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Register a new userLarge-$N_c$ and Large-$N_F$ Limits of SU($N_c$) Gauge Theories with Fermions in Different Representations
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We present calculations of certain limits of scheme-independent series expansions for the anomalous dimensions of gauge-invariant fermion bilinear operators and for the derivative of the beta function at an infrared fixed point in SU($N_c$) gauge theories with fermions transforming according to two different representations. We first study a theory with $N_f$ fermions in the fundamental representation and $N_{f}$ fermions in the adjoint or symmetric or antisymmetric rank-2 tensor representation, in the limit $N_c to infty$, $N_f to infty$ with $N_f/N_c$ fixed and finite. We then study the $N_c to infty$ limit of a theory with fermions in the adjoint and rank-2 symmetric or antisymmetric tensor representations.
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We present a calculation of the $eta$-$eta$ mixing in the framework of large-$N_c$ chiral perturbation theory. A general expression for the $eta$-$eta$ mixing at next-to-next-to-leading order (NNLO) is derived, including higher-derivative terms up to fourth order in the four momentum, kinetic and mass terms. In addition, the axial-vector decay constants of the $eta$-$eta$ system are determined at NNLO. The numerical analysis of the results is performed successively at LO, NLO, and NNLO. We investigate the influence of one-loop corrections, OZI-rule-violating parameters, and $mathcal{O}(N_c p^6)$ contact terms.
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