SUSY-Yukawa Sum Rule at the LHC

TL;DR

The paper introduces the SUSY-Yukawa sum rule linking quark and squark properties, offering a test of supersymmetry's role in solving the hierarchy problem, with potential LHC measurements to validate it.

Contribution

It proposes a new sum rule derived from SUSY principles that connects physical masses and mixing angles, providing a novel way to test SUSY at the LHC.

Findings

The sum rule relates quark and squark couplings to the Higgs.

LHC measurements could test the sum rule and constrain squark mixing angles.

The sum rule offers a consistency check for SUSY as a solution to the hierarchy problem.

Abstract

We propose the "supersymmetric (SUSY) Yukawa sum rule", a relationship between physical masses and mixing angles of the third-generation quarks and squarks. The sum rule follows directly from a relation between quark and squark couplings to the Higgs, enforced by SUSY. It is exactly this relation that ensures the cancellation of the one-loop quadratic divergence in the Higgs mass from the top sector. Testing the sum rule experimentally would thus provide a powerful consistency check on SUSY as the solution to the gauge hierarchy problem. While such a test will most likely have to await a future next-generation lepton collider, the LHC experiments may be able to make significant progress towards this goal. If some of the terms entering the sum rule are measured at the LHC, the sum rule can be used (within SUSY framework) to put interesting constraints on the other terms, such as the mixing angles among third-generation squarks. We outline how the required mass measurements could be performed, and estimate the accuracy that can be achieved at the LHC.