[Paper Review] Froggatt-Nielsen meets Mordell-Weil: A Phenomenological Survey of Global F-theory GUTs with U(1)s

Sven Krippendorf, Sakura Schäfer‐Nameki+1 more|arXiv (Cornell University)|Jul 21, 2015

Black Holes and Theoretical Physics52 references4 citations

TL;DR

This paper conducts a phenomenological survey of global F-theory GUTs with U(1) symmetries by combining Froggatt-Nielsen (FN) flavor mechanisms with the Mordell-Weil group classification of U(1) charges. It identifies a small class of U(1) charge assignments and matter distributions that yield the exact MSSM spectrum with realistic quark and lepton Yukawa textures consistent with CKM and PMNS mixing, while suppressing proton decay and R-parity violating operators.

ABSTRACT

In F-theory, U(1) gauge symmetries are encoded in rational sections, which generate the Mordell-Weil group of the elliptic fibration of the compactification space. Recently the possible U(1) charges for global SU(5) F-theory GUTs with smooth rational sections were classified arXiv:1504.05593 [hep-th]. In this paper we utilize this classification to probe global F-theory models for their phenomenological viability. After imposing an exotic-free MSSM spectrum, anomaly cancellation (related to hypercharge flux GUT breaking in the presence of U(1) gauge symmetries), absence of dimension four and five proton decay operators and other R-parity violating couplings, and the presence of at least the third generation top Yukawa coupling, we generate the remaining quark and lepton Yukawa textures by a Froggatt-Nielsen mechanism. In this process we require that the dangerous couplings are forbidden at leading order, and when re-generated by singlet vevs, lie within the experimental bounds. We scan over all possible configurations, and show that only a small class of U(1) charge assignments and matter distributions satisfy all the requirements. The solutions give rise to the exact MSSM spectrum with realistic quark and lepton Yukawa textures, which are consistent with the CKM and PMNS mixing matrices. We also discuss the geometric realization of these models, and provide pointers to the class of elliptic fibrations with good phenomenological properties.

Motivation & Objective

• To identify phenomenologically viable global F-theory GUTs with U(1) symmetries that realize the MSSM spectrum without exotic states.
• To constrain U(1) charge assignments using anomaly cancellation, proton decay suppression, and R-parity conservation.
• To implement a Froggatt-Nielsen mechanism for flavor structure, ensuring realistic quark and lepton masses and mixing angles.
• To identify geometrically realizable models by linking charge patterns to elliptic fibration types and rational sections.
• To provide a systematic survey of viable models beyond local constructions, focusing on global consistency and phenomenological viability.

Proposed method

• Utilizes the classification of F-theoretic U(1) charges from smooth rational sections of elliptic fibrations, derived from the Mordell-Weil group.
• Applies anomaly cancellation conditions for MSSM-U(1) mixed anomalies, including linear and quadratic anomaly constraints.
• Imposes constraints to forbid dimension-four and dimension-five proton decay operators and R-parity violating couplings.
• Employs a Froggatt-Nielsen mechanism with flavon fields to generate hierarchical Yukawa textures, ensuring leading-order suppression of dangerous couplings.
• Performs a systematic scan over all consistent U(1) charge assignments and matter curve distributions to identify viable models.
• Maps viable charge patterns to geometric realizations via elliptic fibration constructions, identifying fiber types and base geometries.

Experimental results

Research questions

• RQ1 Which U(1) charge assignments in global F-theory GUTs with smooth rational sections yield an exotic-free MSSM spectrum with realistic flavor textures?
• RQ2 Can the Froggatt-Nielsen mechanism generate quark and lepton Yukawa couplings consistent with observed mixing matrices while suppressing proton decay?
• RQ3 Are there U(1) charge configurations that satisfy all anomaly cancellation conditions and forbid dangerous R-parity violating operators?
• RQ4 What are the geometric realizations of viable F-theory models, and which elliptic fibration types support phenomenologically viable charge patterns?
• RQ5 Why do known geometric constructions fail to satisfy anomaly and proton decay constraints, and can the broader F-theoretic charge set resolve this?

Key findings

• Only a small class of U(1) charge assignments and matter curve distributions satisfy all phenomenological constraints, including anomaly cancellation, proton decay suppression, and realistic flavor textures.
• The viable models yield the exact MSSM spectrum with hierarchical Yukawa couplings consistent with the CKM and PMNS mixing matrices.
• The Froggatt-Nielsen mechanism successfully generates realistic quark and lepton masses, with leading-order couplings suppressed by flavon VEVs within experimental bounds.
• Models with two U(1) symmetries and specific charge patterns (e.g., (Haba1), (Haba2), (BaEnGo1)-(BaEnGo3)) are identified as viable, with explicit charge assignments and fiber types provided.
• The study identifies new classes of elliptic fibrations that solve anomaly constraints and suppress dangerous operators, which are not realizable in known geometric constructions.
• The texture (D.5) from local F-theory models cannot be realized in global F-theory models with five or fewer bar{5} representations due to incompatibility with anomaly cancellation and proton decay constraints.