Figure 1

${\tilde{\chi }}_1^0$ branching ratios versus $m_0$ for $A_0=-100\mathrm{GeV}$, $m_{1/2}=350\mathrm{GeV}$, $\tan \beta =10$, and $\mu >0$; for the sake of clarity we present in each panel only part of the decay channels. We took the $R$-parity violating parameters for each mSUGRA point such that they are compatible with neutrino data and the neutralino decay length is maximized.Reuse & Permissions

Figure 2

${\tilde{\chi }}_1^0$ decay length versus $m_{1/2}$ for $A_0=-100\mathrm{GeV}$, $\tan \beta =10$, and $\mu >0$. The width of the $m_0$ bands is due to the variation of the BRpV parameters in such a way that the neutrino masses and mixing angles are within $3\sigma$ of their best fit values.Reuse & Permissions

Figure 3

Reconstructed invariant mass spectrum of displaced-vertices after applying the cuts in Sec. 3. Here we chose $m_{1/2}=350\mathrm{GeV}$, $m_0=400\mathrm{GeV}$, $A_0=-100\mathrm{GeV}$, $\mu >0$, $\tan \beta =10$, and the $R$-parity violating parameters for each mSUGRA point such that they are compatible with neutrino data and the neutralino decay length is maximized.Reuse & Permissions

Figure 4

Expected number of events for an integrated luminosity of $8{\mathrm{fb}}^{-1}$ as a function of the neutralino decay length for $A_0=-100\mathrm{GeV}$, $\mu >0$, $\tan \beta =10$, and the $R$-parity violating parameters for each mSUGRA point such that they are compatible with neutrino data and the neutralino decay length is maximized.Reuse & Permissions

Figure 5

Same as Fig. 4 but fixing $m_0=100\mathrm{GeV}$.Reuse & Permissions

Figure 6

Reach of Fermilab Tevatron Run-II using the displaced vertex signal in the $m_{1/2}\otimes m_0$ plane for $\mu >0$. In the points below the solid line the expected number of events ($NEv$) is greater than $4$, while the region below the dashed line exhibits a sizable statistics ($NEv>15$) for $\mathcal{L}=2{\mathrm{fb}}^{-1}$. The black squares denote points with an expected number of events greater than $4$ for an integrated luminosity of $8{\mathrm{fb}}^{-1}$, while the gray (green) squares indicate the points presenting a high statistics ($NEv>15$) for this luminosity. Moreover, points denoted by diamonds have $2<NEv<4$ with $8{\mathrm{fb}}^{-1}$, while the stars correspond to points with $NEv<2$ for $\mathcal{L}=8{\mathrm{fb}}^{-1}$. The present direct search limits are violated at the points indicated with a round black circles, while the white circles mark the points where the neutralino is no longer the LSP. The choice of the remaining parameters is the following: In (a) $\tan \beta =10$, $A_0=-100\mathrm{GeV}$, and the $R$-parity violating parameters for each mSUGRA point are such that they are compatible with neutrino data and the neutralino decay length is maximized (best case scenario). In (b) we kept the mSUGRA parameters as in (a); however, we took the $R$-parity violating parameters for each mSUGRA point such that they are compatible with neutrino data and the neutralino decay length is minimized (worst case scenario). In (c) the parameters are as in (a) but for $A_0=1000\mathrm{GeV}$. Panel (d) was obtained using the parameters in (a) except for $\tan \beta =40$.Reuse & Permissions

Figure 7

Reach of the Fermilab Tevatron Run-II using the displaced vertex signal in the $m_{1/2}\otimes m_0$ plane. The conventions and all the parameters are as in Fig. 6a except for an increase in the integrated luminosity from $8{\mathrm{fb}}^{-1}$ to $25{\mathrm{fb}}^{-1}$.Reuse & Permissions

Figure 8

Reach of Fermilab Tevatron Run-II requiring the reconstruction of at least one displaced instead of two displaced vertices. All conventions and parameters are as in Fig. 6a. For comparison, the shaded area indicates the enhancement in the region with $NEv>2$ for an integrated luminosity of $8{\mathrm{fb}}^{-1}$ within the single vertex search when compared with Fig. 6a.Reuse & Permissions