General mass formula in broken supersymmetry

Abstract

The mass formula El(-1)2J(W + 1 ) m J 2 = 0 is derived for a very general class of interactions with spontaneously broken supersymmetry. It shows the vanishing of the graded trace o f the square of the mass operator, with m, the mass associated with a (real) field of spin J. This mass relation is shown to be true even in the presence of explicit breaking, provided it fulfills suitable requirements.

The soft supersymmetry-breaking Lagrangian: theory and applications

“…This can be seen from the following sum rule, known as the supertrace relation, for particles of spin J [59,17] …”

Reconstruction of supersymmetric theories at high energy scales

“…The Ferrara-Girardello-Palumbo mass sum rule [27] requires supersymmetric particle masses below the corresponding Standard Model particle masses in this case -in obvious disagreement with observations. The elegant concept of spontaneous symmetry breaking, by non-perturbative gluino condensation for instance, can be realized, however, in a hidden sector which interacts with our eigen-world only by gravity.…”

“…The properties of the supersymmetric theories are quite different for dilaton and moduli dominated scenarios. This can be quantified by introducing a mixing angle θ, characterizing theS andT wave functions of the Goldstino, which is associated with the breaking of supersymmetry and which is absorbed to generate the mass of the gravitino:G = sin θS + cos θT (27) The mass scale is set by the second parameter of the theory, the gravitino mass m 3/2 . A dilaton dominated scenario, i.e.…”

Renormalization Group Approach to the SUSY Flavor Problem

“…3 Although we do not know which mechanism is realized in nature, we would like SUSY to be broken in such a way that it still can allow a natural extension of the SM to a higher energy. It has been studied how this requirement can be met, and found that SUSY has to be only softly broken [8]. The softsupersymmetry breaking (SSB) terms are those which do not change the infinity structure of the parameters of the symmetric theory, and do not produce quadratic divergences.…”

“…So they are additional terms in the Lagrangian that do not change the RG functions such as the β and γ functions of the symmetric theory. There exist four types of such terms [8]: (m 2 ) j i φ j φ * i (soft scalar mass terms), B ij φ i φ j (B-terms), Mλλ (gaugino mass terms), h ijk φ i φ j φ k (trilinear scalar couplings), where φ j and λ denote the scalar component in a chiral supermultiplet and the gaugino in a gauge supermultiplet, respectively.…”