Search for neutrinoless <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>β</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:math>EC decay of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>Te</mml:mi><mml:mprescripts/><mml:none/><mml:mn>120</mml:mn></mml:mmultiscripts></mml:math> with CUORE

The Cryogenic Underground Observatory for Rare Events (CUORE) is a large-scale cryogenic experiment searching for neutrinoless double-beta decay ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) in $^{130}\mathrm{Te}$. The CUORE detector is made of natural tellurium, providing the possibility of rare event searches on isotopes other than $^{130}\mathrm{Te}$. In this work we describe a search for neutrinoless positron-emitting electron capture (${\ensuremath{\beta}}^{+}\mathrm{EC}$) decay in $^{120}\mathrm{Te}$ with a total ${\mathrm{TeO}}_{2}$ exposure of 355.7 kg yr, corresponding to 0.2405 kg yr of $^{120}\mathrm{Te}$. Albeit $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ with two final-state electrons represents the most promising channel, the emission of a positron and two 511-keV $\ensuremath{\gamma}$'s make $0\ensuremath{\nu}{\ensuremath{\beta}}^{+}\mathrm{EC}$ decay signature extremely clear. To fully exploit the potential offered by the detector modularity we include events with different topology and perform a simultaneous fit of five selected signal signatures. Using blinded data we extract a median exclusion sensitivity of $3.4\ifmmode\times\else\texttimes\fi{}{10}^{22}$ yr at 90% credibility interval (C.I.). After unblinding we find no evidence of $0\ensuremath{\nu}{\ensuremath{\beta}}^{+}\mathrm{EC}$ signal and set a 90% C.I. Bayesian lower limit of $2.9\ifmmode\times\else\texttimes\fi{}{10}^{22}$ yr on $^{120}\mathrm{Te}$ half-life. This result improves by an order of magnitude the existing limit from the combined analysis of CUORE-0 and Cuoricino.