Search Results (18)

We fit the three finestructure constants of the Standard Model, in which the first approximation of theoretically estimable parameters include (1) a “unified scale”, turning out not equal to the Planck scale and thus only estimable by a very speculative story, the second includes (2) a “number of layers” being a priori the number of families, and the third is (3) a unified coupling related to a critical coupling on a lattice. So formally, we postdict the three fine structure constants! In the philosophy of our model, there is a physical lattice theory with link variables taking values in a (or in the various) “small” representation(s) of the standard model Group. We argue for that these representations function in the first approximation based on the theory of a genuine $SU\left(5\right)$ theory. Next, we take into account fluctuation of the gauge fields in the lattice and obtain a correction to the a priori $SU\left(5\right)$ approximation, because of course the link fluctuations not corresponding to any standard model Lie algebra, but only to the SU(5), do not exist. The model is a development of our old anti-grand-unification model having as its genuine gauge group, close to fundamental scale, a cross-product of the standard model group $S\left(U\right(3)\times U(2\left)\right)$ with itself, with there being one Cartesian product factor for each family. In our old works, we included the hypothesis of the “multiple point criticallity principle”, which here effectively means the coupling constants are critical on the lattice. Counted relative to the Higgs scale, we suggest in our sense that the“unified scale” (where the deviations between the inverse fine structure constants deviate by quantum fluctuations being only from standard model groups, not SU(5)) makes up the 2/3rd power of the Planck scale relative to the Higgs scale or the topquarkmass scale. Full article

In flipped SU(5) grand unified theories, the partial decay lifetimes of certain nucleon decay channels depend generically on an unknown unitary matrix, which arises when left-handed lepton fields are embedded into anti-fundamental representations of SU(5). This dependency is particularly relevant when the neutrino mass matrix has a generic structure, introducing uncertainty in the prediction of nucleon decay branching fractions within flipped SU(5). In this paper, we demonstrate that this uncertainty can be parametrized using two parameters, which can be determined by measuring the partial lifetimes of $p\to {\pi }^0{e}^{+}$, $p\to {\pi }^0{\mu }^{+}$, and $n\to {\pi }^0\overline{\nu }$. In addition, we establish upper limits on the ratios of the decay widths of these channels, offering a potential method to test flipped SU(5) in future nucleon decay experiments. Full article

In the absence of a Grand Unified Theory framework, connecting the values of the mixing parameters in the quark-and-lepton sector is a difficult task, unless one introduces ad hoc relations among the matrices that diagonalize such different kinds of fermions. In this paper, we discuss in detail the possibility that the PMNS matrix is given by the product $U_{PMNS}=V_{CKM}^{★}{T}^{★}$, where T comes from the diagonalization of a see-saw like mass matrix that can be of a Bimaximal (BM), Tri-Bimaximal (TBM) and Golden Ratio (GR) form, and identify the leading corrections to such patterns that allow for a good fit to the leptonic mixing matrix as well as to the CP phase. We also show that the modified versions of BM, TBM and GR can easily accommodate the solar and atmospheric mass differences. Full article

In the Standard Model, ad hoc hypotheses assume the existence of three generations of point-like leptons and quarks, which possess a point-like structure and follow the Dirac equation involving four anti-commutative matrices. In this work, we consider the sedenion hypercomplex algebra as an extension of the Standard Model and show its close link to SU(5), which is the underlying symmetry group for the grand unification theory (GUT). We first consider the direct-product quaternion model and the eight-element octonion algebra model. We show that neither the associative quaternion model nor the non-associative octonion model could generate three fermion generations. Instead, we show that the sedenion model, which contains three octonion sub-algebras, leads naturally to precisely three fermion generations. Moreover, we demonstrate the use of basis sedenion operators to construct twenty-four 5 × 5 generalized lambda matrices representing SU(5) generators, in analogy to the use of octonion basis operators to generate Gell-Mann’s eight 3 × 3 lambda-matrix generators for SU(3). Thus, we provide a link between the sedenion algebra and Georgi and Glashow’s SU(5) GUT model that unifies the electroweak and strong interactions for the Standard Model’s elementary particles, which obey SU(3)$\otimes$SU(2)$\otimes$U(1) symmetry. Full article

