This paper presents a physical and MAC layer analysis of the recently introduced IEEE 802.15.3c standard for multi Gbps communication at 60 GHz. We find the optimal beamwidth of the transmitting antenna, achieving a trade-off between the Piconet Coordinator discovery and the duration of the contention access period (CAP) of the IEEE 802.15.3c MAC superframe. To find the optimal beamwidth, we first analyze the link budget of 60 GHz based directional communication, to identify the transmitting and receiving antenna gain, and hence the minimum beamwidth required to achieve a specific bit error probability (BEP) for a given distance between transmitter and receiver. We introduce a more efficient method for analytically modeling the binary exponential backoff (BEB) process during the CSMA/CA based CAP of the superframe, using a 1-dimentional Markov chain. Numerical results for the required antenna gain and optimal beamwidth, demonstrate the usefulness of our analysis technique.