arXiv subjects

Seyed Khaki

Publications and source records attributed to Seyed Khaki.

2 recordsLinked to original sources

arXiv2024

An examination of the hierarchy problem beyond the Standard Model

As the Higgs field is a weak isospin doublet of the SU(2) symmetry, the Standard Model requires any symmetry solution to the Higgs hierarchy problem to be SU(2) invariant, a constraint on the type of the symmetry. However, the hierarchy problem is about the size. The size of SU(2) for the Higgs boson can be calculated by $|$SU$_2(\ell)|=\ell^3-\ell$, having the Higgs mass $M_H=1/\ell_{H}\approx125$ GeV. To find the origin of the relative smallness of the Higgs mass in Planck units, alternatively, we search for the origin of such a large order assuming that it stems from an unknown field theory X beyond the Standard Model. Accordingly, this order, which corresponds to the quantum of the Higgs field, should determine the order of quantum/core of X symmetry, its automorphism group. We calculate $|$Aut(X)$|\approx8.2\times 10^{53}$, close to the order of the Monster sporadic group, $|\mathbb M|\approx 8.1\times 10^{53}$, the automorphism group of the Monster CFT, which we therefore conjecture to be X. To examine this conjecture, we calculate the mass of a scalar boson whose SU(2) order is determined by $|\mathbb M|$, observing a 125.4 GeV boson mass and a 245.7 GeV VEV. The Monster CFT does not have any spin-1 operators and Kac-Moody symmetry. Therefore, based on the CFT/(A)dS correspondences, it only describes pure gravity without the gauge fields. In search of a gauge theory candidate, we promote SU(2) (double cover of SO(3)), to SO($d$), and show that the same $\mathbb M$-symmetric vacuum configuration reaches the Planck mass of quantum gravity precisely at $d=32$ (with 99\% accuracy). Then, the spin-1 boson mass of the eligible gauge candidates, SO(32) and $E_8\times E_8$, is calculated to be 80.9 GeV. Further, several pieces of evidence are provided supporting the conjecture.

physics.gen-ph↗

arXiv2024

Original $\mathbb F_1$ in emergent spacetime

The existence of a quantum field theory over the "field with one element" was first addressed in 2012 by Bejleri and Marcolli, where it was shown that wonderful compactifications of the graph configuration spaces that appear in the calculation of Feynman integrals, as well as the moduli spaces of curves, admit an $\mathbb F_1$ structure. Recently, we also examined some advantages of studying finite fields $\mathbb F_q$, wherein $\mathbb F_1$ represents the fundamental string with the Planck length, playing a fundamental role in the model. Such a role was briefly described by comparing the similarity between the collapse of the spacetime concept probing the scales below the Planck length and the mathematical collapse of the 'field' concept at $q=1$. In this letter, we elaborate more on this role by explaining how Kapranov and Smirnov's perspective based on the Iwasawa theory is a perfect mathematical fit for string theory. Particularly, their work suggests that the existence of $\mathbb F_1$ alone is sufficient to create other fields $\mathbb F_q$ emergent as its extensions, reflecting the postulate of string theory, where various vibrational modes of the fundamental string manifest as other fields. As support, a couple of evidence are provided that illustrate the physical importance of the Weyl group (known to be a reductive group over $\mathbb F_1$) and explain why the calculation of the amplitudes in the "amplitudes=combinatorial geometry" program (initiated by Arkani-Hamed et al. in 2013) exhibits a combinatorial nature and simplifies the exponentially growing ($\mathcal{O}(4^n)$) calculations of the Feynman diagrams to a polynomially growing order ($\mathcal{O}(n^2)$) in the kinematic space of scattering data for the scalar theory with cubic interactions.

physics.gen-ph↗