  Based on updated nonlinear, convective pulsation models computed for several
values of stellar mass, luminosity and metallicity, theoretical constraints on
the K-band Period-Luminosity (PLK) relation of RR Lyrae stars are presented. We
show that for each given metal content the predicted PLK is marginally
dependent on uncertainties of the stellar mass and/or luminosity. Then, by
considering the RR Lyrae masses suggested by evolutionary computations for the
various metallicities, we obtain that the predicted infrared magnitude M_K over
the range 0.0001< Z <0.02 is given by the relation
MK=0.568-2.071logP+0.087logZ-0.778logL/Lo, with a rms scatter of 0.032 mag.
Therefore, by allowing the luminosities of RR Lyrae stars to vary within the
range covered by current evolutionary predictions for metal-deficient (0.0001<
Z <0.006) horizontal branch models, we eventually find that the infrared
Period-Luminosity- Metallicity (PLZK) relation is
MK=0.139-2.071(logP+0.30)+0.167logZ, with a total intrinsic dispersion of 0.037
mag. As a consequence, the use of such a PLZK relation should constrain within
+-0.04 mag the infrared distance modulus of field and cluster RR Lyrae
variables, provided that accurate observations and reliable estimates of the
metal content are available. Moreover, we show that the combination of K and V
measurements can supply independent information on the average luminosity of RR
Lyrae stars, thus yielding tight constraints on the input physics of stellar
evolution computations. Finally, for globular clusters with a sizable sample of
first overtone variables, the reddening can be estimated by using the PLZK
relation together with the predicted MV-logP relation at the blue edge of the
instability strip (Caputo et al. 2000).