For a hundred years, general relativity has been the best theory to describe gravity and space–time and has successfully explained many physical phenomena. At the same time, quantum mechanics provides the most accurate description of the microscopic world, and quantum science technology has evoked a wide range of developments today. Merging these two very successful theories to form a grand unified theory is one of the most elusive challenges in physics. All the candidate theories that wish to unify gravity and quantum mechanics predict the breaking of the weak equivalence principle, which lies at the heart of general relativity. It is therefore imperative to experimentally verify the equivalence principle in the presence of significant quantum effects of matter. Cold atoms provide well-defined properties and potentially nonlocal correlations as the test masses and will also improve the limits reached by classical tests with macroscopic bodies. The results of rigorous tests using cold atoms may tell us whether and how the equivalence principle can be reformulated into a quantum version. In this paper, we review the principles and developments of the test of the equivalence principle with cold atoms. The status of the experiments and the key techniques involved are discussed in detail. Finally, we give an outlook on new questions and opportunities for further exploration of this topic. Full article

We explore the potential of ultimate unification of the Standard Model matter and gauge sectors into a single $E_8$ superfield in ten dimensions via an intermediate Pati–Salam gauge theory. Through a consistent realisation of a ${\mathbb{T}}^6/({\mathbb{Z}}_6\times {\mathbb{Z}}_2\times {\mathbb{Z}}_2)$ orbifolding procedure and renormalisation group evolution of gauge couplings, we establish several novel benchmark scenarios for New Physics that are worth further phenomenological exploration. Full article

Six-dimensional spinors with $Spin(3,3)$ symmetry are utilized to efficiently encode three generations of matter. $E_{8(-24)}$ is shown to contain physically relevant subgroups with representations for GUT groups, spacetime symmetries, three generations of the standard model fermions, and Higgs bosons. Pati–Salam, $SU\left(5\right)$, and $Spin\left(10\right)$ grand unified theories are found when a single generation is isolated. For spacetime symmetries, $Spin(4,2)$ may be used for conformal symmetry, $Ad{S}_5\to d{S}_4$, or simply broken to $Spin(3,1)$ of a Minkowski space. Another class of representations finds $Spin(2,2)$ and can give $Ad{S}_3$ with various GUTs. An action for three generations of fermions in the Majorana–Weyl spinor $\mathbf{128}$ of $Spin(4,12)$ is found with $Spin\left(3\right)$ flavor symmetry inside $E_{8(-24)}$. The 128 of $Spin(12,4)$ can be regarded as the tangent space to a particular pseudo-Riemannian form of the octo-octonionic Rosenfeld projective plane $E_{8(-24)}/Spin(12,4)=\left(\mathbb{O}sx\mathbb{O}\right){\mathbb{P}}^2$. Full article

Intercultural theology is increasingly a major subject matter of 21st-century scholarly inquiry. This results in an interreligious discourse and encounter at different levels. However, gone are the days when the aim is to identify or even to fuse certain overlapping magisteria. A linguistic-cultural approach takes us beyond mergers or grand unified theories. To speak of reality as a whole is not to talk about the whole of reality. Creatio continua, the radical newness of each moment and phase unfolds in unpredictable ways. The ecological crisis of planet earth has forced all responsible researchers to engage with the Anthropocene by establishing space for a common earth religion. Through ressourcement, it appears that the sophiology of theologians of the Russian Silver Age (e.g., Solovyov, Bulgakov, and Florensky) can open up a vista in the spirit of aggiornamento to a meta-religious approach recognising the infinite capacity of humanity to transcend particularised religious identities and so belong in different ways too, with, and in God. In the end, sophiology is a form of progressive Christianity that puts together philosophy and faith by promoting an ecological public theology that is concerned about raising society’s awareness about creation as material nature. Full article

