Measurements of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">H</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow><mml:mi mathvariant="normal">Λ</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:mmultiscripts></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">H</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow><mml:mi mathvariant="normal">Λ</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:mmultiscripts></mml:mrow></mml:math> Lifetimes and Yields in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>Au</mml:mi><mml:mo>+</mml:mo><mml:mi>Au</mml:mi></mml:mrow></mml:math> Collisions in the High Baryon Density Region

We report precision measurements of hypernuclei _{Λ}^{3}H and _{Λ}^{4}H lifetimes obtained from Au+Au collisions at sqrt[s_{NN}]=3.0 GeV and 7.2 GeV collected by the STAR experiment at the Relativistic Heavy Ion Collider, and the first measurement of _{Λ}^{3}H and _{Λ}^{4}H midrapidity yields in Au+Au collisions at sqrt[s_{NN}]=3.0 GeV. _{Λ}^{3}H and _{Λ}^{4}H, being the two simplest bound states composed of hyperons and nucleons, are cornerstones in the field of hypernuclear physics. Their lifetimes are measured to be 221±15(stat)±19(syst) ps for _{Λ}^{3}H and 218±6(stat)±13(syst) ps for _{Λ}^{4}H. The p_{T}-integrated yields of _{Λ}^{3}H and _{Λ}^{4}H are presented in different centrality and rapidity intervals. It is observed that the shape of the rapidity distribution of _{Λ}^{4}H is different for 0%-10% and 10%-50% centrality collisions. Thermal model calculations, using the canonical ensemble for strangeness, describes the _{Λ}^{3}H yield well, while underestimating the _{Λ}^{4}H yield. Transport models, combining baryonic mean-field and coalescence (jam) or utilizing dynamical cluster formation via baryonic interactions (phqmd) for light nuclei and hypernuclei production, approximately describe the measured _{Λ}^{3}H and _{Λ}^{4}H yields. Our measurements provide means to precisely assess our understanding of the fundamental baryonic interactions with strange quarks, which can impact our understanding of more complicated systems involving hyperons, such as the interior of neutron stars or exotic hypernuclei.