Impurity scattering [1\,2] and/or higher order loop processes in the clean system [3] cause a redistribution of the critical scattering at the hot lines all over the Fermi surface\, leading to a weakly momentum dependent critical self-energy. We derive a self-consistent equation for the qp effective mass which allows for two physical solutions: the usual weak coupling spin density wave solution and a strong coupling solution featuring a power law divergence of the effective mass as a function of energy scale. The resulting spin excitation spectrum obeys E/T scaling with dynamical exponent z=4 and correlation length exponent nu=1/3\, in excellent agreement with data for YbRh2Si2 [1\,2]. Results of our theory applied to three-dimensional metals featuring quasi-two-dimensional spin fluctuations will be presented with the aim of explaining the observed properties of the AFM quantum critical point of CeCu(6-x)Aux \, in particular the E/T scaling exhibited by inelastic neutron scattering data. In that case we find z=8/3 and nu=3/7[3]. Finally\, the microscopic underpinning of our theory will be addressed\, including the issues of qp renormalization\, vertex corrections\, interaction of bosonic fluctuations in the renormalization group sense\, and higher loop corrections [3].

[1] P. Woelfle\, and E. Abrahams\, Phys. Rev. B 84\, 041101 (2011); Ann. Phys. (Berlin) 523\, 591 (2011); Phys. Rev. B 80\, 235112 (2009).

[2] E.Abrahams and P. Woelfle\, PNAS \, 3228 (2012).

[3] E. Abrahams\, J. Schmalian\, and P. Woelfle\, to be published.

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