Grand unified theories (GUTs) may result in the $E_6$-inspired composite Higgs model (E${}_6$CHM) at low energies, almost stabilizing the electroweak scale. We consider an orbifold GUT in 6 dimensions in which the $E_6$-gauge group is broken to the gauge symmetry of the standard model (SM) while different multiplets of the SM fermions come from different 27-plets. The strongly coupled sector of the E${}_6$CHM is confined on the brane where $E_6$ is broken down to its $SU(6)$ subgroup. Near the scale of $f\gtrsim 5\mathrm{TeV}$, this approximate $SU(6)$ symmetry is expected to be further broken down to its $SU(5)$ subgroup, which contains the SM-gauge group. Such a breakdown leads to a set of pseudo-Nambu–Goldstone bosons (pNGBs) that includes an SM-like Higgs doublet. The approximate gauge coupling unification in the E${}_6$CHM takes place at high energies when the right-handed top quark is a composite fermion. To ensure anomaly cancellation, the weakly coupled sector of this model contains extra exotic matter beyond the SM. We discuss the mechanism of the generation of matter–antimatter asymmetry within the variant of the E${}_6$CHM in which the baryon number and CP invariance are violated. Full article

The tremendous phenomenological success of the Standard Model (SM) suggests that its flavor structure and gauge interactions may not be arbitrary but should have a fundamental first-principle explanation. In this work, we explore how the basic distinctive properties of the SM dynamically emerge from a unified New Physics framework tying together both flavor physics and Grand Unified Theory (GUT) concepts. This framework is suggested by a novel anomaly-free supersymmetric chiral ${\mathrm{E}}_6\times \mathrm{SU}{\left(2\right)}_{\mathrm{F}}\times \mathrm{U}{\left(1\right)}_{\mathrm{F}}$ GUT containing the SM. Among the most appealing emergent properties of this theory is the Higgs-matter unification with a highly-constrained massless chiral sector featuring two universal Yukawa couplings close to the GUT scale. At the electroweak scale, the minimal SM-like effective field theory limit of this GUT represents a specific flavored three-Higgs doublet model consistent with the observed large hierarchies in the quark mass spectra and mixing already at tree level. Full article

The natural extension to the $\mathrm{SU}\left(5\right)$ Georgi-Glashow grand unification model is to enlarge the gauge symmetry group. In this work, the $\mathrm{SU}\left(7\right)$ symmetry group is examined. The Cartan subalgebra is determined along with their commutation relations. The associated roots and weights of the $\mathrm{SU}\left(7\right)$ algebra are derived and discussed. The raising and lowering operators are explicitly constructed and presented. Higher dimensional representations are developed by graphical as well as tensorial methods. Applications of the $\mathrm{SU}\left(7\right)$ Lie group to supersymmetric grand unification as well as applications are discussed. Full article

The Free Energy Principle (FEP) is currently one of the most promising frameworks with which to address a unified explanation of life-related phenomena. With powerful formalism that embeds a small set of assumptions, it purports to deal with complex adaptive dynamics ranging from barely unicellular organisms to complex cultural manifestations. The FEP has received increased attention in disciplines that study life, including some critique regarding its overall explanatory power and its true potential as a grand unifying theory (GUT). Recently, FEP theorists presented a contribution with the main tenets of their framework, together with possible philosophical interpretations, which lean towards so-called Markovian Monism (MM). The present paper assumes some of the abovementioned critiques, rejects the arguments advanced to invalidate the FEP’s potential to be a GUT, and overcomes criticism thereof by reviewing FEP theorists’ newly minted metaphysical commitment, namely MM. Specifically, it shows that this philosophical interpretation of the FEP argues circularly and only delivers what it initially assumes, i.e., a dual information geometry that allegedly explains epistemic access to the world based on prior dual assumptions. The origin of this circularity can be traced back to a physical description contingent on relative system-environment separation. However, the FEP itself is not committed to MM, and as a scientific theory it delivers more than what it assumes, serving as a heuristic unification principle that provides epistemic advancement for the life sciences. Full article

