Abstract
We stress the potential usefulness of renormalization group invariants. Especially particular combinations thereof could for instance be used as probes into patterns of supersymmetry breaking in the MSSM at inaccessibly high energies. We search for these renormalization group invariants in two systematic ways: on the one hand by making use of symmetry arguments and on the other by means of a completely automated exhaustive search through a large class of candidate invariants. At the one-loop level, we find all known invariants for the MSSM and in fact several more, and extend our results to the more constrained pMSSM and dMSSM, leading to even more invariants. Extending our search to the two-loop level we find that the number of invariants is considerably reduced.
Highlights
(MSSM) will be one of the main focuses for the second run of the Large Hadron Collider
Particular combinations thereof could for instance be used as probes into patterns of supersymmetry breaking in the MSSM at inaccessibly high energies
If any of the several possible breaking mechanisms is realized in nature, this will be signified by a characteristic unification of some soft supersymmetry breaking parameters at a high energy scale
Summary
Let us consider a renormalized theory with a running parameter p(μ). We define the corresponding β-function as follows: β(p) ≡ 16π2 dp , dt (2.1). We can use the invariants in (2.4) to check whether the unification of w, x, y, z is realized in nature Suppose that these scalar masses unify to the value s at some scale, we would have. The top-down method requires knowledge of both the unification scale and value in order to evolve the parameters down to experimentally accessible scales. The use of RG invariants requires no knowledge of the unification scale or value whatsoever, so that this problem is avoided. In our example the sum rule of eq (2.6) does not involve the parameter v, which does not participate in the unification anyway Both the top-down and bottom-up methods require a value for v to numerically evolve the other parameters. Both methods will be applied to find invariants for the MSSM, the dMSSM, and the pMSSM
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