Naturalness and GUT Scale Yukawa Coupling Ratios in the CMSSM

TL;DR

This paper examines the fine-tuning and Yukawa coupling ratios at the GUT scale within the CMSSM, considering current and future collider constraints, and explores the implications for Yukawa unification.

Contribution

It provides a detailed analysis of fine-tuning levels in the CMSSM under collider constraints and investigates the GUT scale Yukawa coupling ratios compatible with these constraints.

Findings

Fine-tuning can remain below 20 with 10/fb of data even without SUSY discovery.

Allowed $y_\tau/y_b$ ratio ranges from 1.31 to 1.70 under certain constraints.

Approximate $b-\tau$ Yukawa unification is possible with relaxed $(g-2)_\mu$ constraints.

Abstract

We analyse the fine-tuning in the Constrained Minimal Supersymmetric Standard Model (CMSSM) in the light of the present and expected ATLAS and CMS SUSY searches. Even with 10/fb of data and no discovery of SUSY valid regions might remain with fine-tuning less than 20. Moreover we investigate the fine-tuning price of GUT scale Yukawa coupling relations. Considering a 2$\sigma$ constraint for $(g-2)_\mu$ and fine-tuning less than 30 yields an allowed range of $y_\tau/y_b = [1.31,1.70]$, which points towards the alternative GUT prediction $y_\tau/y_b = 3/2$. Relaxing the $(g-2)_\mu$ constraint to 5$\sigma$ extends the possible region to [1.02,1.70], allowing for approximate $b-\tau$ Yukawa coupling unification.