Improved statistics for F-theory standard models

TL;DR

This paper introduces elementary techniques to simplify the analysis of matter curves in F-theory models, enabling improved statistical bounds on the absence of vector-like exotics in Standard Models.

Contribution

It presents new combinatorial methods for analyzing singular matter curves in F-theory, improving the accuracy of statistical bounds on exotic particles.

Findings

Enhanced statistical bounds on vector-like exotics.

Elementary techniques simplify complex geometric computations.

Optimal results achieved with current geometric information.

Abstract

Much of the analysis of F-theory-based Standard Models boils down to computing cohomologies of line bundles on matter curves. By varying parameters one can degenerate such matter curves to singular ones, typically with many nodes, where the computation is combinatorial and straightforward. The question remains to relate the (a priori possibly smaller) value on the original curve to the singular one. In this work, we introduce some elementary techniques (pruning trees and removing interior edges) for simplifying the resulting nodal curves to a small collection of terminal ones that can be handled directly. When applied to the QSMs, these techniques yield optimal results in the sense that obtaining more precise answers would require currently unavailable information about the QSM geometries. This provides us with an opportunity to enhance the statistical bounds established in earlier research regarding the absence of vector-like exotics on the quark-doublet curve.