The neutralino sector of the semi-constrained next-to-minimal supersymmetric standard model is explored under recent experimental constraints, with special attention to dark matter (DM) limits. The effects of the upper and lower bounds of dark matter relic density and recent direct detection constraints on spin-independent and -dependent cross-sections are thoroughly analyzed. Particularly, we show which regions of the parameter space are ruled out due to the different dark matter constraints and the corresponding model-specific parameters: $\lambda ,\kappa ,A_{\lambda }$, and $A_{\kappa }$. We analyze all annihilation and co-annihilation processes (with heavier neutralinos and charginos) that contribute to the dark matter relic density. The mass components of the dark matter candidate, the lightest neutralino ${\tilde{\chi }}_1^0$, are studied, and the decays of heavy neutralinos and charginos, especially ${\tilde{\chi }}_2^0$ and ${\tilde{\chi }}_1^{+}$, into the lightest neutralino are examined. We impose semi-universal boundary conditions at the Grand Unified Theory scale, and require a moderate range of $tan\beta \lesssim 10$. We find that the allowed parameter space is associated with a heavy mass spectrum in general and that the lightest neutralino is mostly Higgsino with a mass range that resides mostly between 1000 and 1500 GeV. However, smaller mass values can be achieved if the DM candidate is bino-like or singlino-like. Full article

Local supersymmetry (SUSY) provides an attractive framework for the incorporation of gravity and unification of gauge interactions within Grand Unified Theories (GUTs). Its breakdown can lead to a variety of models with softly broken SUSY at low energies. In this review article, we focus on the SUSY extension of the Standard Model (SM) with an extra $U{\left(1\right)}_N$ gauge symmetry originating from a string-inspired $E_6$ GUTs. Only in this $U\left(1\right)$ extension of the minimal supersymmetric standard model (MSSM) can the right-handed neutrinos be superheavy, providing a mechanism for the baryon asymmetry generation. The particle content of this exceptional supersymmetric standard model (E ${}_6$ SSM) includes three 27 representations of the $E_6$ group, to ensure anomaly cancellation. In addition it also contains a pair of $SU{\left(2\right)}_W$ doublets as required for the unification of gauge couplings. Thus, E ${}_6$ SSM involves exotic matter beyond the MSSM. We consider symmetries that permit suppressing flavor changing processes and rapid proton decay, as well as gauge coupling unification, the gauge symmetry breaking and the spectrum of Higgs bosons in this model. The possible Large Hadron Collider (LHC) signatures caused by the presence of exotic states are also discussed. Full article

String/M theory is formulated in 10 and 11 space-time dimensions; in order to describe our universe, we must postulate that six or seven of the spatial dimensions form a small compact manifold. In 1985, Candelas et al. showed that by taking the extra dimensions to be a Calabi–Yau manifold, one could obtain the grand unified theories which had previously been postulated as extensions of the Standard Model of particle physics. Over the years since, many more such compactifications were found. In the early 2000s, progress in nonperturbative string theory enabled computing the approximate effective potential for many compactifications, and it was found that they have metastable local minima with small cosmological constant. Thus, string/M theory appears to have many vacuum configurations which could describe our universe. By combining results on these vacua with a measure factor derived using the theory of eternal inflation, one gets a theoretical framework which realizes earlier ideas about the multiverse, including the anthropic solution to the cosmological constant problem. We review these arguments and some of the criticisms, with their implications for the prediction of low energy supersymmetry and hidden matter sectors, as well as recent work on a variation on eternal inflation theory motivated by computational complexity considerations. Full article