Renormalization of Supersymmetry Breaking Parameters Revisited

Abstract

413The full renormalization group equations in the minimal SU(3)x SU(2)x U(l) gauge model with softly broken supersymmetry, which are originally given in the paper [Prog. Theor. Phys. 68 (1982), 927] are re·examined and corrected.Supersymmetry has recently attracted much attention as it provides a viable principle to solve the hierarchy problem in grand unified theories.,),2) It is well known that a scheme with spontaneously broken supersymmetry at low energies (~0(100 GeV» is plagued with difficulties owing to the famous mass sum rule. 3) Thus the supersymmetry breaking terms in the effective low energy theory should be explicit and soft,2) though they may be messages from a hidden sector in which supersymmetry is spontaneously broken at a large mass scale (~0(10'O GeV»!)In a previous paper we have studied the renormalization of these soft breaking parameters in the supersymmetric SU(3)xSU (2)x U(l) gauge model with the minimal set of chi~al matter-Higgs multiplets. S) We obtained an important result that the weak gauge symmetry breaking can be induced by the renormalization effects on these soft breaking parameters, provic;led that the top quark. is sufficiently heavy.S) On the other hand, it has recently been recognized that the explicit and soft supersymmetry breaking terms in the effective lagrangian naturally appear in the spontaneously broken N = 1 supergravity theory.S),7) Furthermore it has also been pointed out that the light singlet, which is necessary inorder to break the weak gauge symmetry at the tree level, is dangerous because it destabilizes the light-heavy hierarchy. B) Thus there is growing interest in the set of renormalization group equations for the breaking parameters in the minimal mode1. 9 )"O) Unfortunately; the original results given in the previous paper contain several errors (i.e., equations for ms, "', m,o).S) There are already independent calculations for the breaking parameters which originate from the spontaneous breakdown of the N=l supergravity.'O) In this short note, we shall give corrected set of renormalization group equations for parameters defined in the previous paper for the sake of completeness, since our breaking parameters are somewhat more general than those obtained from the N = 1 supergravity.The minimalSU(3)xSU(2)x U(1) gauge model consists of vector multiplets V" V2 and V3, corresponding respectively to U(1), SU(2) and SU(3), three generations of quark-lepton chiral multiplets and two Higgs chiral multiplets. Their representation contents and component fields are shown in Tables I, II and III. We neglect Yukawa couplings except those for the third generation:where i and j( =1,2) are the SU(2) indices and p( =1,2,3) the SU(3) index. The Grassman integration measure and the component expansion of a left-chiral superfield ¢ are defined as Jd 2 88 2 =1 and ¢ =exp( -i1roap8 P )(A + !28¢ + 8 2 F). The supersymmetry breaking masses of matter scalars and of gauge fermions are shown in Table IV. For the Higgs multiplets, we consider the following gauge invariant mass ter...

The soft supersymmetry-breaking Lagrangian: theory and applications

“…With plausible boundary conditions at a high scale (certain couplings such as the top quark Yukawa of O(1) and no bare Higgs mass parameter µ in the superpotential), low energy supersymmetry can provide the explanation of the origin of electroweak symmetry breaking [11,12,13,14,15]. To oversimplify a little (this will be expanded in Section 4.1), the SM effective Higgs potential has the form V = m 2 h 2 + λh 4 .…”

“…The soft supersymmetry-breaking operators comprise a consistent truncation of all possible operators in that the presence of soft supersymmetry-breaking parameters does not regenerate "hard" supersymmetrybreaking terms at higher order. The complete set of possible soft supersymmetrybreaking parameters was first classified in the seminal papers [37,13,14,15]. The classic proof of Girardello and Grisaru [37] will not be repeated here.…”

“…The β-functions and anomalous dimensions γ are functions of the gauge couplings and superpotential parameters. Typically soft supersymmetry breaking masses generated this way are of order the gravitino mass suppressed by a loop factor, 15) which implies that for soft masses of order a TeV, the gravitino mass should be about two orders of magnitude larger. An interesting feature of Eq.…”

“…Arguably the most important success of supersymmetry is that it can provide a natural mechanism for understanding Higgs physics and electroweak symmetry breaking [11,12,13,14,15]. While the basic physics here is nearly two decades old, it is less familiar to many particle physicists today than it should be.…”

“…Nevertheless, a celebrated features of the MSSM is that the up-type Higgs soft mass-squared parameter does get driven negative via renormalization group running due to the large top quark Yukawa coupling [11,12,13,14,15]. This can be seen upon an inspection of the renormalization group equations for the relevant soft parameters.…”