Flavour Changing Neutral Currents in Intersecting Brane Models

TL;DR

The paper shows that in intersecting D-brane models, localization of chiral fermions at separate brane intersections induces FCNCs through gauge KK modes, threatening low-scale phenomenology. It develops both a field-theory calculation and a full string-theory disk amplitude analysis, obtaining consistent four-fermion operators and natural UV regularization of KK sums via string dynamics. The Kaon sector bounds force the lightest KK mode, and hence the string scale, to be well above the TeV scale (e.g. $M_1$ in the hundreds to thousands of TeV range and $M_s \gtrsim 10^2$ TeV), with instanton effects further strengthening limits when the string length is near the compactification scale. Consequently, non-supersymmetric intersecting-brane models are phenomenologically disfavoured, and the work has important implications for UV completions and experimental expectations of such string-inspired constructions.

Abstract

Intersecting D-brane models provide an attractive explanation of family replication in the context of string theory. We show, however, that the localization of fermion families at different brane intersections in the extra dimensions introduces flavour changing neutral currents mediated by the Kaluza-Klein excitations of the gauge fields. This is a generic feature in these models, and it implies stringent bounds on the mass of the lightest Kaluza-Klein modes (becoming severe when the compactification radii are larger than the string length). We present the full string calculation of four-fermion interactions in models with intersecting D-branes, recovering the field theory result. This reveals other stringy sources of flavour violation, which give bounds that are complementary to the KK bounds (i.e. they become severe when the compactification radii are comparable to the string length). Taken together these bounds imply that the string scale is larger than $M_s\gtrsim 10^2$ TeV, implying that non-supersymmetric cases are phenomenologically disfavoured.

Figures (5)

• Figure 1: Brane configuration in a model of D6-branes intersecting at angles. The leptonic sector is not represented while the baryonic, left, right and orientifold image of the right are respectively the dark solid, faint solid, dashed and dotted. 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 distance parameters are measured in units of $2 \pi R$ with $R$ the corresponding radius (except $\tilde{\epsilon}^{(3)}$ which is measured in units of $6 \pi R$).
• Figure 2: The generic 4 fermion diagram with branes intersecting in a 2-torus.
• Figure 3: Subleading contribution to the 4 fermion diagram with branes intersecting in a 2-torus.
• Figure 4: Instanton contribution to flavour violating processes such as $\tau \to ee \mu$. The string contribution is proportional to minus the exponential of the shaded area.
• Figure 5: Lower bound on the string scale as a function of the compactification length (in terms of the string length) coming from the contribution of gluon KK modes (solid line) and from instanton contributions (dashed line).