The hierarchy problem and gravity
gravitational force per unit mass, alongside a smaller theoretical minimum for the mass of a black hole. In turn, the difference between the Plank mass and the mass of the W and Z bosons would be significantly reduced, demonstrating how the strength of gravity directly affects this mass difference and correspondingly highlighting the vast separation in the orders of magnitude of these two forces. The strengths of the forces described in the Standard Model are dictated by the masses of the bosons that mediate them. Experiments at ATLAS have accurately calculated the mass of the W boson to be approximately 80.4 GeV/c^2 at 0.02% uncertainty, 9 and the Z boson at 91.2 GeV/c^2, which are immensely lighter than the Planck mass, although they are the heaviest force mediators. 10 These masses are influenced by their level of interaction with the Higgs field, through a mechanism known as electroweak symmetry breaking, and thus the energy of the Higgs field is crucial in understanding the hierarchy problem. 11 The Higgs field’s energy is determined by the mass of the Higgs boson, which is where the hierarchy problem begins to surface. It is widely accepted that quantum mechanics imposes limits at the Planck scale: an extremely high energy of up to 10^28 eV, beyond which the effects of quantum gravity are thought to arise. 12 However, the Higgs field does not seem to adhere to this concept, as naturally it seems to apply only up to the TeV scale; the energy of the Higgs field is measured at around 250 GeV, yet this contradicts the idea that quantum field theory is applicable to the order of the Planck scale. 13 This discrepancy introduces us to the notion of unnaturalness, in which the mass of the Higgs boson is seemingly fine-tuned by an unknown means, in spite of its presumed alignment with the Planck scale. 14 The observed Higgs mass is calculated from the combination of its intrinsic mass and the energy it receives from its quantum environment. The latter, often referred to as the ambient quantum correction, is the energy received due to the particle’s surround ings, with this being the primary focus of the hierarchy problem. 15 Notably, the terms ‘energy’ and ‘mass’ can be used interchangeably. 16 At the order of the Planck scale, the ambient quantum energy is extremely high, leading to the assumption of the energy of the Higgs particle to be of a similar order, although we know this not to be the case. The simplified equation for the overall quantum correction received by the Higgs boson can be seen as the product of the mass of the bosons – W, Z and Higgs – subtracted by the masses of the fermions – namely, top quarks – in the quantum environment, and the maximum ambient energy which in this case is the Planck energy. 17 In order to achieve the energy of 125 GeV, the initial multiplier must be extremely small, thus necessitating that the effects of the bosons are almost identical to those of the fermions. This exemplifies the idea of unnaturalness, as these two parameters must be linked for them to cancel out, although there is no evident explanation for this phenomenon. As a result, it can be viewed as though the strength disparity of the weak force and gravity arises due to the unnatural fine-tuning of
9 Atlas 2023c. 10 The Pasayten Institute 2021. 11 Coyle 2019.
12 Tinelmis 2024a. 13 Strassler 2011. 14 Lykken, Solving the hierarchy problem . 15 Lincoln 2013. 16 Perkowitz, E = mc 2 . 17 Lincoln 2013.
93
Made with FlippingBook flipbook maker