Flavour in Intersecting Brane Models and Bounds on the String Scale

TL;DR

This paper demonstrates that non-supersymmetric intersecting brane models, which initially predict factorizable Yukawas $Y_{ij}=a_i b_j$ and a rank-one fermion spectrum, can nevertheless realize realistic flavour via four-fermion operators induced by string instantons and one-loop threshold corrections. These instanton effects generate nonfactorizable corrections to Yukawas, allowing the first two generations to acquire mass and mixing after radiative effects, while also fixing the compactification radii near the string length. However, a comprehensive analysis of FCNC and CP-violation observables shows that the string scale must be very large, $M_S \gtrsim 10^3$–$10^4$ TeV (with EDMs and SN1987A bounds contributing additional constraints), making TeV-scale strings untenable in the non-supersymmetric setting. While the mechanism provides a path to realistic flavour in these models, it simultaneously reveals a severe fine-tuning problem, favoring supersymmetric realizations or other resolutions of the hierarchy problem. The work also discusses how SUSY might enable alternative flavour mechanisms, e.g., through soft-breaking A-terms, though a fully realistic SUSY-based flavour sector remains to be established.

Abstract

We study flavour issues in nonsupersymmetric intersecting brane models. Specifically, the purpose of the present paper is twofold: (i) to determine whether realistic flavour structures can be obtained in these models, and (ii) to establish whether the non-supersymmetric models address the gauge hierarchy problem. To this end, we find that realistic flavour structures, although absent at tree level, can arise even in the simplest models after effects of 4 fermion instanton--induced operators and radiative corrections have been taken into account. On the other hand, our analysis of flavour changing neutral currents (FCNC), electric dipole moments (EDM), supernova SN1987A and other constraints shows that the string scale has to be rather high, 10^4 TeV. This implies that non-supersymmetric intersecting brane models face a severe finetuning problem. Finally, we comment on how non--trivial flavour structures can arise in supersymmetric models.

Figures (11)

• Figure 1: Threshold correction to Yukawa couplings. The black dot in the loop diagram represents a chirality changing four fermion amplitude.
• Figure 2: Brane configuration in a model of D6-branes intersecting at angles. The leptonic sector is not presented here while the baryonic, left, right branes and orientifold image of the right brane are the dark solid, faint solid, dashed and dotted lines, respectively. The intersections corresponding to the quark doublets ($i=-1,0,1$), up type singlets ($j=-1,0,1$) and down type singlets ($j^\ast=-1,0,1$) are denoted by an empty circle, full circle and a cross, respectively. All distances are measured in units of $2 \pi R$ with $R$ being the corresponding radius (except $\tilde{\epsilon}^{(3)}$ which is measured in units of $6 \pi R$).
• Figure 3: Generic 4 point string scattering diagram.
• Figure 4: $t$-channel Higgs exchange as a "double instanton".
• Figure 5: "Irreducible" instanton contribution to 4 fermion operators.