[Paper Review] Reconstruction of Supersymmetric Theories at High Energy Scales

W. Porod|ArXiv.org|Sep 15, 2000

Particle physics theoretical and experimental studies21 citations

TL;DR

This paper proposes a bottom-up approach to reconstructing supersymmetric theories at high energy scales—specifically in minimal supergravity (mSUGRA) and gauge-mediated supersymmetry breaking (GMSB)—by evolving low-energy particle measurements from a linear collider up to the GUT or messenger scale. It demonstrates that high-precision electroweak-scale data, especially from a future $e^+e^-$ linear collider, enables accurate reconstruction of fundamental parameters, with gaugino and slepton masses reconstructed with high fidelity, while squark and Higgs parameters face larger uncertainties due to pseudo-fixed point behavior and large Yukawa couplings.

ABSTRACT

We have studied the reconstruction of supersymmetric theories at high scales by evolving the fundamental parameters from the electroweak scale upwards. Universal minimal supergravity and gauge mediated supersymmetry breaking have been taken as representative alternatives. Pseudo-fixed point structures require the low-energy boundary values to be measured with high precision.

Motivation & Objective

• To determine the mechanism of electroweak symmetry breaking after supersymmetry discovery by reconstructing high-scale supersymmetric theories from low-energy data.
• To assess the feasibility of reconstructing fundamental parameters of supersymmetric models at the GUT or messenger scale using precision measurements.
• To compare the effectiveness of bottom-up versus top-down approaches in testing the structure of supersymmetry at high scales.
• To evaluate the impact of experimental uncertainties from linear collider and LHC data on the accuracy of high-scale parameter reconstruction.

Proposed method

• The study uses two-loop renormalization group equations (RGEs) to evolve mass parameters from the electroweak scale to the GUT scale ($M_U$) or messenger scale ($M_m$).
• It assumes high-precision measurements of sparticle masses and production cross sections from a future $e^+e^-$ linear collider with $\sim$1 ab$^{-1}$ luminosity and 1 TeV energy.
• Experimental errors are modeled based on statistical uncertainties, reconstruction efficiencies (e.g., 20% for cross sections), and conservative inflation for $\tau$-rich decays.
• The gluino mass is assumed to be measured at the LHC with 10 GeV uncertainty, while other parameters are derived from LC data.
• The analysis includes threshold corrections and checks consistency with $b \to s\gamma$ and the $\rho$-parameter to ensure phenomenological viability.
• The reconstruction is performed by inverting the RGE evolution using measured low-energy observables and their uncertainties to infer high-scale parameters.

Experimental results

Research questions

• RQ1 Can the fundamental parameters of mSUGRA and GMSB be reconstructed at high energy scales using only low-energy experimental data?
• RQ2 How accurately can gaugino, sfermion, and Higgs mass parameters be reconstructed when starting from electroweak-scale measurements?
• RQ3 To what extent does pseudo-fixed point behavior in the RGEs limit the precision of high-scale reconstruction for squark and Higgs parameters?
• RQ4 Can the GMSB scenario be distinguished from mSUGRA based on the pattern of mass parameter evolution to high scales?
• RQ5 What role does high-precision linear collider data play in resolving ambiguities in the reconstruction of supersymmetric models?

Key findings

• The gaugino mass parameters ($M_1$, $M_2$, $M_3$) are reconstructed with excellent accuracy at the GUT scale, as shown by narrow bands in Fig. 1a.
• Slepton mass parameters are also reconstructed with high precision, as evidenced by the tight bands in Fig. 1b.
• Squark mass parameters exhibit larger uncertainties due to significant contributions from $M_3$ in the RGE evolution, which itself has a relatively large error.
• The Higgs mass parameter $M_{H_2}$ shows pseudo-fixed point behavior due to large Yukawa couplings, leading to weak dependence on initial high-scale values and reduced reconstruction accuracy.
• In GMSB, sfermion mass parameters evolve to a common value at the messenger scale $M_m$, and $M_{H_2}$ approaches the left-chiral slepton mass $M_{L_1}$, confirming the characteristic GMSB pattern.
• The bottom-up approach reveals that the squark sector is less constrained in top-down fits, highlighting the superiority of the bottom-up method in testing high-scale theory structure.