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{{Refimprove|date=February 2013}}
{{expert|Physics|reason=This article reads like an essay and fails to clearly define the problem, or give clear reasons why everyday expectations should be met. (For example, is the [[Riemann hypothesis]], which seems like an impossible coincidence, a problem of this type?)|date=June 2024}}
In [[particle physics]] the '''little hierarchy problem''' in the [[Minimal Supersymmetric Standard Model]] (MSSM) is a refinement of the [[hierarchy problem]]. According to [[quantum field theory]], the mass of the [[Higgs boson]] must be rather light for the [[electroweak theory]] to work. However, the loop corrections to the mass are naturally much greater; this is known as the hierarchy problem. New physical effects such as [[supersymmetry]] may in principle reduce the size of the loop corrections, making the theory natural. However, it is known from experiments that new physics such as [[superpartner]]s does not occur at very low energy scales, so even if these new particles reduce the loop corrections, they do not reduce them enough to make the renormalized Higgs mass completely natural. The expected value of the Higgs mass is about 10% of the size of the loop corrections which shows that a certain "little" amount of [[Fine-tuning (physics)|fine-tuning]] seems necessary.<ref name="HitoshiMurayama">
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Particle physicists have different opinions as to whether the little hierarchy problem is serious.
By supersymmetrizing the Standard Model, one arrives at a hypothesized solution to the gauge hierarchy, or big hierarchy, problem in that supersymmetry guarantees cancellation of quadratic divergences to all orders in perturbation theory. The simplest supersymmetrization of the SM leads to the Minimal Supersymmetric Standard Model or MSSM. In the MSSM, each SM particle has a partner particle known as a super-partner or
sparticle. For instance, the left- and right-electron helicity components have scalar partner selectrons {{overset|lh=0.6|~|e}}{{sub|L}} and {{overset|lh=0.6|~|e}}{{sub|R}} respectively, whilst the eight colored gluons have eight colored spin-1/2 gluino superpartners. The MSSM Higgs sector must necessarily be expanded to include two rather than one doublets leading to five physical Higgs particles h, H, A and H{{sup|±}}, whilst three of the eight Higgs component fields are absorbed by the W{{sup|±}} and Z bosons to make them massive. The MSSM is actually
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Nonetheless, verification of weak scale SUSY (WSS, SUSY with superpartner masses at or around the weak scale as characterized by ''m''(W, Z, h) ≈ 100 GeV) requires the direct observation of at least some of the superpartners in sufficiently energetic colliding beam experiments.{{clarify|date=August 2018}} As recent as 2017, the CERN Large Hadron Collider, a p–p collider operating at centre-of-mass energy 13 TeV, has not found any evidence for superpartners. This has led to mass limits on the gluino ''m''{{sub|{{overset|lh=0.6|~|g}}}} > 2 TeV and on the lighter top squark ''m''{{sub|{{overset|lh=0.6|~|t}}{{sub|1}}}} > 1 TeV (within the context of certain simplified models that are assumed to make the experimental analysis more tractable). Along with these limits, the rather large measured value of ''m''{{sub|h}} ≈ 125 GeV seems to require TeV-scale highly mixed top squarks. These combined measurements have raised concern now about an emerging Little Hierarchy problem characterized by ''m''{{sub|W,Z,h}} ≪ ''m''{{sub|sparticle}}. Under the Little Hierarchy, one might expect the now log-divergent light Higgs mass to blow up to the sparticle mass scale unless one fine-tunes. The Little Hierarchy problem has led to concern that WSS is perhaps not realized in nature, or at least not in the manner typically expected by theorists in years past.
In the MSSM, the light Higgs mass is calculated to be
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