Decaying Asymmetric Dark Matter Relaxes the AMS-Fermi Tension

The first result of AMS-02 confirms the positron fraction excess observed by PAMELA, but the spectrum is somewhat softer than that of PAMELA. In the dark matter (DM) interpretation it brings a tension between AMS-02 and Fermi-LAT, which reported an excess of the electron plus positron flux. In this work we point out that the asymmetric cosmic ray from asymmetric dark matter (ADM) decay relaxes the tension. It is found that in the case of two-body decay a bosonic ADM around 2.4 TeV and decaying into $\mu^-\tau^+$ can significantly improve the fits. Based on the $R-$parity-violating supersymmetry with operators $LLE^c$, we propose a minimal model to realize that ADM. The model introduces only a pair of singlets $(X,\bar X)$ with a tiny coupling $LH_uX$, which makes the ADM share the lepton asymmetry and decay into $\mu^-\tau^+$ along the operator $LLE^c$.