In this paper we develop a Markov Chain Monte Carlo code to study the dark matter properties in frameworks to interpret the recent observations of cosmic ray electron/positron excesses .
We assume that the dark matter particles couple dominantly to leptons and consider two cases , annihilating or decaying into lepton pairs , respectively .
The constraint on the central density profile from H.E.S.S .
observation of diffuse \gamma -rays around the Galactic center is also included in the Markov Chain Monte Carlo code self-consistently .
In the numerical study , we have considered two cases of the background : fixed e ^ { + } e ^ { - } backgrond and the relaxed one .
Two data sets of electrons/positrons , i.e .
PAMELA+ATIC ( Data set I ) and PAMELA+Fermi-LAT+H.E.S.S .
( Data set II ) , are fitted independently , considering the current inconsistence between the observational data .
We find that for the Data set I , dark matter with m _ { \chi } \approx 0.70 TeV for annihilation ( or 1.4 TeV for decay ) and a non-negligible branching ratio to e ^ { + } e ^ { - } channel is favored ; while for the Data set II , m _ { \chi } \approx 2.2 TeV for annihilation ( or 4.5 TeV for decay ) and the combination of \mu ^ { + } \mu ^ { - } and \tau ^ { + } \tau ^ { - } final states can best fit the data .
We also show that the background of electrons and positrons actually will significantly affect the branching ratios .
The H.E.S.S .
observation of \gamma -rays in Galactic center ridge puts a strong constraint on the central density profile of the dark matter halo for the annihilation dark matter scenario .
In this case the NFW profile which is regarded as the typical predication from the cold dark matter scenario , is excluded with a high significance ( > 3 \sigma ) .
For the decaying dark matter scenario , the constraint is much weaker .