as heavy as 1 TeV , that the processes (1) and (2) severely constrain the form of the squark mass matrices.