Zwicky Transient Facility and Globular Clusters: The Period-Luminosity and Period-Wesenheit Relations for SX Phoenicis Variables in the gri-Band

SX Phoenicis (SXP) variables are short period pulsating stars that exhibit a period-luminosity (PL) relation. We derived the gri-band PL and extinction-free period-Wesenheit (PW) relations, as well as the period-color (PC) and reddening-free period-Q-index (PQ) relations for 47 SXP stars in located in 21 globular clusters using the optical light curves taken from Zwicky Transient Facility (ZTF). These empirically relations were derived for the first time in the gri filters except for the g-band PL relation. We used our gi band PL and PW relations to derive a distance modulus to Crater II dwarf spheroidal which hosts one SXP variable. Assuming that the fundamental and first-overtone pulsation mode for the SXP variable in Crater II, we found distance moduli of $20.03\pm 0.23$ mag and $20.37\pm 0.24$ mag, respectively, using the PW relation, where the latter is in excellent agreement with independent RR Lyrae based distance to Crater II dwarf galaxy.