This raises three important questions:
1. What is the physical origin of this scattering [and the associated self energy]? Superconducting, D-density wave, antiferromagnetic, or gauge fluctuations?
2. Is this scattering relevant to the superconductivity? i.e., do the same interactions produce the superconductivity and/or do these interactions make the metallic state unstable to superconductivity?
3. Is this relevant to formation of the pseudogap in the underdoped region? e.g., as the self energy increases in magnitude with decreasing doping does the pseudogap just result from new poles in the spectral function?
I focus here on possible answers to 1. as there are already some attempts to answer this question in the literature. Back in 1998, Ioffe and Millis published a PRB paper focusing on the phenomenology of such a scattering rate but Section IV of their paper considered how superconducting fluctuations could produce an anisotropic scattering rate. They suggested that in the overdoped region the rate should scale with T^2, but it should be kept in mind this depends on what assumptions one makes about the temperature dependence of the correlation length.
Walter Metzner and colleagues have been investigating D-density wave fluctuations near a quantum critical point associated with a Pomeranchuk instability [A PRL with Dell'Anna summarises the main results, including a scattering rate which scales with temperature]. Their starting point is an effective Hamiltonian which has a d-wave form factor built into it. But this is motivated by an earlier PRL which found that the forward scattering they deduced for the Hubbard model from renormalisation group flows.
Maslov and Chubukov have also published papers on the subject, such as this PRB.
A key question is what experiments might be a smoking gun to distinguish the different origin of the scattering. I wonder whether the observed weak dependence of the scattering on magnetic field [at least up to 50 Tesla] may help.
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