Large $$N_c$$ scaling of meson masses and decay constants

Abstract

Abstract We perform an ab initio calculation of the $$N_c$$Nc scaling of the low-energy couplings of the chiral Lagrangian of low-energy strong interactions, extracted from the mass dependence of meson masses and decay constants. We compute these observables on the lattice with four degenerate fermions, $$N_f=4$$Nf=4, and varying number of colours, $$N_c=3$$Nc=3–6, at a lattice spacing of $$a\simeq 0.075$$a≃0.075 fm. We find good agreement with the expected $$N_c$$Nc scaling and measure the coefficients of the leading and subleading terms in the large $$N_c$$Nc expansion. From the subleading $$N_c$$Nc corrections, we can also infer the $$N_f$$Nf dependence, that we use to extract the value of the low-energy couplings for different values of $$N_f$$Nf. We find agreement with previous determinations at $$N_c=3$$Nc=3 and $$N_f=2, 3$$Nf=2,3 and also, our results support a strong paramagnetic suppression of the chiral condensate in moving from $$N_f=2$$Nf=2 to $$N_f=3$$Nf=3.