The scale of neutrino masses is distinct from that of other particles, hinting towards an alternative mass generation mechanism beyond the Standard Model. One promising approach is to consider neutrinos acquiring Majorana masses through spontaneous symmetry breaking of the global U(1)_{B−L} symmetry, with the corresponding Goldstone boson denoted as the Majoron. The particle can potentially be discovered via the hypothetical Majoron-emitting double beta decay (0νββϕ). Observing such a process would illuminate numerous physics searches, including neutrino mass generation, leptogenesis of matter-antimatter asymmetry, and potential candidates for dark matter particles.

In this thesis, the capability of the LUX-ZEPLIN (LZ) experiment to search for 0νββϕ in 136Xe is demonstrated. For the most commonly searched n = 1 mode, a conservative lifespan of 500 live-days will enable LZ to exclude T_{1/2} < 4.75 × 10^23 yr at 90% CL. The T_{1/2} sensitivities to n = 2, 3, 7 modes are also studied, showing that LZ will likely reach competitive results against the current best limits. As a validation, the LZ SR1 0νββϕ background model constrains the half-life of the 2νββ decay of 136Xe to T_{1/2} = 2.25 ± 0.22 × 10^21 yr, in agreement with the literature value of T_{1/2} = 2.165 ± 0.016(stat) ± 0.059(sys) × 10^21 yr as obtained by EXO-200 [3]. A search for the n = 1 0νββϕ mode is performed with the LZ SR1 data set, showing that LZ can set a lower limit of T_{1/2} > 2.1 × 10^23 yr at 90% CL with an 83.4 kg · yr exposure of 136Xe. This provides a concrete demonstration that LZ is capable of searching for 136Xe 0νββϕ and reaching competitive results in its full lifespan. It also highlights the general-purpose nature of a multi-tonne scale liquid xenon TPC and adds to the potential scientific goals of next-generation detectors.