Predicting the SUSY breaking scale in SUGRA models with degenerate vacua

Abstract

In N = 1 supergravity the scalar potential may have supersymmetric (SUSY) and non-supersymmetric Minkowski vacua (associated with supersymmetric and physical phases) with vanishing energy density. In the supersymmetric Minkowski (second) phase some breakdown of SUSY may be induced by non-perturbative effects in the observable sector that give rise to a tiny positive vacuum energy density. Postulating the exact degeneracy of the physical and second vacua as well as assuming that at high energies the couplings in both phases are almost identical, one can estimate the dark energy density in these vacua. It is mostly determined by the SUSY breaking scale M S in the physical phase. Exploring the two-loop renormalization group (RG) flow of couplings in these vacua we find that the measured value of the cosmological constant can be reproduced if M S varies from 20 TeV to 400 TeV. We also argue that this prediction for the SUSY breaking scale is consistent with the upper bound on M S in the higgsino dark matter scenario.

Cosmological Constant in SUGRA Models with Degenerate Vacua

“…In the simplest scenario when c n = 0, V hid has two minima, at z = 0 and z = − 2µ 0 3 , corresponding to the extremum points of the hidden sector superpotential. At these points, the SUGRA scalar potential (20) attains its absolute minimal value, namely approximately zero. In the vacuum where…”

“…In order to illustrate this, let us first consider the limit where n = 0 and Y t (Q) 0. In this case, the Landau pole in the evolution of α 3 (Q) disappears, and the solutions of the two-loop RGEs (31) are attracted to the infrared fixed point [20]:…”

“…The successful predictions for the Higgs and top quarks masses (5) suggest that the MPP can be used to explain the tiny dark energy density spread all over the Universe (the cosmological constant ρ Λ ), which is responsible for its accelerated expansion. In previous articles [12][13][14][15][16][17][18][19][20][21][22][23][24], the implementation of the MPP in models based on local supersymmetry, supergravity (SUGRA), was studied. In SUGRA models a huge degree of fine-tuning is required to ensure that the energy density in the physical vacuum is sufficiently small.…”

“…In SUGRA models a huge degree of fine-tuning is required to ensure that the energy density in the physical vacuum is sufficiently small. The successful application of the MPP to (N = 1) supergravity implies the existence of a vacuum in which the low-energy limit of the theory is described by a pure supersymmetric model in flat Minkowski space [12][13][14][15][16][17][18][19][20][21][22][23][24]. According to the MPP, the physical vacuum is the one in which we live, and this second vacuum must have the same vacuum energy density.…”

“…However, in the second vacuum, the dynamical breakdown of SUSY may take place, leading to an exponentially-suppressed value of the vacuum energy density. This energy density is then transferred to the physical vacuum by the assumed degeneracy [12][13][14][15][16][17][18][19][20][21][22][23][24]. The results of the numerical analysis performed in the previous works indicate that in the leading one-loop approximation, the observed value of the cosmological constant can be reproduced, even if the SM gauge couplings are almost identical in both vacua.…”