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Detecting neutrino-less double beta (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mi>ν</mi><mi>β</mi><mi>β</mi></mrow></semantics></math></inline-formula>) decay with high-sensitivity <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mi>ν</mi><mi>β</mi><mi>β</mi></mrow></semantics></math></inline-formula> detectors is of current interest for studying the Majorana neutrino’s nature, the neutrino mass (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula>-mass), right-handed weak currents (RHCs), and others beyond the Standard Model. Many experimental groups have studied <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mi>ν</mi><mi>β</mi><mi>β</mi></mrow></semantics></math></inline-formula> decay with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula>-mass sensitivities on the order of 100 meV and RHC sensitivities on the order of 10<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow><mspace width="-3pt"></mspace><mo> </mo></mrow><mrow><mo>−</mo><mn>9</mn></mrow></msup></semantics></math></inline-formula>–10<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow><mspace width="-3pt"></mspace><mo> </mo></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup></semantics></math></inline-formula>, but no clear <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mi>ν</mi><mi>β</mi><mi>β</mi></mrow></semantics></math></inline-formula> signals have been observed so far in these <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula>-mass and RHC regions. Thus, several experimental groups are developing higher-sensitivity detectors to explore a smaller <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula>-mass region around 15–50 meV, which corresponds to the inverted hierarchy <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula>-mass, and smaller RHC regions on the order of 10<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow><mspace width="-3pt"></mspace><mo> </mo></mrow><mrow><mo>−</mo><mn>10</mn></mrow></msup></semantics></math></inline-formula>–10<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow><mspace width="-3pt"></mspace><mo> </mo></mrow><mrow><mo>−</mo><mn>7</mn></mrow></msup></semantics></math></inline-formula> in the near future. Nuclear matrix elements (NMEs) for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula>-mass and RHC processes are crucial for extracting the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula>-mass and RHCs of particle physics interest from <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mi>ν</mi><mi>β</mi><mi>β</mi></mrow></semantics></math></inline-formula> experiments. This report briefly reviews detector sensitivities and upper limits on the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula>-mass and right-handed currents for several current <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mi>ν</mi><mi>β</mi><mi>β</mi></mrow></semantics></math></inline-formula> detectors and the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula>-mass and RHC sensitivities expected for some near-future ones.