Abstract
We perform an ab initio calculation of the N_c 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, and varying number of colours, N_c=3–6, at a lattice spacing of asimeq 0.075 fm. We find good agreement with the expected N_c scaling and measure the coefficients of the leading and subleading terms in the large N_c expansion. From the subleading N_c corrections, we can also infer the N_f dependence, that we use to extract the value of the low-energy couplings for different values of N_f. We find agreement with previous determinations at N_c=3 and N_f=2, 3 and also, our results support a strong paramagnetic suppression of the chiral condensate in moving from N_f=2 to N_f=3.
Highlights
The ’t Hooft limit of QCD [1] is well known to capture correctly most of its non-perturbative features, such as confinement and chiral symmetry breaking
In this work we presented the first lattice determination using dynamical fermions of the Nc scaling of the couplings in the chiral Lagrangian that contribute to the meson masses and decay constants (see Eqs. (43), (48) and Table 8)
We have been able to disentangle the leading and subleading terms and we found that the subleading contributions are typically non negligible
Summary
The ’t Hooft limit of QCD [1] is well known to capture correctly most of its non-perturbative features, such as confinement and chiral symmetry breaking. In addition to the standard approach, the study of QCD in the large Nc limit can be achieved using reduced models (see [15] for a review) In this context, there has been significant progress regarding the properties of mesons [16,17,18,19,20]. Within the large Nc expansion, the 1/Nc corrections have a well-defined linear dependence on N f , while the ’t Hooft limit is independent on N f Using this fact, we can predict the low-energy couplings at different values of N f up to higher orders in Nc. Using this fact, we can predict the low-energy couplings at different values of N f up to higher orders in Nc This allows us to compare with previous determinations, and check the prediction of paramagnetic suppression at large N f of Refs.
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