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In this paper we develop a Markov Chain Monte Carlo code to study the darkmatter properties in interpreting the recent observations of cosmic rayelectron/positron excesses. We assume that the dark matter particles coupledominantly to leptons and consider two cases separately with annihilating ordecaying into lepton pairs. The constraint on the central density profile fromdiffuse $\gamma$-rays around the Galactic center is also included in the MarkovChain Monte Carlo code self-consistently. In the numerical study, 7 parametersare introduced. We fit two data sets independently and find that for the Dataset I (PAMELA+ATIC), dark matter with $m_{\chi}\approx0.7$ TeV for annihilation(or 1.4 TeV for decay) and pure $e^+e^-$ channel is favored, while for the Dataset II (PAMELA+Fermi-LAT+H.E.S.S.) $m_{\chi}\approx 2$ TeV for annihilation (or4 TeV for decay) and the combination of $\mu^+\mu^-$ and $\tau^+\tau^-$ finalstates can best fit the data. The H.E.S.S. observation of the Galactic center$\gamma$-rays puts a strong constraint on the central density profile of thedark matter halo for the annihilation dark matter scenario. In this case theNFW profile which is regarded as the typical predication from the cold darkmatter scenario, is excluded with a high significance ($>5\sigma$). For thedecaying dark matter scenario, the constraint is much weaker.

A Markov Chain Monte Carlo Study on Dark Matter Property Related to the Cosmic e$^{\pm}$ Excesses