content_image/355679.jpg content_image/355684.jpg content_image/355683.jpg content_image/355682.jpg
<img src='content_image/355679.jpg'>

5. However, the predicted total electron and positron flux are obvious different. 

For a comparison between SH and LH cases, we show in Fig. 6 the results for SH(LH)-I and SH(LH)-III. It is clear that the differences are rather mild for the parameters given in Tab. III. Actually, the SH and LH cases have significant differences in the injection energy spectrum dn k e + /dE . However, the differences are smeared out due to the energy loss processes from the ICS and the synchrotron. 

## B. Neutrinos 

The expected muon neutrino flux coming from the galactic center (GC) and arriving at the Earth can be estimated by [31] 

<img src='content_image/355684.jpg'>

where the neutrino oscillation probabilities P$_{ν}$$_{α}$$_{→}$$_{ν}$$_{µ}$ are P$_{ν}$$_{e}$$_{→}$$_{ν}$$_{µ}$ = 0 . 22, P$_{ν}$$_{µ}$$_{→}$$_{ν}$$_{µ}$ = 0 . 39 and P$_{ν}$$_{τ}$$_{→}$$_{ν}$$_{µ}$ = 0 . 39 [32]. One can have the same results for the muon anti-neutrino flux Φ$_{¯}$ $_{ν$_{µ}$}$. The averaged number flux J$_{ΔΩ}$ in a cone with half-angle φ around GC is given by 

<img src='content_image/355683.jpg'>

where ΔΩ = 2 π (1 − cos φ ) is the solid angle. The above equation can be written as the following form 

<img src='content_image/355682.jpg'>

