Related papers: Anthropic Argument for Three Generations
2$\leftrightarrow$3 symmetry is realized by the breaking from alterating group of degree 4 ($A4$) symmetry. $A4$ explains why the generation number is three. However the mass matrices are realized in the form of the breaking to…
The Ewens sampling formula with parameter $\alpha$ is the distribution on $S_n$ which gives each $\pi\in S_n$ weight proportional to $\alpha^{C(\pi)}$, where $C(\pi)$ is the number of cycles of $\pi$. We show that, for any fixed $\alpha$,…
We present a unified model without the need for an ad hoc Standard Model hypothesis; we explain why there are three generations of charged and neutral leptons, why neutrinos have a vanishingly small mass, and why flavor-mixing emerges and…
It is pointed out that the set theory gave the exact symmetry while the group theory did not. The triplicity of quarks and leptons is also pointed out. The reason of seven families of particles and in each family eight number of particles…
In the absence of a fundamental theory that precisely predicts values for observable parameters, anthropic reasoning attempts to constrain probability distributions over those parameters in order to facilitate the extraction of testable…
We study the following model for a diploid population of constant size $N$: Every individual carries a random number of (genetic) elements. Upon a reproduction event each of the two parents passes each element independently with probability…
Consider a branching process with a homogeneous reproduction law. Sampling a single cell uniformly from the population at a time $T > 0$ and looking along the sampled cell's ancestral lineage, we find that the reproduction law is…
We live in a world brimming with uncertainty, where we constantly have to make a lot of decisions under incomplete information. We are firm believers that our subjective belief cannot be computed by rigorous mathematical formula; instead…
Genetic Programming is an evolutionary algorithm that generates computer programs, or mathematical expressions, to solve complex problems. In this Guide, we demonstrate how to use Genetic Programming to develop surrogate models to mitigate…
We study effects of beyond the Standard Model physics coupling third generation quarks to leptons of the first two generations. We parametrize these effects by dimension-six effective operators, and we also consider related simplified UV…
We consider a branching random walk in time-inhomogeneous random environment, in which all particles at generation $k$ branch into the same random number of particles $\mathcal{L}_{k+1}\ge 2$, where the $\mathcal{L}_k$, $k\in\mathbb{N}$,…
A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction, disjunction, inverse, and conditional fallacies, as well as unpacking effects and partitioning effects. Quantum…
We turn back to the hypothesis that the Pauli principle, acting intrinsically within leptons and quarks, is the origin of their three generations. The adequate formalism is based on the generalized Dirac equations arising (in the…
A considerable amount of the standard model's three-generation structure can be realised from just the $8\hspace{.3mm}\mathbb{C}$-dimensional algebra of the complex octonions. Indeed, it is a little-known fact that the complex octonions can…
Natural selection explains how life has evolved over millions of years from more primitive forms. The speed at which this happens, however, has sometimes defied formal explanations when based on random (uniformly distributed) mutations.…
We explore the possible implications that new families, that are being searched for at the LHC, would have on neutrino masses. In particular, we have explored the possibility that the smallness of the observed neutrino masses is naturally…
The concept of a random Lagrangian is proposed. It is considered as a basis for a new view of the old problems such as renormalization, nonzero vacuum energy and the anthropic principle. It gives rise to nontrivial consequences both in…
The full-blown multiverse hypothesis, chaosogenesis, is refuted on the grounds of the large scale and high precision of the already discovered laws of nature. A selection principle is required not only to explain the possibility of life and…
We consider the minimal extension of the Standard Model with three generations of massive neutrinos that mix. We then determine the parameters of the model that satisfy all experimental constraints.
In this talk I begin with some general discussion of model building in particle theory, emphasizing the need for motivation and testability. Three illustrative examples are then described. The first is the Left-Right model which provides an…