By considering analytical expressions for the self-energies of intervalley and intravalley phonons in graphene, we describe the behavior of D, 2D, and D$$ Raman bands with changes in doping ($mu$) and light excitation energy ($E_L$). Comparing the self-energy with the observed $mu$ dependence of the 2D bandwidth, we estimate the wavevector $q$ of the constituent intervalley phonon at $hbar vqsimeq E_L/1.6$ ($v$ is electrons Fermi velocity) and conclude that the self-energy makes a major contribution (60%) to the dispersive behavior of the D and 2D bands. The estimation of $q$ is based on an image of shifted Dirac cones in which the resonance decay of a phonon satisfying $q > omega/v$ ($omega$ is the phonon frequency) into an electron-hole pair is suppressed when $mu < (vq-omega)/2$. We highlight the fact that the decay of an intervalley (and intravalley longitudinal optical) phonon with $q=omega/v$ is strongly suppressed by electron-phonon coupling at an arbitrary $mu$. This feature is in contrast to the divergent behavior of an intravalley transverse optical phonon, which bears a close similarity to the polarization function relevant to plasmons.
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