We present a theoretical calibration of the RR Lyrae period-luminosity ( PL ) relation in the UBVRIJHK Johnsons-Cousins-Glass system .
Our theoretical work is based on calculations of synthetic horizontal branches ( HBs ) for several different metallicities , fully taking into account evolutionary effects besides the effect of chemical composition .
Extensive tabulations of our results are provided , including convenient analytical formulae for the calculation of the coefficients of the period-luminosity relation in the different passbands as a function of HB type .
We also provide “ average ” PL relations in IJHK , for applications in cases where the HB type is not known a priori ; as well as a new calibration of the M _ { V } - { [ M / H ] } relation .
These can be summarized as follows :

M _ { I } = 0.471 - 1.132 \log P + 0.205 \log Z, M _ { J } = -0.141 - 1.773 \log P + 0.190 \log Z, M _ { H } = -0.551 - 2.313 \log P + 0.178 \log Z, M _ { K } = -0.597 - 2.353 \log P + 0.175 \log Z, and

M _ { V } = 2.288 + 0.882 \log Z + 0.108 ( \log Z ) ^ { 2 } .