QCD Corrections to Flavor-Changing Neutral Currents in the Supersymmetric Standard Model

TL;DR

The paper addresses flavor-changing neutral current constraints in the MSSM focusing on K-Kbar mixing. It develops a rigorous effective field theory approach to compute leading QCD corrections to the ΔS=2 Lagrangian across three gluino/squark mass hierarchies, deriving Wilson coefficients and performing renormalization-group evolution to the hadronic scale. The results show that QCD corrections substantially tighten bounds on flavor-violating squark mass insertions, often by factors up to about 3, with especially strong implications for naturalness when either the gluino or squarks are light. These corrections are essential for reliable FCNC constraints and have broad relevance for SUSY model-building and interpretations of flavor data.

Abstract

We compute the leading QCD corrections to K-Kbar mixing in the supersymmetric standard model with general soft supersymmetry-breaking parameters. We construct the ΔS=2 effective Lagrangian for three hierarchies of supersymmetric particle masses, namely, when the gluino mass is comparable to, much greater than, or much less than the masses of the first two generation squarks. We find that the QCD corrections tighten the limits on squark mass splittings by more than a factor of two.

Figures (4)

• Figure 1: The matching of the S-matrices in the full and effective theories, at the scale $M_{\tilde{q}}$, for the case of $M_{\tilde{g}} \ll M_{\tilde{q}}$. At one loop, the $\Delta S=1$ operator generates a subleading $\Delta S=2$ operator, of order $M_{\tilde{g}}^2/M_{\tilde{q}}^4$.
• Figure 2: The matching of the S-matrices in the full and effective theories, at the scale $\mu=M_{\tilde{g}}$, for the case $M_{\tilde{g}} \gg M_{\tilde{q}}$. The $\Delta S=0$ operator generates a leading $\Delta S=2$ operator, whose coefficient exactly matches the $x \gg 1$ limit of the corresponding box diagram. This implies that the Wilson coefficient of the first $\Delta S=2$ operator on the right-hand side is zero.
• Figure 3: Limits on the $\mathop{\rm Re} \delta$'s as a function of the common first two generation squark mass, $M_{\tilde{q}}$, for a light gluino mass of $M_{\tilde{g}} = 200$ GeV. The solid lines describe our effective field theory result. The dashed lines correspond to decoupling the supersymmetric particles at $M_{\rm SUSY}= {\sqrt {M_{\tilde{q}} M_{\tilde{g}}}}$, without including the leading order QCD corrections.
• Figure 4: The same as Fig. \ref{['fig1']}, as a function of $M_{\tilde{g}}$, for light first two generation squarks, $M_{\tilde{q}}=200$ GeV.