Radiative Fermion Masses in Local D-Brane Models

TL;DR

This work analyzes how radiative corrections can generate nonzero masses for the lightest SM fermions in local D-brane models built on del Pezzo singularities within the Large Volume Scenario. It identifies approximate global $U(1)$ and related symmetries that enforce a tree-level zero mass for the up quark, then examines how bulk effects in LVS break these symmetries and induce loop-generated masses. The authors show that LVS can significantly enhance radiative masses compared to generic gravity-mediated setups, potentially yielding phenomenologically viable values, while also addressing flavor-changing neutral current constraints from sfermion and extra-Higgs sectors. The findings point to a viable path toward realistic fermion mass hierarchies in string-inspired models, albeit with stringent requirements on Higgs spectra and flavor structure, and motivate explicit calculations of RG running and alternative symmetry-breaking mechanisms.

Abstract

In the context of D-brane model building, we present a realistic framework for generating fermion masses that are forbidden by global symmetries. We show that the string theoretical Large volume scenario circumvents the standard lore that fermion masses generated by loop effects are too small in generic gravity mediated scenarios. We argue that the fact that in toric singularity models, the up quark masses have always a zero eigenvalue, corresponding to the lightest generation, is due to the presence of approximate global symmetries that we explicitly identify in del Pezzo singularities. These symmetries are broken by global effects and therefore proportional to inverse powers of the volume. We estimate the generic size of radiative corrections to fermion masses in different phenomenological manifestations of the Large volume scenario. Concrete realizations in terms of flavor violating soft-terms are estimated and contrasted with current bounds on flavour changing neutral currents. Contributions from generic extra Higgs-like fields set bounds on their masses close to the GUT scale to produce realistic fermion masses.

Figures (4)

• Figure 1: The $dP_1$ quiver with two additional $D7$ gauge groups. An arrow between any given nodes corresponds to bi-fundamental matter. An arrow starting at node $i$ and ending at node $j$ corresponds to a field $X_{ij}$ transforming as $(N_j,\bar{N}_i).$ Identifying gauge groups $1$ and $6$ with $U(1)$ symmetries, gauge group $3$ with $U(3)$ and gauge group $2$ with $U(2)$ leads to Standard Model matter content as discussed in 0810.5660.
• Figure 2: Left: Flavour change in the Standard Model. Middle: Supersymmetric version of diagram on the left. Off-diagonal contributions in the scalar mass matrix can lead to additional contributions involving gluinos. Right: Contribution from the additional Higgs to the same FCNC process.
• Figure 3: Schematic diagram for radiative corrections to quark masses. The diagram needs to include one Higgs insertion and one SUSY breaking F-term insertion.
• Figure 4: Left: 1-loop contribution to the up-mass involving additional Higgs fields. Right: 1-loop induced up-quark mass involving gluinos and using non-diagonal entries in the squark mass matrix Hall:1985dx .