[Paper Review] A Cosmological Upper Bound on Superpartner Masses

Lawrence J. Hall, Joshua T. Ruderman+1 more|arXiv (Cornell University)|Feb 11, 2013

Cosmology and Gravitation Theories4 citations

TL;DR

This paper derives a cosmological upper bound on superpartner masses by analyzing the gravitino's relic abundance in models where the lightest supersymmetric particle (LSP) is a stable gravitino. It shows that if superpartners were in thermal equilibrium and the gravitino is the LSP, superpartner masses are constrained to below ~10 TeV due to overclosure of the universe, with the bound arising from the geometric mean of the matter-radiation equality temperature and the Planck scale.

ABSTRACT

If some superpartners were in thermal equilibrium in the early universe, and if the lightest superpartner is a cosmologically stable gravitino, then there is a powerful upper bound on the scale of the superpartner masses. Typically the bound is below tens of TeV, often much lower, and has similar parametrics to the WIMP miracle.

Motivation & Objective

• To establish a cosmological upper bound on superpartner masses independent of naturalness or electroweak fine-tuning.
• To investigate the constraints on superpartner masses when the gravitino is the lightest supersymmetric particle (LSP) and the LSP is cosmologically stable.
• To explore how the bound changes under different assumptions about reheating temperature ($T_R$), superpartner mass scale ($\tilde{m}$), and gravitino mass ($m_{3/2}$).
• To assess the viability of models with heavy superpartners by analyzing late decays and non-thermal production of gravitinos.
• To determine the conditions under which the bound can be evaded, particularly when the LSP is not produced via thermal freeze-out.

Proposed method

• Derives the relic abundance of gravitinos from thermal scattering, freeze-in, and freeze-out processes, assuming superpartners were in thermal equilibrium.
• Uses the condition that the gravitino abundance must not overclose the universe to derive an upper bound on $\tilde{m}$, the superpartner mass scale.
• Applies the bound $\tilde{m}^2 \lesssim \frac{a}{C_D} T_{\text{eq}} M_{\text{Pl}}$ when thermal freeze-out is suppressed, yielding $\tilde{m} \lesssim 10^3$ TeV for $T_R = \tilde{m}$.
• Analyzes the impact of late decays of the next-to-lightest supersymmetric particle (NLSP) on big bang nucleosynthesis (BBN), excluding regions with excessive hadronic or electromagnetic decays.
• Considers gravity mediation scenarios where $m_{3/2}/\tilde{m} \sim M_*/M_{\text{Pl}}$, and evaluates bounds for different $M_*$ and $T_R$ values.
• Evaluates the role of non-degenerate superpartner masses and their impact on BBN and the gravitino abundance.

Experimental results

Research questions

• RQ1 What is the maximum superpartner mass scale allowed by cosmological overclosure if the gravitino is the LSP and superpartners were in thermal equilibrium?
• RQ2 How does the upper bound on $\tilde{m}$ depend on the reheating temperature $T_R$ and the gravitino mass $m_{3/2}$?
• RQ3 In what scenarios can the thermal freeze-out bound on superpartner masses be evaded, and what are the cosmological constraints in those cases?
• RQ4 How do late decays of the next-to-lightest supersymmetric particle (NLSP) affect the viability of models with heavy superpartners?
• RQ5 What are the implications of gravity mediation for the superpartner mass scale and the gravitino relic abundance?

Key findings

• The superpartner mass scale $\tilde{m}$ is bounded above by approximately 10 TeV when the gravitino is the LSP and superpartners were in thermal equilibrium, due to overclosure from overproduced gravitinos.
• The bound $\tilde{m}^2 \lesssim \frac{a}{C_D} T_{\text{eq}} M_{\text{Pl}}$ yields $\tilde{m} \lesssim 10^3$ TeV when thermal freeze-out is suppressed, with the bound tightening for higher reheating temperatures.
• The region where $m_{3/2} \approx \tilde{m}$ is most constrained by BBN, especially for $T_R \gtrsim \tilde{m}$, and is excluded if the gravitino is too warm.
• Models with $M_* \sim M_{\text{Pl}}$ and $T_R \sim 10^9$ GeV are viable for $m_{3/2} \sim 200$ GeV and $\tilde{m}_{\text{nc}} \lesssim 5$ TeV, compatible with thermal leptogenesis.
• The bound can be evaded if the LSP is not the gravitino and its couplings are arbitrarily weak, allowing superpartners to be arbitrarily heavy.
• Non-degenerate superpartner masses with large splittings are constrained by BBN, especially from hadronic decays of the NLSP, which rapidly exclude large mass differences.