arXiv subjects

Navid Ardakanian

Publications and source records attributed to Navid Ardakanian.

4 recordsLinked to original sources

arXiv2026

The exact column texture: tree-level Yukawa universality in heterotic $Z_3 \times Z_3$ orbifolds

On $T^6/(Z_3 \times Z_3)$ heterotic orbifolds where three quark generations arise from $Z_3$ fixed-point triplication, we prove that the leading-order tree-level Yukawa amplitude -- the three-point coupling among massless string states -- has an exact column texture: $Y_{\rm lead}(i,j) = c\,\varepsilon^{q_R[j]}$, with the $O(1)$ coefficient $c$ universal across all left-handed generations $i$. Five independent lines of evidence are given: (1) the worldsheet instanton geometry on the $SU(3)$ root lattice gives identical areas for all non-degenerate triangles, making the geometric $O(1)$ coefficient exactly $1$; (2) the generation direction necessarily has trivial Wilson line, rendering all three generations gauge-identical, as verified across all 77 MSSM-like models in the Mini-Landscape classification; (3) an extension to two-Wilson-line models, verified on the complete Parr-Vaudrevange-Wimmer classification of 3,337 $Z_3 \times Z_3$ MSSM models, confirms that no Wilson line configuration can break gauge blindness; (4) the Kähler metric is generation-universal by $Δ(54)$ representation theory; (5) the full Froggatt-Nielsen chain computation with 534 trilinear superpotential couplings and vacuum-aligned singlet VEVs produces left-circulant Yukawa matrices whose eigenstructure is generation-universal. The Froggatt-Nielsen column texture is therefore not an approximation but an exact property of the leading-order string amplitude. Non-trivial $O(1)$ coefficients, which are required for CKM mixing angles beyond the Wolfenstein hierarchy, must originate from beyond-leading-order contributions: integrated-out heavy messenger propagators (tree-level in the low-energy effective theory), vacuum-alignment effects, multi-instanton corrections, or loop corrections.

hep-ph↗

arXiv2026

Why Quarks and Leptons Demand Different Symmetries: A Systematic $Z_3$ Froggatt-Nielsen Analysis

We present a systematic analysis of a minimal supersymmetric $Z_3$ discrete flavor symmetry as a solution to the fermion mass hierarchy problem. With generation-dependent $Z_3$ charges on the right-handed chiral superfields and a single flavon chiral superfield, holomorphy of the superpotential restricts the Yukawa operators so that a single expansion parameter $ε\simeq 0.015$ structurally accounts for the hierarchical pattern of quark and charged lepton mass ratios with $\mathcal{O}(1)$ Yukawa couplings. A Monte Carlo scan over $10^5$ random $\mathcal{O}(1)$ coefficient sets confirms that adjacent-generation mass ratios generically fall within the experimental ranges. The CKM mixing angles are reproducible with specific coefficient choices ($χ^2/\text{dof} \simeq 1.6$) but are not structurally predicted. Extended to neutrinos within a type-I seesaw, the framework fails decisively on two fronts. First, the mass spectrum is far too hierarchical: $Δm_{21}^2/Δm_{31}^2 \lesssim 10^{-4}$, two orders of magnitude below the observed $0.030$. Second, the PMNS mixing angles are generically $\mathcal{O}(1)$ random -- consistent with Haar-distributed unitaries -- providing no mechanism to predict the observed pattern. When $M_R$ carries the $Z_3$ charge structure dictated by the Majorana charge algebra, an unsuppressed off-diagonal entry combines with the hierarchical column texture of the Dirac mass: the seesaw congruence transformation over-suppresses both light masses $m_1, m_2$ to $\mathcal{O}(ε^3)$, deepening the ratio $Δm_{21}^2/Δm_{31}^2$ to $\mathcal{O}(ε^6) \sim 10^{-11}$. These results motivate a sectorial view of flavor where different fermion sectors arise from distinct symmetry mechanisms.

