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Register a new userUpper bounds on sparticle masses from naturalness or how to disprove weak scale supersymmetry
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While it is often stated that the notion of electroweak (EW) naturalness in supersymmetric models is subjective, fuzzy and model-dependent, here we argue the contrary: electroweak naturalness can be elevated to a {it principle} which is both objective and predictive. We demonstrate visually when too much fine-tuning sets in at the electroweak scale which corresponds numerically to the measure Delta_{BG}~Delta_{EW}> 30. While many constrained SUSY models are already excluded by this value, we derive updated upper bounds on sparticle masses within the two-extra parameter non-universal Higgs model (NUHM2). We confirm the classic Barbieri-Giudice (BG) result that Delta_{BG}<30 implies mu <350 GeV. However, by combining dependent soft terms which appear as multiples of m_{3/2} in supergravity models, then we obtain m(gluino)< 4 TeV as opposed to the BG result that m(gluino)<350 GeV. We compare the NUHM2 results to a similar scan in the pMSSM with 19 weak scale parameters. In the pMSSM with complete one-loop scalar potential plus dominant two-loop terms, then a m(gluino)<7 TeV bound is found. Our tabulation of upper bounds provides a target for experimenters seeking to discover or else falsify the existence of weak scale supersymmetry. In an Appendix, we show contributions to the naturalness measure from one-loop contributions to the weak scale scalar potential.
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We present our work on reconstructing sparticle masses in purely hadronic decay chains, using the $k_T$ jet-algorithm on Monte Carlo simulated events at LHC energies.
Perturbative supersymmetry breaking on the landscape of string vacua is expected to favor large soft terms as a power-law or log distribution, but tempered by an anthropic veto of inappropriate vacua or vacua leading to too large a value for the derived weak scale -- a violation of the atomic principle. Indeed, scans of such vacua yield a statistical prediction for light Higgs boson mass m_h~ 125 GeV with sparticles (save possibly light higgsinos) typically beyond LHC reach. In contrast, models of dynamical SUSY breaking (DSB) -- with a hidden sector gauge coupling g^2 scanned uniformly -- lead to gaugino condensation and a uniform distribution of soft parameters on a log scale. Then soft terms are expected to be distributed as $m_{rm soft}^{-1}$ favoring small values. A scan of DSB soft terms generally leads to $m_hll 125$ GeV and sparticle masses usually below LHC limits. Thus, the DSB landscape scenario seems excluded from LHC search results. An alternative is that the exponential suppression of the weak scale is set anthropically on the landscape via the atomic principle.
We use the idea of partial compositeness in a minimal supersymmetric model to relate the fermion and sfermion masses. By assuming that the Higgs and third-generation matter is (mostly) elementary, while the first- and second-generation matter is (mostly) composite, the Yukawa coupling hierarchy can be explained by a linear mixing between elementary states and composite operators with large anomalous dimensions. If the composite sector also breaks supersymmetry, then composite sfermions such as selectrons are predicted to be much heavier than the lighter elementary stops. This inverted sfermion mass hierarchy is consistent with current experimental limits that prefer light stops ($mathcal{O}(10)$ TeV) to accommodate the 125 GeV Higgs boson, while predicting heavy first- and second-generation sfermions (${gtrsim 100}$ TeV) as indicated by flavor physics experiments. The underlying dynamics can be modelled by a dual 5D gravity theory that also predicts a gravitino dark matter candidate ($gtrsim$ keV), together with gauginos and Higgsinos, ranging from 10-90 TeV, that are split from the heavier first- and second-generation sfermion spectrum. This intricate connection between the fermion and sfermion mass spectrum can be tested at future experiments.
Gauge coupling unification and the stability of the Higgs vacuum are among two of the cherished features of low-energy supersymmetric models. Putting aside questions of naturalness, supersymmetry might only be realised in nature at very high energy scales. If this is the case, the preservation of gauge coupling unification and the stability of the Higgs vacuum would certainly require new physics, but it need not necessarily be at weak scale energies. New physics near the unification scale could in principle ensure Grand Unification, while new physics below $mu sim 10^{10}$ GeV could ensure the stability of the Higgs vacuum. Surprisingly however, we find that in the context of a supersymmetric SO(10) Grand Unified Theory, gauge coupling unification and the Higgs vacuum stability, when taken in conjunction with existing phenomenological constraints, require the presence of $mathcal{O}$(TeV)-scale physics. This weak-scale physics takes the form of a complex scalar SU(2)$_L$ triplet with zero hypercharge, originating from the $mathbf{210}$ of SO(10).
Mirage mediation realized in the KKLT flux compactification can naturally suppress the up-type Higgs soft mass at low energy scales, and consequently it can reduce the degree of electroweak fine-tuning up to a loop factor. Interestingly, this feature holds even in high-scale supersymmetry as long as the gauge coupling unification is achieved for light Higgsinos below TeV. Under the experimental constraints on the observed Higgs boson, it turns out that mirage mediation can exhibit low electroweak fine-tuning better than a few percent for stops between about 2 and 6 TeV, i.e., at the same level as in the weak scale supersymmetry, if the Higgsinos are around or below a few hundred GeV.
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