The hierarchy problem and gravity
the Higgs mass – an extremely small value compared to the Planck scale beyond which it should break down – as far as current observations and experiments suggest.
A popular theory among physicists to address this problem involves the proposition of supersymmetric particles, which proposes a relationship between all fermions and bosons. 18 Currently, there are seven natural symmetries, all of which are quantified by numbers. 19 No further similar symmetries are possible, according to the Coleman-Mandula theorem, 20 although this does not include symmetries that are quantified by Grassmann numbers – the numbers that are responsible for the quantum field of fermions. This introduces the possibility of a translational symmetry between the fermionic and bosonic spacetimes, interchanging bosons and fermions. 21 Since each particle is assigned to another opposing particle with a 1/2 spin value difference from the original particle, the numbers of integer- spin fermions and half integer-spin bosons are equal, resulting in an almost perfect cancellation of their effects. 22 Hence, it is possible to remove the notion of unnatural fine-tuning in calculating the Higgs mass. Mathematically, supersymmetry prevents a quadratic divergence in the Higgs mass correction, replacing it with a logarithmic divergence, which aligns with the theoretical requirements for a natural explanation of the Higgs mass. 23 Furthermore, supersymmetric particles serve as potential dark matter candidates, whilst additionally providing an explanation for how the strong, weak, and electromagnetic forces were originally unified at the extremely high energies of the Big Bang. 24 This consequently elevates the possibility of the particles’ existence, although it does not help in strengthening its validity as a solution for the hierarchy problem. However, the underlying concern with this theory is its lack of experimental confirmation; research at CERN and Fermilab – currently undergoing operations up to 13.6 TeV – have yet to detect the existence of any such supersymmetric particles. 25 This lack of evidence is serving to increasingly invalidate this theory in explaining this hierarchy problem, particularly due to the supersymmetric particles not having a mass equivalence, which would have otherwise been confirmed by modern research. Therefore, the ideal supersymmetric theory is not valid, yet current energy levels at the LHC are far below the order of the Planck scale which leaves a significant gap in the search for higher energy supersymmetric particles. There exists an additional theory of the Higgs boson as a composite particle of which its entire form would be experimentally present at higher energy collisions that exceed our current capabilities. 26 This would potentially alter our current understanding of the Higgs mechanism, as it could align with aspects of technicolour theory, where additional massless fermions contribute to the effect of particle mass arising, as opposed to of electroweak symmetry breaking. 27
18 CERN, Supersymmetry. 19 Purdue, SUSY. 20 Leonhardt 2016. 21 Purdue, SUSY. 22 CERN, Supersymmetry. 23 Smith 2019. 24 CERN, Supersymmetry.
25 Atlas 2023b. 26 Smith 2019. 27 Modern Physics, Technicolor theories .
94
Made with FlippingBook flipbook maker