The Supersymmetric Flavor Problem

The supersymmetric SU(3)×SU(2)×U(1) theory with minimal particle content and general soft supersymmetry breaking terms has 110 physical parameters in its flavor sector: 30 masses, 39 real mixing angles and 41 phases. The absence of an experimental indication for the plethora of new parameters places severe constraints on theories posessing Planck or GUT-mass particles and suggests that theories of flavor conflict with naturalness. We illustrate the problem by studying the processes μ → e+ γ and K0−K̄0 mixing which are very sensitive probes of Planckian physics: a single Planck mass particle coupled to the electron or the muon with a Yukawa coupling comparable to the gauge coupling typically leads to a rate for μ → e+ γ exceeding the present experimental limits. A possible solution is that the messengers which transmit supersymmetry breaking to the ordinary particles are much lighter than MPlanck. On leave of absence from the Physics Department, Stanford University, Stanford, Ca. 94305, USA. Work supported in part by NSF Grant NSF-PHY-9219345 Work supported in part by NSF Grant NSF-PHY-9219345 and an NSF Graduate Fellowship. E-mail: [email protected] 1 Naturalness versus Flavor: A Conflict Nature is ambivalent about Flavor; Quark masses violate it significantly whereas neutral processes conserve it very accurately. This ambivalence leads to a conflict that has to be resolved in every theory. In the standard model it led to the GIM mechanism. In SUSY-GUTS and the supersymmetric standard model [1] it led to the hypothesis that squarks and sleptons of the same color and charge have the same mass, independent of the generation that they belong to. We call this “horizontal universality”. A stronger version of this hypothesis is that all squarks and sleptons have the same mass atMGUT [1]. This is called “universality” and is a fundamental ingredient of the minimal version of the Supersymmetric Standard Model (MSSM). Universality ensures that the sparticle masses are isotropic in flavor space and thus do not cause any direct flavor violations. Flavor nonconservation in the MSSM originates in the quark masses and is under control. The hypotheses of universality or horizontal universality are difficult to implement in realistic theories. The reason is simple: the physics that splits particles also splits sparticles. The degree to which this happens is the crucial question; the answer is model dependent. In the MSSM and the minimal SUSYGUT [1] the interfamily sparticle splittings that are dynamically induced are adequately small. Such minimal theories leave fundamental questions unanswered and are unlikely to be the last word. In more ambitious theories addressing (even small parts of) the problem of flavor, the interfamily sparticle splittings are invariably large and cause unacceptable flavor violations unless the sparticle masses are heavy [2]. However, heavy sparticles spoil naturalness, which was the original reason for low energy SUSY; it implies that parameters related to electroweak symmetry breaking must be tuned to high accuracy. Thus, generic theories addressing the problem of flavor conflict with naturalness. These theories require a new mechanism to supress flavor violations to solve this conflict. In this paper, we first present the general supersymmetrized standard model. Next we review sources of flavor dependance in the supersymmetry violating terms and the naturalness criterion that limits the masses of the new supersymmetric partners. We then use the experimental constraints from the flavor changing processes μ → e + γ and K − K̄ mixing to quantify the conflict between sparticle non-universality and naturalness, illustrating the need for a mechanism to supress flavor changing processes. Finally, we discuss a possible supression mechanism. 2 Supersymmetric Kobayashi-Maskawa.