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In this work we study a class of leptophilic dark matter models, where thedark matter interacts with the standard model particles via the$U(1)_{L_i-L_j}$ gauge boson, to explain the $e^{\pm}$ excess in cosmic raysobserved by ATIC and PAMELA experiments, and more recently by Fermi experiment.There are three types of $U(1)_{L_i-L_j}$ models: a) $U(1)_{L_e - L_\mu}$, b)$U(1)_{L_e - L_{\tau}}$, and c) $U(1)_ {L_e-L_\tau}$. Although ATIC or Fermidata is consistent with PAMELA data separately, ATIC and Fermi data do notagree with each other. We therefore aim to identify which of the three modelscan explain which data set better. We find that models a) and b) can givecorrect dark matter relic density and explain the ATIC and PAMELA datasimultaneously recur to the Breit-Wigner enhancement. Whereas model c) with alarger $Z^\prime$ mass can explain Fermi and PAMELA data simultaneously. In allcases the model parameters are restricted to narrow regions. Future improveddata will decide which set of data are correct and also help to decide thecorrect dark matter model.

Parameters in a Class of Leptophilic Dark Matter Models from PAMELA, ATIC and FERMI