Searching for Beyond the Standard Model physics using the improved description of $^{100}$Mo $2νββ$ decay spectral shape with CUPID-Mo
The current experiments searching for neutrinoless double-$β$ ($0νββ$) decay also collect large statistics of Standard Model allowed two-neutrino double-$β$ ($2νββ$) decay events. These can be used to search for Beyond Standard Model (BSM) physics via $2νββ$ decay spectral distortions. $^{100}$Mo has a natural advantage due to its relatively short half-life, allowing higher $2νββ$ decay statistics at equal exposures compared to the other isotopes. We demonstrate the potential of the dual read-out bolometric technique exploiting a $^{100}$Mo exposure of 1.47 kg $\times$ y, acquired in the CUPID-Mo experiment at the Modane underground laboratory (France). We set limits on $0νββ$ decays with the emission of one or more Majorons, on $2νββ$ decay with Lorentz violation, and $2νββ$ decay with a sterile neutrino emission. In this analysis, we investigate the systematic uncertainty induced by modeling the $2νββ$ decay spectral shape parameterized through an improved model, an effect never considered before. This work motivates searches for BSM processes in the upcoming CUPID experiment, which will collect the largest amount of $2νββ$ decay events among the next-generation experiments.