The Supersymmetric Flavor Problem

TL;DR

The Supersymmetric Flavor Problem analyzes how general soft SUSY-breaking terms introduce numerous new flavor parameters, challenging naturalness and conflicting with FCNC constraints from μ→e+γ and K0−K0bar. It introduces a U(3)5 flavor symmetry framework, counts physical parameters, and shows that non-universal soft terms are generically generated by high-scale flavor physics and RG running, creating sizable interfamily splittings and dangerous flavor violations. Through quantitative bounds on slepton and squark mass splittings, the paper demonstrates a tension: naturalness prefers light superpartners, while flavor data pushes toward degeneracy or heavier spectra unless a suppression mechanism is invoked. It proposes light messenger scenarios, where SUSY breaking is communicated at a scale well below MPl or MGUT, decoupling soft terms from Planck/GUT flavor dynamics and suppressing FCNCs, guiding future model-building toward SM-flavor-safe SUSY realizations with a naturally light electroweak scale.

Abstract

The supersymmetric $SU(3)\times SU(2)\times U(1)$ 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 $μ\rightarrow e + γ$ and $K^0 - \bar{K}^0$ 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 $μ\rightarrow e + γ$ exceeding the present experimental limits. A possible solution is that the messengers which transmit supersymmetry breaking to the ordinary particles are much lighter than $M_{\rm Planck}$.

Figures (5)

• Figure 1: $m_0=50$ GeV: Fractional mass splittings ( left) and physical masses of sleptons ( top right) and down squarks ( bottom right).
• Figure 2: $m_0=100$ GeV: Fractional mass splittings ( left) and physical masses of sleptons ( top right) and down squarks ( bottom right).
• Figure 3: $m_0=200$ GeV: Fractional mass splittings ( left) and physical masses of sleptons ( top right) and down squarks ( bottom right).
• Figure 4: $m_0=400$ GeV: Fractional mass splittings ( left) and physical masses of sleptons ( top right) and down squarks ( bottom right).
• Figure 5: Schematic diagram illustrating how SUSY breaking is communicated from the hidden sector $H$ via a messenger $M$ to $SU_3 \times SU_2 \times U_1$ carrying sparticles $L$. $L$ can be light $\sim M_W$ or heavy $\sim M_{\rm GUT}$.