Abstract
The supersymmetry preserving mu parameter in SUSY theories is naively expected to be of order the Planck scale while phenomenology requires it to be of order the weak scale. This is the famous SUSY mu problem. Its solution involves two steps: 1. first forbid mu, perhaps via some symmetry, and then 2. re-generate it of order the scale of soft SUSY breaking terms. However, present LHC limits suggest the soft breaking scale m_{soft} lies in the multi-TeV regime whilst naturalness requires mu~ m_{W,Z,h}~ 100 GeV so that a Little Hierarchy (LH) appears with mu << m_{soft}. We review twenty previously devised solutions to the SUSY mu problem and re-evaluate them in light of whether they are apt to support the LH. We organize the twenty solutions according to: 1. solutions from supergravity/superstring constructions, 2. extended MSSM solutions, 3. solutions from an extra local U(1)' and 4. solutions involving Peccei-Quinn (PQ) symmetry and axions. Early solutions would invoke a global Peccei-Quinn symmetry to forbid the mu term while relating the mu solution to solving the strong CP problem via the axion. We discuss the gravity-safety issue pertaining to global symmetries and the movement instead toward local gauge symmetries or R-symmetries, either continuous or discrete. At present, discrete R-symmetries of order M (Z_M^R) which emerge as remnants of Lorentz symmetry of compact dimensions seem favored. Even so, a wide variety of regenerative mechanisms are possible, some of which relate to other issues such as the strong CP problem or the generation of neutrino masses. We also discuss the issue of experimental verification or falsifiability of various solutions to the mu problem. Almost all solutions seem able to accommodate the LH.
Highlights
REFORMULATING THE μ PROBLEM FOR THE LHC ERASupersymmetry (SUSY) provides a solution to the big hierarchy problem—why does the Higgs mass not blow up to the GUT/Planck scale?—via a neat cancellation of quadratic divergences which is required by extending the Poincaregroup of spacetime symmetries to its maximal structure [1,2]
SUSY is supported indirectly via the confrontation of data with virtual effects in that 1) the measured gauge couplings unify under minimal supersymmetric Standard Model (MSSM) renormalization group evolution [3], 2) the measured value of mt falls in the range required for a radiatively driven breakdown of electroweak
The new LHC Higgs mass measurement and sparticle mass limits seem to have exacerbated the so-called little hierarchy problem (LHP) [8]: why does the Higgs mass not blow up to the soft SUSY-breaking scale msoft ≳ several TeV, or what stabilizes the apparent hierarchy mh ≪ msoft? The LHP opens up the naturalness question: how can it be that the weak scale mweak ∼ mW;Z;h ∼ 100 GeV without unnatural fine-tunings of dimensionful terms in the MSSM
Summary
Supersymmetry (SUSY) provides a solution to the big hierarchy problem—why does the Higgs mass not blow up to the GUT/Planck scale?—via a neat cancellation of quadratic divergences which is required by extending the Poincaregroup of spacetime symmetries to its maximal structure [1,2]. While this may seem to be a tuning in itself, such a selection seems to automatically emerge from SUSY within the string-landscape picture [18,19] In this scenario, there is a statistical attraction towards large soft terms which must be balanced by the anthropic requirement that EW symmetry be properly broken and with a weak-scale magnitude not too far from its measured value[20]. (2) extended MSSM solutions, (3) solutions from an extra local Uð1Þ0 and (4) solutions involving PQ symmetry and axions Many of these solutions tend to relate the μ parameter to the scale of soft SUSY breaking which would place the μ parameter well above the weak scale and require significant EW fine-tuning. Some pedagogical reviews providing an in-depth overview of supersymmetric models of particle physics can be found in Ref. [2]
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