Comparison of SUSY spectrum calculations and impact on the relic density constraints from WMAP

TL;DR

The paper quantitatively assesses how uncertainties in SUSY spectrum calculations affect neutralino relic-density predictions within mSUGRA by comparing four public spectrum codes (ISAJET, SoftSUSY, SPHENO, Suspect) linked to micrOMEGAs. It shows that even small mass differences can yield sizable differences in the relic density, with the largest effects in stau co-annihilation and Higgs-resonance regions (e.g., large $\tan\beta$). The study highlights the sensitivity of the $\mu$ parameter and $m_A$ to input choices and higher-order corrections, and demonstrates substantial code-to-code variability in certain parameter spaces, including the focus-point regime and scenarios with non-zero $A_0$. An online comparison tool is provided to facilitate cross-code checks. The results emphasize the need to account for theoretical uncertainties in relic-density constraints from WMAP, suggesting the use of code envelopes and improved higher-order calculations for robust phenomenology.

Abstract

We compare results of four public supersymmetric (SUSY) spectrum codes, Isajet, Softsusy, Spheno and Suspect to estimate the present-day uncertainty in the calculation of the relic density of dark matter in mSUGRA models. We find that even for mass differences of about 1% the spread in the obtained relic densities can be 10%. In difficult regions of the parameter space, such as large tan(beta) or large m_0, discrepancies in the relic density are much larger. We also find important differences in the stau co-annihilation region. We show the impact of these uncertainties on the bounds from WMAP for several scenarios, concentrating on the regions of parameter space most relevant for collider phenomenology. We also discuss the case of non-zero A_0 and the stop co-annihilation region. Moreover, we present a web application for the online comparison of the spectrum codes.

Figures (6)

• Figure 1: Comparison of results in the $m_0$--$m_{1/2}$ plane, for $A_0 = 0$, $\tan\beta=10$, $\mu>0$, and $m_t=175$ GeV. The red (dark) and orange (light) full lines show the variation of the $2\sigma$ upper limit $\Omega<0.1287$ when micrOMEGAs 1.3.2 is linked to ISAJET 7.71, SOFTSUSY 1.9 or SPHENO 2.2.2. The orange line basically comes from SOFTSUSY 1.9 while the red one comes from ISAJET 7.71. In addition, the upper bound from SPHENO 2.2.2 is shown as green dotted line, and that of SUSPECT 2.3 as blue dashed line. The light, medium and dark gray shaded areas show the regions where the relative differences in $\Omega$, $\delta\Omega$ of eq. (\ref{['eq:domega']}), are 4--10%, 10--30% and $>$30%, respectively. Also shown are contours of minimal (full black lines) and maximal (dashed black lines) $h^0$ masses as obtained by the spectrum codes. The yellow region on the left is excluded by LEP2 constraints; in the yellow triangle in the bottom right corner $m_{\tilde{\tau}_1}<m_{\tilde{\chi}^0_{1}}$ in ISAJET 7.71. The yellow lines show the boundaries of the excluded region in the other codes.
• Figure 2: Comparison of results analogous to Fig. \ref{['fig:tb10']} but for $\tan\beta=40$ (left) and $\tan\beta=50$ (right); $A_0 = 0$, $\mu>0$, and $m_t=175$ GeV. The red and orange lines show again the variation of the bound $\Omega<0.1287$ due to differences in the spectra from ISAJET 7.71, SOFTSUSY 1.9 and SPHENO 2.2.2. In the right panel, the blue dashed line shows in addition how the upper curve would move when including SUSPECT 2.3.
• Figure 3: WMAP allowed regions of $0.0945\leq\Omega\leq 0.1287$ for $\tan\beta=50$, $A_0 = 0$, $\mu>0$, $m_t=175$ GeV; left: ISAJET 7.71 and SOFTSUSY 1.9, right: SPHENO 2.2.2 and SUSPECT 2.3.
• Figure 4: WMAP allowed regions (blue) in the $m_0$--$m_{1/2}$ plane for large $m_0$; $\tan\beta=10$, $A_0 = 0$, $\mu>0$, $m_t=175$ GeV. In the dark blue bands $0.0945 \leq \Omega \leq 0.1287$, while in the light blue bands $\Omega < 0.0945$. In the gray areas there is no radiative EWSB; the yellow regions are excluded by the LEP bound $m_{\tilde{\chi}^\pm_{1}}>103$ GeV.
• Figure 5: Comparison of results analogous to Fig. \ref{['fig:tb4050']}b ($\tan\beta=50$) but for $A_0 = m_{1/2}$. The red and orange lines show the variation of the bound $\Omega<0.1287$ due to differences in the spectra. The dashed red and orange lines show the situation when only comparing SOFTSUSY 1.9 and SPHENO 2.2.2. The gap between the dashed and the full red lines is due to a lighter $\tilde{\tau}_1$ and hence more $\tilde{\tau}$ co-annihilation in ISAJET 7.71; the gap between the dashed and the full orange lines is due to smaller $\tilde{\chi}^0_1$ and $A^0$ masses in ISAJET 7.71. The dashed blue line shows again how the maximal $\Omega$ moves when including SUSPECT 2.3.