hep-ph↗

arXiv2026

Mass Hierarchies Without Mixing: Abelian Froggatt-Nielsen Models with Uncharged Left-Handed Doublets

Abelian flavor charges on right-handed fermions produce left-handed anarchy: we prove that all abelian discrete Froggatt-Nielsen models with uncharged left-handed doublets yield Haar-random PMNS and CKM matrices, regardless of $\mathbb{Z}_N$ group order, charge assignment, or Majorana mass structure. Scanning $\mathbb{Z}_3$ through $\mathbb{Z}_7$ with 12 charge assignments and $10^5$ Monte Carlo samples each, we demonstrate that the mass spectrum failure previously identified for $\mathbb{Z}_3$ -- the seesaw over-suppression mechanism that pushes $Δm^2_{21}/Δm^2_{31}$ to $\sim 10^{-11}$ -- is specific to $\mathbb{Z}_3$ and avoidable for $N \geq 4$. The mixing angle failure, however, is universal and irreducible. The PMNS angles from every abelian model are statistically consistent with Haar-random unitary matrices, with median $\sin^2θ_{12} \approx \sin^2θ_{23} \approx 0.50$ and $\sin^2θ_{13} \approx 0.31$ across all models tested. The same applies to the CKM: the joint probability of achieving CKM-like mixing from generic $O(1)$ coefficients is $< 2 \times 10^{-6}$. We identify the algebraic origin of this obstruction: abelian groups have only one-dimensional representations, so each generation transforms as an independent singlet with 18 free parameters for three Dirac mass matrices -- far exceeding the 10 physical observables. The transition to non-abelian flavor symmetries such as $A_4$, whose triplet representation reduces free parameters to 4 at leading order, is required specifically for mixing structure. This obstruction applies to the well-motivated subclass of models where left-handed fields are uncharged; models that assign abelian charges to both left- and right-handed fields can evade it.

hep-ph↗

arXiv2026

From seesaw over-suppression to trimaximal mixing: why $A_4$ is the minimal resolution of the $Z_3$ neutrino failure

We investigate whether the type-I seesaw mechanism can rescue the $Z_3$ Froggatt--Nielsen framework for neutrinos and find that it cannot. With right-handed Majorana masses carrying the $Z_3$ charge structure dictated by the Majorana bilinear -- where suppression powers follow $(q_i+q_j)\bmod 3$ -- the mass matrix contains an unsuppressed off-diagonal entry whose dominance in $M_R^{-1}$, combined with the hierarchical column texture of $M_D$, over-suppresses the two lightest neutrino masses to $\mathcal{O}(\varepsilon^3)$ while $m_3$ remains $\mathcal{O}(1)$. This pushes the solar-to-atmospheric mass ratio to a median $Δm^2_{21}/Δm^2_{31}\sim 4\times 10^{-11}$ -- eight orders of magnitude below the observed value of $0.030$. We prove this failure is universal across all six permutations of the charges $(2,1,0)$ and show analytically that the generic ratio scales as $Δm^2_{21}/Δm^2_{31}\sim\mathcal{O}(\varepsilon^6) \sim 10^{-11}$, with fewer than $0.01\%$ of parameter-space points exceeding $\varepsilon^2\approx 2\times 10^{-4}$. The PMNS angles remain Haar-random, carrying no information from the expansion parameter. We then show that $A_4$, the alternating group of order 12, is the minimal discrete symmetry resolving both failures. Its triplet representation provides two independent vacuum parameters controlling the solar and atmospheric mass scales separately, while constraining the PMNS matrix to the trimaximal TM$_1$ pattern. The TM$_1$ solar sum rule predicts $\sin^2θ_{12}=0.318$ ($1.2σ$ from NuFit 6.0, $1.0σ$ from JUNO), and the atmospheric sum rule yields a parameter-free $(\sin^2θ_{23},\,\cosδ)$ correlation predicting $δ\approx -71^\circ$, testable at DUNE and T2HK.

hep-ph↗