9 FIG. 8: Super-K terrestrial neutrino limits on the cross section per nucleon times the branching ratio to different annihilation channels for the iSI DM (left) and iSD DM (right). 1 / √ C$_{⊕}$C$_{A}$ , C$_{A}$ ≡ 〈 σv 〉 /V$_{⊕}$$_{eff}$ respectively. It is also useful to define a critical capture rate for the Earth as C c ⊕ ≡ 1 /C$_{A}$t 2 ⊕ ∼ 10 $^{14}$s − $^{1}$(TeV /m$_{χ}$ ) 3 / $^{2}$. If C$_{⊕}$ > C c $_{⊕}$, the DM capture and annihilation in the Earth could reach equilibrium. only show the most stringent constraints assuming all the DM annihilation products are τ $^{+}$τ $^{−}$. We can see the results in FIG. 8 and we find that the constraints from Earth-born neutrinos are weaker than those from the Sun. The most stringent con- straints arise from small δ and m$_{χ}$ ∼ (10, 50) GeV. V. CONCLUSION AND DISCUSSION Inelastic dark matter (iDM) is an excellent can- didate to explain the DAMA annual modulation result. Recently, the CDMS II announced the ob- servation of two signal events and set a more strin- gent constraint to the iDM model to account for DAMA results. The mass of the iDM is not heavier than 100 GeV and the DM-nucleon cross section is typically 10 − 4 pb (or higher) for iSI case and is 10 pb (or higher) for iSD case. In this work, we discuss the constraints by neu- trino signals from solar and terrestrial iDM anni- hilations motivated after DAMA and CDMS II re- sults. The neutrino flux from the Sun or Earth depends on the capture rate and the constraint on DM-nucleon cross section is quite different from the eDM case. For iSI/iSD scattering, the main contribution to the capture rate in the Sun is from Fe/Al and in the latter case, the capture from H is highly kinematically suppressed. Although the types of nuclei that contribute to the capture rate are quite different in iSI and iSD DM models, the constraints for the iDM annihilation channels for the typical DM-nucleon cross section are ac- tually similar. The Super-K null results set very Here we use the upper limit for up-going muon flux from the center of the Earth provided by Super-K [29] to constrain the iDM model. We It is straightforward to get numerical results by using the method in Sec II. Here we use the mass density profile and the composition of the Earth provided by Ref. [20] and [33] respectively. For simplicity, we assume the Earth is in free space [16]. If the gravitational interaction of the Sun is taken into account, there is a correction factor of O(1) [35] to the capture rate. In FIG. 7, we show the results of terrestrial iDM capture rate for SI and SD scattering processes. We find that for very heavy or light DM, the capture process is highly suppressed. So we only give the capture rate for the iDM with typical mass in the range of (10, 50) GeV which is similar to the mass of nuclei of interest. It is interesting to notice that there are surges as δ is varying. The peaks of these surges ( χ ′ − → 0) are quite similar to the “resonant enhancement” in the eDM case when DM mass reaches to the nuclei’s mass as discussed in Ref. [16] and is absent if the DM is not light enough. For the iDM scenario, we need to notice that for the n species of nuclei of interest here, there are 2n inelastic capture conditions to be satisfied or obeyed. So if the mass of DM is similar to that of the nuclei, the terrestrial capture rate is very sensitive to the parameters of m$_{N}$ , m$_{χ}$ and δ . 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