Tackling the Supersymmetric Flavour Problem in String Models

In this work we address one of the phenomenological issues of beyond the Standard Model scenarios which embed Supersymmetry, namely the Supersymmetric Flavour Problem, in the context of String Theory. Indeed, the addition of new interactions to the Standard Model generically spoils its flavour structure which is one of its major achievements since it for example leads to a very elegant understanding of the absence of flavour changing neutral currents in the leptonic sector and of the stability of the proton, thanks to accidental symmetries. We focus on a subset of the phenomenologically dangerous operators, namely the soft scalar masses. One way out of the Supersymmetric Flavour Problem is to geographically separate the observable and hidden sectors along a fifth dimension, gravity being the only interaction propagating in the bulk. In such scenarios, the soft scalar masses are vanishing at the classical level since there is no direct contact term between the observable and hidden multiplets and tend to be universal at the loop-level. However such setups hardly ever come about in String Theory, which is one of the most promising candidates of quantum gravity. In order to make contact with the five-dimensional picture, we focus on the prototypical case of the E8 × E8 Heterotic M-Theory which, in a certain regime, effectively looks five-dimensional and embeds matter fields on two end-of-the-world branes. In these scenarios, not only gravity but also vector multiplets propagate in the five-dimensional bulk, effectively spoiling the sequestered picture. However, since the contact terms responsible for the appearance of soft scalar masses arise due to the exchange of heavy vectors, they do enjoy a current-current structure which can be exploited to inhibit the emergence of soft scalar masses by postulating a global symmetry in the hidden sector. In order to assess the possibility of realising such a mechanism, we first study the full dependence of the Kähler potential on both the moduli and the matter fields in the case of orbifold and Calabi-Yau compactifications. We then determine whether an effective sequestering may be achieved thanks to a global symmetry and argue that whereas for orbifold models our strategy can naturally be put at work, it can only be implemented in a subset of Calabi-Yau models.