Determining the Dark Matter Relic Density in the Minimal Supergravity Stau-Neutralino Coannihilation Region at the Large Hadron Collider

We examine the stau-neutralino coannihilation (CA) mechanism of the early Universe. We use the minimal supergravity (mSUGRA) model and show that from measurements at the CERN Large Hadron Collider one can predict the dark matter relic density with an uncertainty of 6% with $30{\mathrm{fb}}^{-1}$ of data, which is comparable to the direct measurement by the Wilkinson Microwave Anisotropy Probe. This is done by measuring four mSUGRA parameters $m_0$, $m_{1/2}$, $A_0$, and $\tan \beta$ without requiring direct measurements of the top squark and bottom squark masses. We also provide precision measurements of the gaugino, squark, and lighter stau masses in this CA region without assuming gaugino universality.

Figure 1

(Top) The $p_T^{\mathrm{vis}}$ distribution of the lower-energy $\tau$’s using the OS-LS technique in the three samples (arbitrary luminosity) of SUSY events with $\Delta M=5.1$, 10.6, and 16.9 GeV, where only the ${\tilde{\tau }}_1$ mass is changed at our reference point. (Bottom) The $p_T^{\mathrm{vis}}$ slope (as $\alpha$ in the text) as a function of the relative change of $M_{{\tilde{\tau }}_1}$ (therefore $\Delta M$) or $M_{{\tilde{\chi }}_1^0}$ from its reference value with the other SUSY masses fixed. The bands correspond to statistical uncertainties with $10{\mathrm{fb}}^{-1}$.

Figure 2

(Top) The $M_{j\tau \tau }^{(2)}$ distributions using the OS-LS technique for SUSY events at our reference point, but with $M_{{\tilde{q}}_L}=660\mathrm{GeV}$ (yellow or light gray histogram) and 840 GeV (green or dark gray histogram), where 748 GeV is our reference point. (Bottom) The peak position of the mass distribution as a function of $M_{{\tilde{\chi }}_1^0}$ or $M_{\widetilde{q_L}}$. The bands correspond to statistical uncertainties with $10{\mathrm{fb}}^{-1}$.

Figure 3

The dependence of $M_{j\tau \tau }^{(2)\mathrm{peak}}$ (top) and $M_{\mathrm{eff}}^{\mathrm{peak}}$ (bottom) as a function of $m_{1/2}$ and $m_0$. The bands correspond to statistical uncertainties with $10{\mathrm{fb}}^{-1}$.

Figure 4

The dependence of $M_{\mathrm{eff}}^{(b)\mathrm{peak}}$ (top) and $M_{\tau \tau }^{\mathrm{peak}}$ (bottom) as a function of $\tan \beta$ and $A_0$. The bands correspond to statistical uncertainties with $10{\mathrm{fb}}^{-1}$.

Figure 5

Contour plot of the $1\sigma$ uncertainty in the ${\Omega }_{{\tilde{\chi }}_1^0}{h}^2\mathrm{\text{−}}\Delta M$ plane with 10 and $50{\mathrm{fb}}^{-1}$ (outer and inner ellipses).