A Review of Naturalness and Dark Matter Prediction for the Higgs Mass in MSSM and Beyond

Abstract

Within a two-loop leading-log approximation, we review the prediction for the lightest Higgs mass (m h ) in the framework of constrained MSSM (CMSSM), derived from the naturalness requirement of minimal fine-tuning (∆) of the electroweak scale, and dark matter consistency. As a result, the Higgs mass is predicted to be just above the LEP2 bound, m h = 115.9 ± 2 GeV, corresponding to a minimal ∆ = 17.8, value obtained from consistency with electroweak and WMAP (3σ) constraints, but without the LEP2 bound. Due to quantum corrections (largely QCD ones for m h above LEP2 bound), ∆ grows ≈ exponentially on either side of the above value of m h , which stresses the relevance of this prediction. A value m h > 121 (126) GeV cannot be accommodated within the CMSSM unless one accepts a fine-tuning cost worse than ∆ > 100 (1000), respectively. We review how the above prediction for m h and ∆ changes under the addition of new physics beyond the MSSM Higgs sector, parametrized by effective operators of dimensions d=5 and d=6. For d=5 operators, one can obtain values m h ≤ 130 GeV for ∆ < 10. The size of the supersymmetric correction that each individual operator of d=6 brings to the value of m h for points with ∆ < 100 (< 200), is found to be small, of few ≤ 4 GeV (≤ 6 GeV) respectively, for M = 8 TeV where M is the scale of new physics. This value decreases (increases) by approximately 1 GeV for a 1 TeV increase (decrease) of the scale M . The relation of these results to the Atlas/CMS supersymmetry exclusion limits is presented together with their impact for the CMSSM regions of lowest fine-tuning. †

Composite Higgsino

“…(A.2), there are also contributions from other operators and it have been discussed, for example, in refs. [64][65][66][67][68][69]. 13 Open Access.…”

Fine tuning in the constrained exceptional supersymmetric standard model

“…Moreover, imposing universal boundary conditions, which is what characterises the cE 6 SSM, means that all low energy SUSY parameters can be expanded in terms of a few GUT-scale universal and fundamental input parameters, namely,…”

“…The large radiative contributions from stops needed to raise it to the observed value typically imply very large fine tuning. For example the constrained MSSM (cMSSM) [5] has been shown to require fine tuning of O(1000) if it is to contain a 125 GeV Higgs mass [6,7].…”

Flavour physics constraints in the BMSSM

“…For M of the order of a few TeV, the non-renormalizable corrections of the BMSSM are sizeable and they have been analyzed in the context of electroweak baryogenesis [15][16][17], dark matter [16,[18][19][20][21][22][23][24], Higgs phenomenology [25][26][27] and collider phenomenology [28,29]. In a nutshell, it has been shown that the consequence of this simple extension of the MSSM including higher order operators which are suppressed by inverse powers of a scale of new physics somewhat higher than the electroweak breaking scale, can significantly relax the constraints coming from the above mentioned physical observables.…”