Testing Split Supersymmetry with Inflation

TL;DR

The paper investigates how inflation can test split supersymmetry by leveraging quasi-single-field inflation with an extra scalar of mass $m \sim H$ that couples to the inflaton, producing a bispectrum with equilateral non-Gaussianity and a mass-dependent squeezed-limit exponent $\alpha = \frac{3}{2} - \sqrt{\frac{9}{4} - \frac{m^2}{H^2}}$. It argues that high-scale SUSY leaves a distinctive imprint in the primordial bispectrum, measurable through equilateral $f_{\rm NL}^{\rm equil.}$ and squeezed-limit scaling, enabling a direct probe of SUSY during inflation even when superpartners are inaccessible at colliders. The authors present forecasts for an ideal 3D survey showing that $\alpha=2$ can be excluded at up to $\sim 3\sigma$ for Planck-consistent amplitudes and that precision on $\alpha$ improves with larger $|f_{\rm NL}^{\rm equil.}|$, though their results are conservative by focusing on squeezed configurations. They discuss potential degeneracies and how the trispectrum, multiple-field scenarios, or excited states could be distinguished, highlighting the practical potential of upcoming CMB and LSS measurements to reveal or constrain high-scale SUSY scenarios. Overall, the work emphasizes inflation as a unique, high-energy laboratory for split supersymmetry with concrete, testable predictions for next-generation cosmological surveys.

Abstract

Split supersymmetry (SUSY) -- in which SUSY is relevant to our universe but largely inaccessible at current accelerators -- has become increasingly plausible given the absence of new physics at the LHC, the success of gauge coupling unification, and the observed Higgs mass. Indirect probes of split SUSY such as electric dipole moments (EDMs) and flavor violation offer hope for further evidence but are ultimately limited in their reach. Inflation offers an alternate window into SUSY through the direct production of superpartners during inflation. These particles are capable of leaving imprints in future cosmological probes of primordial non-gaussianity. Given the recent observations of BICEP2, the scale of inflation is likely high enough to probe the full range of split SUSY scenarios and therefore offers a unique advantage over low energy probes. The key observable for future experiments is equilateral non-gaussianity, which will be probed by both cosmic microwave background (CMB) and large scale structure (LSS) surveys. In the event of a detection, we forecast our ability to find evidence for superpartners through the scaling behavior in the squeezed limit of the bispectrum.

Figures (6)

• Figure 1: Unification prediction in split supersymmetry as a function of common fermionic ($\mu$) and scalar ($\tilde{m}$) superpartner masses using two-loop running split, neglecting weak-scale and unification-scale thresholds. In the left panel we take a common physical mass scale for all fermionic superpartners, while in the right panel we take the gluino to be twice as heavy as the other fermions. The diagonal bands represent the $1\sigma, 2\sigma, 3\sigma$ constraints corresponding to $\alpha_3(M_Z)=0.1184\pm0.0007$, where we have taken the experimental inputs $\alpha_{em}^{-1}(M_Z) = 127.916$ and $\sin^2 \theta_W(M_Z)=0.23116$. The solid black contours indicate the one-loop unification scale in units of GeV.
• Figure 2: The relative normalization of the amplitude of the likelihood function in the squeezed and equilateral limits, as defined by $C_{\bar{\alpha}}$. The function was computed for varying fiducial values of $\bar{\alpha}$ using the QSFI template in (\ref{['equ:template']}).
• Figure 3: The confidence level at which $\alpha = 2$ can be ruled out as a function of varying $\bar{f}_{NL}$ and $\bar{\alpha}$. The forecasted contours use $\sigma_{f_{\rm NL}} = 10$, $\epsilon = 10^{-1}$ and $\epsilon_* = 3\times10^{-3}$.
• Figure 4: The 1$\sigma$ and 2$\sigma$ error contours on the measurement of $\bar{\alpha} = 0.25$ for varying values of $\bar{f}_{NL}$. The forecasted contours use $\sigma_{f_{\rm NL}} = 10$, $\epsilon = 10^{-1}$ and $\epsilon_* = 3\times10^{-3}$. While the plot shows clear measurements of $\alpha < 2$, it appears to show results compatible with $\alpha = 0$. This is an artifact of our flat prior on $\tilde{C}$ and our assumption that the dominant signal is in the equilateral template. For $\bar{\alpha} \sim 0$, the squeezed limit dominates the signal to noise and we would see this as a detection of $f_{\rm NL}^{\rm local}$.
• Figure 5: The confidence level at which $\alpha = 2$ can be ruled out as a function of varying $\epsilon$, $\bar{f}_{NL}$ and $\bar{\alpha}$. The forecasted contours use $\sigma_{f_{\rm NL}} = 10$ and $\epsilon_* = 3\times10^{-3}$. The 2$\sigma$ and 3$\sigma$ contours are shown for $\epsilon = 0.1,0.175,0.25$. Our ability to rule out $\alpha =2$ improves significantly as we include more information from equilateral configurations.