Disoriented and Plastic Soft Terms: A Dynamical Solution to the Problem of Supersymmetric Flavor Violations

We postulate that the orientation of the soft supersymmetry-breaking terms in flavor space is not fixed by tree level physics at the Planck scale; it is a dynamical variable which depends on fields that have no tree level potential. These fields can be thought of as either moduli or as the Nambu-Goldstone bosons of the spontaneously broken flavor symmetry which is non-linearly realized by the soft terms. We show that the soft terms align with the quark and lepton Yukawa couplings, just as spins align with an external magnetic field. As a result, the soft terms conserve individual lepton numbers and do not cause large flavor or CP violations. The vacuum adjusts so as to allow large sparticle splittings to naturally coexist with flavor conservation. Consequently, the resulting phenomenology is different from that of minimal supersymmetric theories. We also propose theories in which the shape of the soft terms in flavor space is a dynamical variable which depends on fields that have no tree level potential. This dynamically leads to partial degeneracy among sparticles and further supression of flavor violations. The ideas of this paper suggest a connection between the space of moduli and the spontaneously broken flavor group. On leave of absence from the Physics Department, Stanford University, Stanford CA 94305, USA. On leave of absence from INFN, Sezione di Padova, Padua, Italy. 1. Universal versus Disoriented Soft Terms The soft supersymmetry(SUSY)-breaking terms [1, 2] are important for at least two reasons. First, they are the key ingredient which made the construction of realistic supersymmetric theories possible [1]. Second, they are experimentally measurable quantities since they determine the masses of sparticles. In early works, motivated by the need to avoid large flavor violations, it was postulated that soft terms satisfy universality [1]. Universality states that the squarks and sleptons of the three families are all degenerate in mass at some scale ∼ MGUT. Universality has a geometric interpretation which is useful to appreciate. To do this, consider the limit in which all but the gauge couplings of the supersymmetric standard model are set to zero. The resulting theory possesses a U(3) global symmetry which is called flavor symmetry. The 3 stands for the number of families and the 5 for the number of SU(3)×SU(2)×U(1) superfield members in a family, which will be labelled by A = Q, Ū , D̄, L, Ē. The flavor symmetry is simply a manifestation of the fact that gauge forces do not distinguish particles with identical gauge quantum numbers. Universality states that the five 3 × 3 sparticle squared mass matrices mA are flavor singlets, i.e. proportional to the identity. They are spheres in flavor space and they realize the flavor symmetry in the Wigner mode. In this paper we wish to suggest an alternative mechanism to universality for avoiding large flavor violations. Let Λ be a high energy scale at which supersymmetry breaking occurs and the soft terms are determined. Λ can be of the order of the Planck mass MPL – as in supergravity – or smaller, equal to the mass of the messengers that communicate supersymmetry breaking to the ordinary particles. Our fundamental hypothesis is that physics at the scale Λ fixes the eigenvalues of the soft terms mA but leaves their direction in flavor U(3) space undetermined. In other words, the potential energy VΛ of the sector which determines the soft terms at the scale Λ is flavor U(3) invariant. VΛ does not depend on the U(3) angles which are flat directions of the potential and which will be called here “moduli”. The moduli determine the direction in which the soft terms point in flavor space. They can be thought of as the Goldstone bosons of the flavor group which is spontaneously broken by the soft terms mA themselves and are therefore “disoriented” in flavor space. Therefore, the simplest way to state our hypothesis is: the soft terms realize the flavor symmetry in the Goldstone mode. In contrast, universality states that the soft terms realize the flavor symmetry in the Wigner mode. Our next assumption is that at energies below Λ we have the minimal supersymmetric particle content (along with the decoupled gauge singlet Goldstones/moduli). We will show that the orientation of the soft terms is determined by physics at lower energies – in particular the flavor-breaking fermion masses – in a calculable way. A simple analogy is to think of the soft terms mA as a spin ~s in space and U(3)A as ordinary rotational invariance. The magnitude of ~s is determined by some unspecified “high energy” dynamics to be non-zero. This forces rotational invariance to break spontaIn section 6 we will also discuss the case of supersymmetric GUTs.