The calibration of the RGB tip as a standard candle - Extension to near infrared colors and higher metallicity

New empirical calibrations of the Red Giant Branch Tip in the I, J, H and K bands based on two fundamental pillars, namely omega Centauri and 47 Tucanae, have been obtained by using a large optical and near infrared photometric database. Our best estimates give M-I(TRGB)=-4.05+/-0.12, M-J(TRGB)=-5.20+/-0.16, M-H(TRGB)=-5.94+/-0.18 and M-K(TRGB)=-6.04+/-0.16 at [M/H] 1.5 (omega Cen) and M-I(TRGB)=-3.91+/-0.13, M-J(TRGB)=-5.47+/-0.25, M-H(TRGB)=-6.35+/-0.30 and M-K(TRGB)=-6.56+/-0.20 at [M/H]similar or equal to -0.6 (47 Tuc). With these new empirical calibrations we also provide robust relations of the TRGB magnitude in the I, J, H, and K bands as a function of the global metallicity. It has also been shown that our calibrations self-consistently provide a distance modulus of the Large Magellanic Cloud in good agreement with the standard value ((m-M)(0) similar or equal to 18.50)).