Higher Dimensional Operator Corrections to the Goldstino Goldberg-Treiman Vertices

The goldstino-matter interactions given by the Goldberg-Treiman relations can receive higher dimensional operator corrections of O(q2/M2), where M denotes the mass of the mediators through which SUSY breaking is transmitted. These corrections in the gauge mediated SUSY breaking models arise from loop diagrams, and an explicit calculation of such corrections is presented. It is emphasized that the Goldberg-Treiman vertices are valid only below the mediator scale and at higher energies goldstinos decouple from the MSSM fields. The implication of this fact on gravitino cosmology in GMSB models is mentioned. ∗email: [email protected] The light gravitino to matter interactions are dominated by the spin 1 2 longitudinal component of gravitino which is essentially the goldstino eaten by the gravitino via supersymmetric Higgs mechanism. At energies much higher than the gravitino mass, the supersymmetric version of the equivalence theorem [1, 2] allows one to replace the gravitino with the goldstino. The low energy interactions of a goldstino to matter fields, which in this letter assumed to be the fields in the minimal supersymmetric standard model (MSSM), are completely fixed model-independently by the so called goldstino GoldbergTreiman vertices [1, 3] which depend on the mass splittings of superparteners. This is similar to the Goldberg-Treiman relations in pion-nucleon interactions which also depend on the chiral symmetry breaking parameters, namely, the nucleon masses. At high energies the goldstino Goldberg-Treiman interactions are expected to get corrections of O(q) where q denotes generic Lorentz invariants of the external momenta. At a first glance, one might think that this correction is suppressed by 1 F , where F is the goldstino decay constant, in analogy to the correction in the pion-nucleon interaction which is of O(q/f 2 π). However, unlike in the pion-nucleon case in which there is only one fundamental scale, namely, fπ, there can be multiple scales in realistic SUSY models, so it is possible that the correction is suppressed by 1 M X , where MX is an intermediate scale between the MSSM scale and √ F . If this is indeed the case, the corrections can be much larger than a naive expectation based on the analogy to the Goldberg-Treiman relations in hadron physics. In this letter, we show that the corrections to the goldstino Goldberg-Treiman couplings can be suppressed by an intermediate scale by an explicit calculation of such corrections in gauge mediated SUSY breaking (GMSB) models [4]. In GMSB models, SUSY breaking occurs in a hidden sector and is transmitted to the MSSM sector through gauge interactions between mediators and the MSSM fields. Generally the mediator scale can be much lower than the SUSY breaking scale. Because the SUSY breaking occurs in the hidden sector there is no tree level coupling between the goldstino and the MSSM fields, and the Goldberg-Treiman vertices are induced through loop diagrams. Since the goldstino-matter interaction arise from loops, it becomes clear that the correction to the the Goldberg-Treiman vertices can be O(q/M), where M denotes the mass of the mediators that go through the loop diagrams, unless there is